Thermodynamics

The modynamics
M . V. P abaha an
Assis an P o esso
Depa men o Mechanical Enginee ing
Sh ee Venka eshwa a Hi-Tech Enginee ing College
Gobiche ipalayam - 638455
D . J. M. P abhudass
Associa e P o esso
Depa men o Mechanical Enginee ing
S i Sai am Ins i u e o Technology
Sai Leo Naga , Wes Tamba am, Chennai - 600044
D . N. Poyyamozhi
Assis an P o esso G ade-I
Depa men o Mechanical Enginee ing
Panimala Enginee ing College
Bangalo e T unk Road, Va adha ajapu am, Poonamallee, Chennai - 600123
D . V. T. Vimalanan h
Assis an P o esso
Depa men o Mechanical Enginee ing
Academy o Ma i ime Educa ion and T aining
Kana hu , Chennai - 603112
Edi ion De ails (I,II,III): I
ISBN: 978-93-6786-795-2
Mon h & Yea : Sep embe , 2025
Copy igh @ M . V. P abaha an
D . J. M. P abhudass
D . N. Poyyamozhi
D . V. T. Vimalanan h
Pages: 249
P ice: 850/-

Abou he Au ho s’
M . V. P abaha an , ME (THERMAL ENGINEERING)
is an Assis an P o esso in Mechanical Enginee ing a
Sh ee Venka eshwa a Hi-Tech Enginee ing College, E ode.
He holds a B.E. and M.E. om Anna Uni e si y . He has
published in epu ed jou nals .Wi h academic and indus y
expe ience, he eaches subjec s like Hea and mass T ans e ,
The modynamics, The mal Enginee ing, S eng h o
Ma e ials and Enginee ing G aphics. He is a Li e Membe o
ISTE .
D . J. M. P abhudass is an Associa e P o esso in he
Depa men o Mechanical Enginee ing a S i Sai am
Ins i u e o Technology wi h o e 20 yea s o eaching
expe ience. He holds a B.E in Mechanical Enginee ing,
M.Tech in The mal Enginee ing and Ph.D. wi h esea ch
in e es s in composi e ma e ials. He has au ho ed
in e na ional publica ions in epu ed Jou nals. D .
P abhudass has success ully guided and men o ed nume ous
s uden eams in na ional compe i ions. His academic
excellence is e lec ed in achie ing 100% esul s in mul iple
co e mechanical subjec s. A membe o SAE, ISTE, and
IEEE, he has o ganized and pa icipa ed in se e al
wo kshops, con e ences, and FDPs. He also se es as
Depa men NAAC Coo dina o and Depa men S a egis ,
os e ing inno a ion and echnical excellence among
s uden s
D . N. Poyyamozhi ea ned his unde g adua e deg ee in
Mechanical Enginee ing in 2009 and comple ed his
pos g adua e s udies in 2011. Cu en ly se ing as an
Assis an P o esso G ade-I a Panimala Enginee ing
College, he specializes in The mal Ene gy S o age Sys ems.
Wi h o e 34 esea ch pape s published, he has p esen ed his
wo k a bo h na ional and in e na ional con e ences. D .
Poyyamozhi is also ac i ely in ol ed in o ganizing
wo kshops and deli e ing gues lec u es. In addi ion o his
academic con ibu ions, he holds mo e han ou pa en s and
has au ho ed a book.
D . V. T. Vimalanan h is an Assis an P o esso in
Mechanical Enginee ing a AMET Uni e si y, Chennai. He
holds a B.E. and M.E. om Anna Uni e si y and a Ph.D. in
Mechanical Enginee ing om Uni e si y College o
Enginee ing, Villupu am. His esea ch ocuses on Al e na e
Fuels, IC Engines, and Pollu ion Con ol. He has published
in epu ed jou nals and p esen ed a in e na ional o ums.
Wi h academic and indus y expe ience, he eaches subjec s
like The modynamics, TQM, and Enginee ing G aphics. He
is a Li e Membe o ISTE, SAE, and IAENG.
D .Vimalanan h has also ained in EV Technology and
Addi i e Manu ac u ing.
Resea ch P o ile: esea chga e.ne /p o ile/Vimalanan h-V-T
P e ace
The modynamics is one o he undamen al pilla s o science and enginee ing, p o iding he
p inciples ha go e n ene gy, hea , and wo k, and hei ans o ma ions. I s applica ions span
ac oss mechanical enginee ing, chemical p ocesses, powe gene a ion, e ige a ion,
ae ospace, enewable ene gy, and coun less o he domains. Unde s anding hese p inciples is
essen ial no only o enginee s and scien is s bu also o anyone seeking o comp ehend he
physical p ocesses ha d i e ou wo ld.
This book has been ca e ully s uc u ed o p o ide bo h cla i y and dep h. I in oduces he
co e concep s o he modynamics in a sys ema ic manne , s a ing om he basic laws and
ex ending o ad anced applica ions in eal-wo ld sys ems. Emphasis has been placed on
blending heo e ical knowledge wi h p ac ical illus a ions, p oblem-sol ing app oaches, and
examples d awn om enginee ing p ac ice.
The ex is designed o s uden s, educa o s, and p o essionals alike. Fo lea ne s, i se es as
a comp ehensi e guide o mas e ing undamen al p inciples and sol ing nume ical p oblems.
Fo eache s, i o e s a s uc u ed esou ce o suppo ins uc ion and class oom discussions.
Fo esea che s and p ac i ione s, i p o ides a eliable e e ence o explo e he modynamic
concep s in he con ex o mode n echnologies.
We ha e also made conscious e o s o p esen he subjec in an accessible way by using
clea explana ions, diag ams, sol ed examples, and exe cises ha encou age sel -lea ning and
applica ion. The in eg a ion o mode n ools and compu a ional me hods has been highligh ed
whe e e ele an , e lec ing he e ol ing na u e o enginee ing educa ion.
While p epa ing his book, we ha e d awn inspi a ion om he pionee ing con ibu ions o
scien is s, enginee s, and educa o s whose wo k con inues o shape he ield o
he modynamics. We humbly hope ha his book will se e as a aluable companion o all
eade s who wish o gain bo h ounda ional knowledge and p ac ical insigh in o he subjec .
Finally, we welcome cons uc i e eedback and sugges ions om eade s, as his book is a
esul o con inuous lea ning and e inemen .
M . V. P abaha an
D . J. M. P abhudass
D . N. Poyyamozhi
D . V. T. Vimalanan h
Acknowledgemen
The comple ion o his book on The modynamics has been a deeply ewa ding and
enligh ening jou ney, made possible h ough he unwa e ing suppo , guidance, and
con ibu ions o many indi iduals and ins i u ions. We ex end ou hea el g a i ude o all
who ha e played a i al ole in b inging his wo k o ui ion.
Fi s and o emos , we exp ess ou since e app ecia ion o ou eache s, men o s, and
colleagues, whose aluable insigh s, cons uc i e eedback, and cons an encou agemen ha e
signi ican ly en iched he dep h and cla i y o his book. Thei expe ise has guided us in
p esen ing bo h he ounda ional p inciples and he p ac ical applica ions o he modynamics
in a comp ehensi e manne .
We a e especially g a e ul o ou amilies o hei uncondi ional lo e, pa ience, and
con inuous suppo h oughou his endea o . Thei belie in ou wo k and hei sac i ices
ha e been a sou ce o s eng h and inspi a ion, enabling us o comple e his book success ully.
Ou deepes hanks also go o he academic and esea ch communi ies in he ields o
he modynamics, ene gy sys ems, and applied sciences. Thei pionee ing esea ch,
inno a ions, and schola ly con ibu ions ha e laid he g oundwo k upon which his book is
buil , and hei wo k con inues o inspi e us o del e deepe in o his essen ial subjec .
We also wish o acknowledge he assis ance o mode n compu a ional ools and esou ces,
which ha e acili a ed p oblem-sol ing, da a analysis, and he p esen a ion o complex
concep s in a clea and accessible way. These ools ha e highligh ed he ele ance o
echnology in ad ancing he unde s anding and eaching o he modynamics.
Abo e all, we exp ess ou p o ound g a i ude o Almigh y God o His guidance, wisdom,
and blessings h oughou his jou ney. His g ace has been ou cons an sou ce o mo i a ion
in o e coming challenges and ensu ing he success ul comple ion o his book.
We hope his book se es as a aluable esou ce o s uden s, educa o s, and p o essionals,
os e ing a deepe unde s anding o he modynamics and i s i al ole in enginee ing, science,
and echnology.
M . V. P abaha an
D . J. M. P abhudass
D . N. Poyyamozhi
D . V. T. Vimalanan h
The modynamics
3
Applica ions o Con inuum Concep
Valid o a mosphe ic ai , wa e , s eam, and common enginee ing luids unde no mal
p essu e and empe a u e condi ions. No alid in a e ied gases (high al i udes, acuum
chambe s, space en i onmen s).
Used ex ensi ely in he modynamics, luid mechanics, and hea ans e whe e bulk
p ope ies a e mo e use ul han molecula da a.
1.2 Compa ison o mic oscopic and mac oscopic app oach
Mic oscopic app oach: Deals wi h he beha io o indi idual molecules, equi ing de ailed
knowledge o molecula mo ion and in e ac ions.
 S udies he beha io o indi idual molecules ha make up he sys em.
 Based on he p inciples o s a is ical mechanics.
 Requi es knowledge o he posi ion, eloci y, and ene gy o each molecule.
 Sys em p ope ies (p essu e, empe a u e, e c.) a e ob ained by s a is ical a e aging
o molecula da a.
 Mo e accu a e a he molecula le el bu complex and compu a ionally hea y o
la ge sys ems.
Mac oscopic app oach (con inuum assump ion): Conside s ma e as con inuously
dis ibu ed, igno ing disc e e molecula na u e. P ope ies such as p essu e, empe a u e, and
eloci y a e desc ibed as poin unc ions.
 S udies he sys em as a whole, wi hou conside ing indi idual molecules.
 Based on classical he modynamics and he con inuum hypo hesis.
 P ope ies like p essu e, empe a u e, olume, and densi y a e ea ed as
con inuous unc ions o space and ime.
 Easie and mo e p ac ical o enginee ing analysis.
 Wo ks well when con inuum assump ion (Kn < 0.01) is alid.
Aspec
Mic oscopic App oach
Mac oscopic App oach
Basis
Indi idual molecules and hei
in e ac ions
O e all sys em ea ed as a
con inuum
Founda ion
S a is ical mechanics, kine ic heo y
Classical he modynamics
P ope ies
De i ed om molecula mo ion (e.g.,
p essu e om molecula collisions)
Measu ed di ec ly as bulk
p ope ies (P, V, T)
Le el o
De ail
P o ides molecula -le el de ails
P o ides a e age/sys em-le el
in o ma ion

The modynamics
4
Complexi y
Ve y high (needs da a o millions o
molecules)
Rela i ely simple and
p ac ical
Applicabili y
Ra e ied gases, nano/mic o scale lows,
plasma physics
Enginee ing sys ems, luids,
gases, hea engines
Example
De e mining eloci y dis ibu ion o
molecules
Measu ing empe a u e o
s eam in a boile
Table. 1.1 Mic oscopic s. Mac oscopic App oach.
1.3 Pa h and Poin Func ions
Pa h Func ions
A pa h unc ion is a quan i y whose alue depends on he speci ic pa h ollowed du ing a
he modynamic p ocess, a he han jus he ini ial and inal s a es o he sys em. Unlike
p ope ies (such as empe a u e, p essu e, o olume) which a e s a e unc ions, pa h
unc ions a e no p ope ies o he sys em. Ins ead, hey ep esen bounda y in e ac ions
like hea and wo k.
Conside a sys em ha changes om an ini ial s a e (poin 1) o a inal s a e (poin 2) on a P–
V diag am. Di e en p ocess pa hs (A, B, and C) can connec hese wo s a es.
Fig. 1.2 G aph o P-V showing Example o he pa h unc ion.
The modynamics
5
Al hough he ini ial and inal s a es a e he same, he a ea unde each cu e (which
ep esen s wo k done) is di e en o each pa h.
Hence, he wo k done and hea ans e ed depend on he pa h, no jus he end s a es.
Examples o Pa h Func ions
1. Wo k (W): Wo k done by o on a sys em depends on how p essu e and olume change
du ing he p ocess. Fo he same ini ial and inal s a es, he wo k di e s depending on whe he
he p ocess is iso he mal, adiaba ic, o poly opic.
Example: Gas expanding slowly s. apidly - wo k alues di e .
2. Hea T ans e (Q): Hea abso bed o ejec ed depends on how ene gy is supplied o
emo ed. The amoun o hea di e s i hea ing is cons an , apid, o in ol es a phase
change, e en i he sys em eaches he same inal s a e.
Cha ac e is ics o Pa h Func ions
1. P ocess Dependen : Thei alues depend on he manne in which he p ocess occu s.
2. Di e en Pa hs, Di e en Values: Same ini ial and inal s a es can yield di e en
amoun s o hea o wo k.
3. Inexac Di e en ials: Pa h unc ions a e exp essed using δQ, δW ins ead o dQ, dW,
indica ing hey a e no exac di e en ials and no p ope ies.
Poin Func ions (S a e Func ions)
A poin unc ion, also known as a s a e unc ion, is a p ope y whose alue depends only on
he s a e o he sys em and no on he pa h aken o each ha s a e. In o he wo ds, poin
unc ions a e de e mined solely by he ini ial and inal s a es, ega dless o he p ocess in
be ween.
Examples o poin unc ions include in e nal ene gy (U), en opy (S), en halpy (H), and
empe a u e (T).
Examples o Poin Func ions
1. In e nal Ene gy (U): I a gas unde goes expansion o comp ession, i s in e nal ene gy
change depends only on he s a ing and ending s a es. The manne o ene gy ans e (slow,
as , hea , o wo k) does no a ec he o al change in in e nal ene gy.
The modynamics
6
2. Tempe a u e (T): I wa e is hea ed om 20°C o 80°C, he empe a u e ise is always
60°C, ega dless o how slowly o apidly he hea ing akes place.
Fig. 1.3 G aph o P-V showing Example o he poin unc ion.
3. En halpy (H): When wa e is con e ed in o s eam a a gi en p essu e, he en halpy
change is ixed and depends only on he ini ial liquid s a e and he inal apo s a e.
Cha ac e is ics o Poin Func ions
1. S a e-Dependen : Thei alues a e de e mined only by he condi ion (s a e) o he sys em,
no he pa h aken.
2. Exac Di e en ials: Poin unc ions can be exp essed in he o m o exac di e en ials
(dU, dH, dT, e c.), meaning hey can be in eg a ed di ec ly.
3. Unique a a S a e: Fo a gi en he modynamic s a e, poin unc ions ha e de ini e alues
ha emain he same no ma e how he s a e was achie ed.
Rela ionship be ween Wo k and In e nal Ene gy
In he modynamics, poin unc ions (s a e unc ions) and pa h unc ions a e in e connec ed.
 Poin unc ions desc ibe he condi ion o a sys em a a gi en s a e (e.g., in e nal
ene gy, en halpy, en opy).
The modynamics
7
 Pa h unc ions desc ibe how he sys em eaches ha s a e h ough ene gy in e ac ions
(e.g., hea , wo k).
Pa h unc ions like hea (Q) and wo k (W) cause changes in poin unc ions such as in e nal
ene gy (U), en halpy (H), and en opy (S).
Key Rela ionships
1. Pa h unc ions d i e changes in poin unc ions: Hea and wo k ans e a e esponsible
o al e ing in e nal ene gy, en halpy, o en opy.
2. Di e en pa hs - di e en Q and W, bu same ΔU: Fo a gi en change o s a e, he wo k
and hea alues depend on he p ocess pa h, bu he change in in e nal ene gy (ΔU) emains
he same because i is a s a e p ope y.
3. Poin unc ions se limi s o pa h unc ions: The change in in e nal ene gy de ines how
hea and wo k in e ac in any he modynamic p ocess.
Aspec
Poin Func ion (S a e Func ion)
Pa h Func ion
De ini ion
Depends only on he s a e o he
sys em
Depends on he pa h aken
be ween s a es
Dependence
Independen o he pa h ollowed
Dependen on he pa h
ollowed
Examples
P essu e, Tempe a u e, Volume,
In e nal Ene gy, En halpy, En opy
Wo k (W), Hea (Q)
Value o Same
S a es
Same alue, no ma e how he s a e
is eached
Di e en alues o di e en
p ocesses
P ocess
In o ma ion
Only ini ial and inal s a es a e
needed
Exac pa h o he p ocess mus
be known
Di e en ials
Exac (pe ec ) di e en ials, w i en
as dU, dH, dS
Inexac (impe ec )
di e en ials, w i en as δQ,
δW
Cyclic P ocess
Ne change o e a cycle = 0
Ne alue o e a cycle ≠ 0
(can be posi i e o nega i e)
Table. 1.2 Di e ence be ween poin and pa h unc ion.
1.4 In ensi e and Ex ensi e P ope ies
In he modynamics, p ope ies o a sys em a e classi ied in o in ensi e and ex ensi e
depending on whe he hey a y wi h he amoun o ma e p esen .
The modynamics
8
1. In ensi e P ope ies
In ensi e p ope ies a e hose ha do no depend on he size o quan i y o ma e in a
sys em. They emain he same ega dless o how much subs ance is p esen .
Fo example, whe he you ha e a d op o wa e o a bucke o wa e , he empe a u e and
boiling poin emain iden ical.
Cha ac e is ics
 Independen o mass o olume.
 Desc ibe he in insic na u e o a subs ance.
 Use ul in iden i ying and compa ing ma e ials.
 O en exp essed as a ios o de i ed p ope ies (e.g., densi y = mass/ olume).
Examples
1. Tempe a u e: A sample o wa e a 25°C s ays a ha empe a u e i espec i e o quan i y.
2. P essu e: A gas di ided be ween wo con aine s s ill exe s he same p essu e.
3. Densi y: Pu e gold always has a densi y o ~19.3 g/cm³, no ma e he sample size.
4. Mel ing/Boiling Poin s: Ice always mel s a 0°C and wa e boils a 100°C (a 1 a m).
5. O he examples: Colo , e ac i e index, conduc i i y, ha dness, su ace ension.
2. Ex ensi e P ope ies
Ex ensi e p ope ies a e hose ha depend on he amoun o ma e p esen in he sys em.
Thei alues scale wi h he size o mass o he sys em.
Fo ins ance, doubling he mass o a subs ance also doubles i s olume and o al ene gy.
Cha ac e is ics
 Di ec ly p opo ional o he amoun o ma e .
 Addi i e in na u e: The o al alue is he sum o he alues o all pa s.
 P o ide quan i a i e a he han quali a i e in o ma ion.
 No sui able o subs ance iden i ica ion, bu essen ial o measu ing o al sys em
beha io .

The modynamics
9
Examples
1. Mass: Two 500 g samples oge he make 1000 g.
2. Volume: Adding mo e ma e inc eases he occupied space.
3. Ene gy: To al in e nal, kine ic, o po en ial ene gy inc eases wi h sys em size.
4. O he Examples: En halpy, en opy, hea capaci y, numbe o moles, leng h.
Rela ionship be ween In ensi e and Ex ensi e P ope ies
In ensi e and ex ensi e p ope ies a e closely ela ed in he modynamics and ma e ial
science. In many cases, a ios o combina ions o ex ensi e p ope ies gi e ise o
in ensi e p ope ies. This ela ionship helps explain why some p ope ies emain cons an
o a subs ance, while o he s a y wi h he amoun o ma e .
Example: Densi y
Densi y is de ined as:
ρ= m
V
 Mass (m) and Volume (V) a e bo h ex ensi e p ope ies.
 Thei a io, densi y (ρ), is an in ensi e p ope y.
No ma e i you ha e 1 mL, 1 L, o 100 L o pu e wa e , he densi y emains app oxima ely
1 g/cm³ a oom empe a u e.
Examples o In ensi e P ope ies De i ed om Ex ensi e Ones
1. Mola Volume (V/n): Ra io o olume o numbe o moles.
2. Speci ic Hea (C/m): Hea capaci y pe uni mass.
3. Mola Mass (M/n): Ra io o mass o numbe o moles.
These de i ed in ensi e p ope ies a e c ucial in chemis y, he modynamics, and ma e ial
science because hey desc ibe he in insic beha io o subs ances independen o
quan i y.
The modynamics
10
Aspec
In ensi e P ope ies
Ex ensi e P ope ies
Dependence
Independen o he amoun o
ma e
Dependen on he amoun o
ma e
E ec o
Subdi ision
Remain unchanged when he
sys em is di ided
Change p opo ionally wi h
subdi ision
Usage
Iden i y and cha ac e ize
subs ances
Measu e he o al amoun o
subs ance
Examples
Tempe a u e, P essu e, Densi y,
Boiling Poin
Mass, Volume, Ene gy,
En opy
Addi i i y
No addi i e
Addi i e in na u e
Rela ion
Linked o he in e nal s uc u e and
in e ac ions o ma e
Linked o he o e all size o
ex en o he sys em
Table. 1.3 Di e ence be ween In ensi e and Ex ensi e P ope ies.
1.5 To al and Speci ic Quan i ies
In he modynamics, many p ope ies a e exp essed in e ms o o al o speci ic quan i ies.
These e ms a e pa icula ly impo an when dealing wi h ex ensi e p ope ies, since hey
depend on he o e all mass o size o he sys em.
By dis inguishing be ween o al and speci ic alues, i becomes easie o analyze
he modynamic sys ems o a ying scales, om a small sample o luid in a es ube o la ge
indus ial sys ems such as boile s and u bines.
To al Quan i ies
A o al quan i y e e s o he comple e o o e all alue o an ex ensi e p ope y o he en i e
sys em. These alues depend di ec ly on he size o mass o he sys em, which means ha i
he mass o he sys em is doubled, he o al p ope y alue also doubles. To al quan i ies a e
gene ally deno ed using uppe case symbols in he modynamics.
Fo example, Volume (V) ep esen s he o al space occupied by he sys em, En halpy (H)
ep esen s he o al hea con en , In e nal Ene gy (U) ep esen s he o al s o ed ene gy, and
En opy (S) measu es he o al diso de o he sys em. Each o hese alues gi es a comple e
pic u e o he ene gy o p ope y con en o he sys em as a whole.
Thus, when we say a gas has a o al en halpy o 500 kJ o a olume o 10 m³, we a e e e ing
o he o al quan i ies o he sys em, which scale wi h he amoun o ma e p esen .
The modynamics
11
Speci ic Quan i ies
To make he modynamic analysis mo e con enien , especially when compa ing sys ems o
di e en sizes, i is common o exp ess p ope ies in e ms o speci ic quan i ies. A speci ic
p ope y is ob ained by di iding an ex ensi e p ope y by he mass o he sys em. Since mass
is also an ex ensi e p ope y, his di ision p oduces a alue ha is independen o he sys em
size, making i an in ensi e p ope y. Speci ic p ope ies a e gene ally deno ed using
lowe case symbols.
Fo ins ance, speci ic olume ( ) is de ined as he olume pe uni mass (V/m), exp essed in
m³/kg. Simila ly, speci ic en halpy (h) is he en halpy pe uni mass (H/m), exp essed in J/kg,
and speci ic in e nal ene gy (u) is in e nal ene gy pe uni mass (U/m). Likewise, speci ic
en opy (s) is he en opy pe uni mass (S/m). These speci ic quan i ies a e pa icula ly use ul
when wo king wi h he modynamic ables, as hey p o ide s anda dized alues ha can be
easily scaled up o down depending on he ac ual mass o he sys em.
As an example, i 2 kg o gas occupies a o al olume o 10 m³, i s speci ic olume can be
calcula ed as:
𝑣=𝑉
𝑚=10
2=5 m3/kg
This alue is independen o he sys em’s o al size and would emain he same e en i we
conside ed a smalle o la ge po ion o he same gas.
Impo ance o To al and Speci ic Quan i ies
The dis inc ion be ween o al and speci ic quan i ies is i al in he modynamic analysis. To al
p ope ies p o ide essen ial in o ma ion when calcula ing o e all ene gy balances in la ge-
scale enginee ing sys ems. Fo example, he o al en halpy o s eam en e ing a u bine is
necessa y o de e mining he o al wo k ou pu .
On he o he hand, speci ic p ope ies simpli y he analysis by gi ing alues pe uni mass.
This makes i easie o compa e subs ances, i espec i e o he amoun a ailable. Enginee s
and scien is s o en use speci ic alues om s eam o e ige an p ope y ables, which can
hen be mul iplied by he ac ual mass o he sys em o ob ain he co esponding o al p ope y.
This dual use o o al and speci ic quan i ies p o ides lexibili y in he modynamics, allowing
bo h la ge-scale sys em analysis and small-scale p ope y compa ison.
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12
1.6 Sys em and hei ypes
In he modynamics, he concep o a sys em o ms he ounda ion o all analysis. A
he modynamic sys em is de ined as a speci ied quan i y o ma e o a pa icula egion in
space selec ed o s udy. The beha io o his sys em is analyzed in e ms o i s p ope ies,
in e ac ions, and ene gy exchanges.
E e y hing ha lies ou side he chosen sys em is e e ed o as he su oundings. In p ac ice,
he su oundings usually deno e he egion in he immedia e neighbo hood ha can ha e a
measu able in luence on he sys em.
The sepa a ion be ween he sys em and i s su oundings is de ined by a bounda y. This
bounda y may be eal o imagina y, and i can ei he be ixed (such as he walls o a igid
con aine ) o mo able (such as a pis on head in a cylinde ). The bounda y plays an essen ial
ole in de e mining whe he mass o ene gy c osses in o o ou o he sys em.
Fig. 1.4 The modynamic Sys em, bounda y, su oundings.
Types o The modynamic Sys ems
The modynamic sys ems a e b oadly classi ied in o h ee ca ego ies depending on whe he
ene gy and mass can c oss he bounda y.
1. Closed Sys em
A closed sys em (also called a con ol mass sys em) consis s o a ixed amoun o ma e .
 Mass: Remains cons an ; no mass c osses he sys em bounda y.
 Ene gy: Hea and wo k in e ac ions a e possible ac oss he bounda y.
 Volume: May change, as he sys em’s bounda y can expand o con ac .
Example:
 Gas con ined in a pis on–cylinde a angemen .
 A sealed con aine o wa e being hea ed (no mass ans e , bu ene gy ans e
occu s).
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19
Cha ac e is ics
 P ocess can be e aced in he opposi e di ec ion.
 P oduces maximum possible wo k ou pu ( o a gi en change o s a e).
 Idealiza ion - no eal p ocess is pe ec ly e e sible.
Examples
 Iso he mal expansion o comp ession o an ideal gas ca ied ou in ini ely slowly.
 F ic ionless pis on–cylinde mo emen .
 Hea ans e be ween wo bodies a he same empe a u e ( heo e ically).
Types o Re e sible P ocesses
a) In e nally Re e sible P ocess
A p ocess is said o be in e nally e e sible i no i e e sibili y occu s wi hin he sys em
du ing he p ocess.
 The sys em passes h ough a con inuous se ies o equilib ium s a es.
 I he p ocess is e e sed, he sys em e aces he same pa h and e u ns o i s o iginal
s a e.
 Howe e , i e e sibili ies may s ill occu ou side he sys em (in he su oundings).
Example: Slow, ic ionless comp ession o expansion o a gas in a pis on–cylinde de ice.
b) Ex e nally Re e sible P ocess
A p ocess is ex e nally e e sible i no i e e sibili y occu s ou side he sys em bounda ies
du ing he p ocess.
 The in e ac ion be ween he sys em and su oundings is pe ec ly balanced.
 Fo ins ance, when hea ans e akes place be ween wo bodies a he same
empe a u e, he e is no ex e nal i e e sibili y.
Example: Hea ans e be ween a sys em and a he mal ese oi a exac ly he same
empe a u e.
2. I e e sible P ocess
An i e e sible p ocess is a eal p ocess ha canno be exac ly e e sed, because i lea es
pe manen changes in he sys em o su oundings. When such a p ocess is e e sed, he
sys em and su oundings do no e u n o hei ini ial s a es.

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20
All na u al p ocesses a e i e e sible o some ex en , because hey in ol e ini e di e ences
in d i ing o ces ( empe a u e, p essu e, chemical po en ial) and include dissipa i e e ec s
such as ic ion, u bulence, elec ical esis ance, o inelas ic de o ma ion.
Causes o I e e sibili y
1. F ic ional e ec s: Mechanical ic ion, iscous d ag in luids.
2. Un es ained expansion o gases: Sudden expansion in o a acuum.
3. Hea ans e ac oss a ini e empe a u e di e ence: Flow o hea om a ho body
a 500 K o a cold body a 300 K.
4. Mixing o di e en subs ances: e.g., di usion o wo gases.
5. Inelas ic de o ma ions: Plas ic de o ma ion o solids.
6. Na u al spon aneous p ocesses: Flow o hea om ho o cold, spon aneous
chemical eac ions.
Cha ac e is ics
 P ocess canno be e aced o es o e bo h sys em and su oundings.
 Wo k ou pu is always less han ha o a e e sible p ocess be ween he same s a es.
 All eal p ocesses a e i e e sible in p ac ice.
Examples
 F ee expansion o a gas in o a acuum.
 Sudden comp ession o expansion o gases.
 Hea ans e h ough a ini e empe a u e di e ence.
 Na u al mixing o gases o liquids.
Types o I e e sible P ocesses
a) In e nal I e e sibili y
An in e nal i e e sibili y a ises due o e ec s wi hin he sys em i sel ha dis u b
equilib ium.
 These include ac o s like ic ion wi hin he wo king luid, u bulence, iscous
dissipa ion, o non-equilib ium chemical eac ions.
 They p e en he sys em om passing h ough a se ies o equilib ium s a es.
Example:
 Viscous e ec s in luid low.
 Combus ion eac ions inside a cylinde .
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21
b) Ex e nal I e e sibili y
An ex e nal i e e sibili y occu s due o dis u bances o dissipa i e e ec s in he
su oundings o he sys em.
 These a e caused by in e ac ions be ween he sys em and i s en i onmen ha a e no
pe ec ly balanced.
Example:
 Mechanical ic ion be ween a mo ing pis on and i s cylinde walls.
 Hea ans e h ough a ini e empe a u e di e ence be ween a ho sou ce and a cold
sys em.
Conside a he modynamic sys em unde going a change om s a e A o s a e B as shown in
he diag am. The manne in which his change occu s de e mines whe he he p ocess is
e e sible o i e e sible.
Re e sible P ocess
A e e sible p ocess is an ideal p ocess ha can be comple ely e e sed, such ha bo h he
sys em and su oundings a e es o ed o hei o iginal s a es wi hou lea ing any ace o he
p ocess.
 In he igu e, he cu ed pa h (A → B) ep esen s he e e sible p ocess.
 Du ing his pa h, he sys em passes h ough a con inuous se ies o equilib ium s a es,
whe e p essu e, empe a u e, and o he p ope ies a e well-de ined a e e y s age.
 Fo a p ocess o be e e sible, i mus occu in ini ely slowly, ensu ing ha he sys em
emains in he modynamic equilib ium h oughou .
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Key Condi ions o Re e sibili y
1. The p ocess mus be quasi-s a ic (in ini ely slow).
2. The e should be no dissipa i e e ec s such as ic ion, u bulence, iscosi y, o hea
ans e h ough a ini e empe a u e di e ence.
3. Each in e media e s a e mus be an equilib ium s a e.
I e e sible P ocess
An i e e sible p ocess is a eal p ocess ha canno be comple ely e e sed, because i
lea es pe manen e ec s on he sys em and su oundings.
 In he igu e, he s aigh dashed line (A → B) shows an i e e sible pa h.
 The sys em does no pass h ough equilib ium s a es du ing he p ocess, and
in e media e s a es canno be de ined p ecisely.
 I e e sibili y a ises due o ac o s like ic ion, un es ained expansion, u bulence,
hea ans e ac oss ini e empe a u e di e ences, o mixing o subs ances.
Special Case: Re e sible Adiaba ic (Isen opic) P ocess
 I he p ocess is adiaba ic (no hea ans e , Q=0) and e e sible, i becomes an
isen opic p ocess.
 In such a case, he en opy emains cons an (ΔS=0).
 These p ocesses a e impo an in analyzing ideal cycles like he Ca no cycle, O o
cycle, and Rankine cycle.
1.10 Hea and Wo k T ans e and I ’s Sign con en ion
Wo k
In he modynamics, wo k is de ined in e ms o i s ex e nal e ec . A sys em is said o pe o m
posi i e wo k du ing a p ocess i he sole ex e nal e ec p oduced by he sys em can be
educed o he li ing o a weigh agains g a i y.
Conside a gas enclosed in a pis on–cylinde a angemen . When he gas expands, he
pis on is pushed upwa d. In his a angemen , no mass is di ec ly li ed agains g a i y.
Howe e , i he pis on is connec ed o an ex e nal mechanism (such as pulleys and weigh s),
he upwa d mo emen o he pis on can esul in he li ing o a mass.
Thus, al hough he pis on i sel only mo es, he ex e nal e ec equi alen o li ing a weigh
allows us o de ine his expansion as wo k done by he sys em.
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23
Fig. 1.9 Expansion o ac ual li ing o mass.
Ex e nal E ec s Only
When e alua ing he modynamic wo k, only he e ec s ex e nal o he sys em bounda ies
a e conside ed. E en s o ene gy ans e s occu ing wi hin he sys em i sel a e no coun ed
as wo k.
Fig. 1.10 Expansion wi hou ac ual li ing o mass.
Example:
Suppose a li (ele a o ) wi h a pe son and sui case is conside ed as a he modynamic
sys em.
I he pe son li s he sui case inside he li , his e en occu s wi hin he sys em bounda ies
and he e o e does no quali y as he modynamic wo k.
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24
On he o he hand, i he en i e li mo es upwa d due o an ex e nal o ce, hen ha mo ion
can be conside ed as wo k done on o by he sys em.
Uni s o Wo k and Powe
In he modynamics, wo k is he p oduc o o ce and displacemen in he di ec ion o he
o ce. In he SI sys em, he uni o o ce is he New on (N), and he uni o dis ance is he
me e (m).
Hence, he uni o wo k becomes:
Wo k = New on-me e (N.m )
 One New on-me e is also known as one Joule (J).
Since he modynamic p ocesses o en in ol e la ge quan i ies o ene gy, wo k is equen ly
exp essed in kilojoules (kJ), whe e: 1 kJ=1000 J
The a e o doing wo k is called powe .
 Powe is exp essed as wo k pe uni ime:
Powe = Wo k
Time
 I s uni in SI is Joule pe second (J/s), which is gi en he special name Wa (W).
Thus,
1Wa =1 Joule
second =1𝑁⋅𝑚
𝑠
Fo la ge-scale applica ions, powe is also exp essed in kilowa s (kW) o megawa s (MW).
Sign Con en ion o Wo k
In he modynamics, a clea sign con en ion is ollowed o a oid con usion:
1. Wo k done by he sys em on he su oundings - Posi i e
Example: Expansion o gas in a pis on-cylinde does wo k on he pis on.

The modynamics
25
2. Wo k done on he sys em by he su oundings - Nega i e
Example: Comp ession o gas by applying ex e nal p essu e.
This con en ion ensu es consis ency when applying he Fi s Law o The modynamics.
Fig. 1.11 Sign con en ion o wo k.
Hea
In he modynamics, hea is de ined as a mode o ene gy ans e be ween sys ems (o
be ween a sys em and i s su oundings) ha occu s solely due o a empe a u e di e ence.
When wo bodies a di e en empe a u es come in con ac , ene gy in he o m o hea lows
om he body a a highe empe a u e o he body a a lowe empe a u e un il he mal
equilib ium is eached.
An impo an poin o no e is ha :
 Hea is no a p ope y con ained in a body.
 Hea can only be ecognized as i c osses he sys em bounda y du ing an in e ac ion.
 Jus like wo k, hea is a pa h unc ion, meaning i s alue depends on he p ocess pa h
aken, no jus he end s a es.
Modes o Hea T ans e
Hea can be ans e ed om one sys em o ano he , o be ween a sys em and i s su oundings,
by h ee dis inc modes: conduc ion, con ec ion, and adia ion.
1. Conduc ion
Conduc ion occu s wi hou any bulk mo emen o ma e . The ans e o ene gy akes
place h ough molecula ib a ions in solids and h ough he mo ion o ee elec ons in
The modynamics
26
me als. I is he dominan mode o hea ans e in solids.
Example: Hea ans e h ough he wall o a u nace o along a me al od hea ed a one end.
2. Con ec ion
Con ec ion occu s due o bulk mo emen o luid pa icles and is he e o e signi ican in
liquids and gases. I combines he e ec s o conduc ion wi hin he luid and ad ec ion due
o luid mo ion.
Types o Con ec ion:
1. Fo ced Con ec ion: When luid mo ion is induced by an ex e nal de ice such as a an,
pump, o blowe .
2. Na u al Con ec ion: When luid mo ion a ises na u ally due o densi y di e ences
caused by empe a u e a ia ions.
Example: Cooling o ho wa e in a essel (na u al con ec ion), cooling o a ca adia o
using a an ( o ced con ec ion).
3. Radia ion
Radia ion is he ans e o hea in he o m o elec omagne ic wa es (p ima ily in a ed
adia ion). Unlike conduc ion and con ec ion, adia ion does no equi e a medium and can
occu e en h ough a acuum.
Gene ally, i is a su ace phenomenon, as su aces emi and abso b adian ene gy. Howe e ,
in ce ain cases like gases con aining wa e apo o ca bon dioxide, adia ion can be a
olume ic phenomenon.
Example: Sola ene gy eaching he Ea h, hea ans e be ween wo pla es sepa a ed by a
acuum.
Sign Con en ion o Hea
To main ain consis ency in he modynamic analysis, he ollowing sign con en ion is used:
 Hea ans e ed in o he sys em → Posi i e
 Hea ans e ed ou o he sys em → Nega i e
Fo example, i hea is supplied o a gas in a pis on–cylinde de ice, i is conside ed posi i e.
Con e sely, i he gas ejec s hea o he su oundings, i is nega i e.
The modynamics
27
Fig. 1.12 Sign con en ion o hea .
1.11 Displacemen wo k
Conside a pis on-cylinde a angemen con aining a luid as shown in Figu e 1.13. I he
p essu e o he luid inside he cylinde is g ea e han he p essu e o he su oundings, he e
will be an unbalanced o ce ac ing on he pis on. As a esul , he pis on will mo e ou wa d.
Fig. 1.13 Pis on-cylinde a angemen con aining a luid.
The o ce ac ing on he pis on is gi en by:
𝐹=𝑃×𝐴
whe e,
 𝑃= p essu e o he luid
 𝐴= a ea o pis on
The modynamics
28
The wo k done by his o ce when he pis on mo es a dis ance 𝑑𝑥 is:
𝛿𝑊=𝐹×𝑑𝑥=(𝑃⋅𝐴)⋅𝑑𝑥
Since he change in olume o he sys em is 𝑑𝑉=𝐴⋅𝑑𝑥,
𝛿𝑊=𝑃𝑑𝑉
This exp ession is called displacemen wo k o 𝑝𝑑𝑉 wo k.
To ob ain he o al wo k done in a p ocess, his inc emen al wo k is in eg a ed om he ini ial
o he inal olume:
𝑊=∫
𝑉2
𝑉1𝑃𝑑𝑉
Thus, he a ea unde he p ocess cu e in a P-V diag am ep esen s he displacemen wo k.
E alua ion o Displacemen Wo k
Cons an P essu e P ocess
Conside a pis on-cylinde a angemen (Figu e 1.14) in which he luid expands while he
p essu e emains cons an h oughou he p ocess.
Fig. 1.14 Pis on-cylinde a angemen .
The modynamics
35
Fig. 1.19 Tempe a u e Scales.
a) Celsius Scale ( ∘𝐂 )
This is also called he cen ig ade scale. De ines he eezing poin o wa e as 0∘C and he
boiling poin o wa e as 100∘C a 1 a m p essu e.
I is a ela i e scale, widely used in daily li e, labo a o ies, and enginee ing p ac ice.
Rela ionship wi h Kel in scale: 𝑇(𝐾)=𝑇( ∘𝐶)+273.15
b) Fah enhei Scale ( ∘𝐅 )
Commonly used in he Uni ed S a es and some o he coun ies. De ines he eezing poin o
wa e as 32∘F and he boiling poin as 212∘F a 1 a m p essu e.

The modynamics
36
I di ides he empe a u e di e ence be ween ice and s eam poin s in o 180 equal di isions.
Con e sion o mulas: 𝑇( ∘𝐹) =9
5𝑇( ∘𝐶)+32
𝑇( ∘𝐶) =5
9(𝑇( ∘𝐹)−32)
c) Kel in Scale (K)
The absolu e he modynamic scale o empe a u e. Absolu e ze o (0 K) is he lowes possible
empe a u e, co esponding o −273.15∘C, whe e molecula mo ion heo e ically ceases.
The eezing poin o wa e =𝟐𝟕𝟑.𝟏𝟓 𝐊, and he boiling poin =𝟑𝟕𝟑.𝟏𝟓 𝐊. The Kel in
scale is he SI uni o empe a u e and is essen ial o all scien i ic and he modynamic
calcula ions. Rela ion wi h Celsius:
𝑇(𝐾)=𝑇( ∘𝐶)+273.15
d) Rankine Scale ( ∘𝐑 )
The absolu e empe a u e scale used in coun ies whe e he Fah enhei sys em is p e e ed.
Ze o Rankine (0∘R) co esponds o absolu e ze o.
F eezing poin o wa e =491.67∘R; Boiling poin =671.67∘R. Con e sion o mulas:
𝑇( ∘𝑅)=𝑇( ∘𝐹)+459.67
𝑇( ∘𝑅)=1.8𝑇(𝐾)
1.14 Fi s Law o The modynamics and Applica ion o closed and
open sys ems
The Fi s Law o The modynamics is a s a emen o he p inciple o conse a ion o
ene gy applied o he modynamic sys ems. I asse s ha ene gy can nei he be c ea ed no
des oyed; i can only be ans e ed om one sys em o ano he o ans o med om one
o m o ano he .
In i s mos gene al o m, he Fi s Law is exp essed as:
“When ene gy is ans e ed o ans o med, he o al ene gy o an isola ed sys em emains
cons an . The inal o al ene gy in all o ms mus be equal o he o iginal o al ene gy.”
The modynamics
37
Fi s Law o The modynamics o a Closed Sys em Unde going a P ocess
The Fi s Law o The modynamics exp esses he p inciple o conse a ion o ene gy. Fo
a closed sys em o cons an mass, ene gy can c oss he sys em bounda y only in wo o ms:
hea (Q) and wo k (W).
Gene al Fo mula ion
The Fi s Law can be exp essed as:
Ene gy En e ed in o he Sys em - Ene gy Le he Sys em = Change in he Ene gy Con en o
he Sys em
I a closed sys em ini ially has an ene gy con en o 𝐸1, ecei es a ne hea inpu 𝑄, and
pe o ms wo k 𝑊, he inal ene gy con en o he sys em becomes 𝐸2.
Thus, 𝑄−𝑊=(𝐸2−𝐸1)
Fig. 1.20 Fi s law o closed sys em.
To al Ene gy Con en o a Sys em
The ene gy con en o a sys em (𝐸) can be exp essed as he sum o h ee majo componen s:
𝐸=𝑈+ Kine ic Ene gy + Po en ial Ene gy
𝐸=𝑈+1
2𝑚𝐶2+𝑚𝑔𝑧
Whe e,
 𝑈 : In e nal ene gy o he sys em
 1
2𝑚𝐶2 : Kine ic ene gy due o sys em eloci y 𝐶
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38
 mgz: Po en ial ene gy due o ele a ion 𝑧 in a g a i a ional ield
Hence, 𝑄−𝑊=Δ𝑈+Δ𝐾𝐸+Δ𝑃𝐸
In e nal Ene gy (U)
The in e nal ene gy ep esen s he mic oscopic ene gy s o ed wi hin he sys em, a ising om:
 Molecula mo ion ( ansla ional, o a ional, ib a ional)
 In e molecula o ces
 Elec on spin and ib a ions
 Chemical bonds
In e nal ene gy is deno ed by 𝐔, and o many he modynamic analyses, i plays he mos
signi ican ole.
Kine ic Ene gy
Kine ic ene gy accoun s o he mo ion o he sys em as a whole wi h eloci y 𝐶.
𝐾𝐸=1
2𝑚𝐶2
Fo s a iona y sys ems, his e m is ze o. In he modynamics, unless speci ically conside ed
(e.g., in nozzles o u bines), he kine ic ene gy e m is o en neglec ed.
Po en ial Ene gy
Po en ial ene gy a ises due o he posi ion o he sys em in a g a i a ional ield.
𝑃𝐸=𝑚𝑔𝑧
Fo sys ems ha emain a he same ele a ion, his e m emains cons an . In p ac ical
he modynamic sys ems, unless he e is signi ican ele a ion change (e.g., hyd o u bines,
wa e pumps), po en ial ene gy is o en neglec ed.
Uni s
The SI uni o ene gy is he Joule (J). Fo la ge-scale sys ems, ene gy is o en exp essed in
kilojoules (kJ).
The modynamics
39
The The modynamic P ope y: En halpy
Conside a s a iona y sys em o ixed mass unde going a quasi-equilib ium p ocess a
cons an p essu e.
Applying he Fi s Law o The modynamics:
𝑄1−2−𝑊1−2=𝐸2−𝐸1
Fo a gene al sys em:
𝐸2−𝐸1=(𝑈2−𝑈1)+𝑚(𝐶22−𝐶12
2)+𝑚𝑔(𝑍2−𝑍1)
Since he sys em is s a iona y, changes in kine ic ene gy and po en ial ene gy a e negligible:
𝐸2−𝐸1=𝑈2−𝑈1
Wo k Te m a Cons an P essu e
The displacemen wo k done is:
𝑊1−2=𝑃(𝑉2−𝑉1)=𝑃2𝑉2−𝑃1𝑉1
Subs i u ing in he Fi s Law:
𝑄1−2=(𝑃2𝑉2−𝑃1𝑉1)+(𝑈2−𝑈1)
Rea anging, 𝑄1−2=(𝑈2+𝑃2𝑉2)−(𝑈1+𝑃1𝑉1)
De ini ion o En halpy
The e ms wi hin he b acke s depend only on he end s a es o he sys em. This combina ion
o p ope ies can be g ouped in o a single he modynamic p ope y, known as en halpy.
𝐻=𝑈+𝑃𝑉
Fo speci ic p ope ies (pe uni mass): ℎ=𝑢+𝑝𝑣
whe e,
 𝐻= en halpy (kJ)
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40
 ℎ= speci ic en halpy ( kJ/kg )
 𝑈= in e nal ene gy (kJ)
 𝑢= speci ic in e nal ene gy ( kJ/kg )
 𝑉= olume (m3)
 𝑣= speci ic olume (m3/kg)
Signi icance o En halpy
 En halpy is a con enien p ope y when analyzing p ocesses a cons an p essu e.
 I combines in e nal ene gy ( U ) and he low ene gy ( PV ) equi ed o push luid
ac oss a sys em bounda y.
 Many p ac ical de ices such as boile s, u bines, condense s, and pumps a e analyzed
in e ms o en halpy changes.
Flow Ene gy
Flow ene gy is de ined as he ene gy equi ed o mo e a mass in o o ou o a con ol olume
agains a p essu e. I ep esen s he wo k needed o push luid ac oss he bounda y o a con ol
olume.
Conside a mass o olume 𝑉 en e ing a con ol olume agains a p essu e 𝑝. To push his
olume ac oss he bounda y, wo k mus be done.
Fig. 1.21 Flow ene gy.

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41
The low ene gy can be de i ed as ollows:
Flow Ene gy = Wo k done in mo ing he mass
= Fo ce × Dis ance
=(𝑝⋅𝐴)⋅𝑑𝑥
=𝑝⋅(𝐴⋅𝑑𝑥)
=𝑝𝑉
whe e,
 𝑝= p essu e
 𝐴= c oss-sec ional a ea
 𝑑𝑥= displacemen
 𝑉=𝐴⋅𝑑𝑥= olume o he mass
Thus, he low ene gy pe uni mass is: 𝑝𝑉
𝑚=𝑝𝑣
whe e 𝑣= speci ic olume.
Rela ion o En halpy
Since en halpy is de ined as he sum o in e nal ene gy and low ene gy, we can w i e:
𝐻=𝑈+𝑝𝑉
o in e ms o speci ic p ope ies, ℎ=𝑢+𝑝𝑣
whe e,
 𝐻= En halpy (kJ)
 𝑈= In e nal ene gy (kJ)
 𝑝𝑉= Flow ene gy (kJ)
 ℎ= Speci ic en halpy (kJ/kg)
 𝑢= Speci ic in e nal ene gy (kJ/kg)
 𝑝𝑣= Flow ene gy pe uni mass (kJ/kg)
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Signi icance o Flow Ene gy
 Flow ene gy a ises only in open sys ems (con ol olumes) whe e mass c osses he
sys em bounda y.
 I ep esen s he wo k equi ed o push luid in o o ou o a sys em.
 In closed sys ems, no low ene gy exis s because he e is no mass ans e .
 Flow ene gy, combined wi h in e nal ene gy, gi es en halpy, which is ex ensi ely
used in analyzing s eady- low de ices such as u bines, comp esso s, nozzles, pumps,
boile s, and condense s.
Fi s Law o The modynamics o a Con ol Volume (Open Sys ems)
In many enginee ing applica ions, mass con inuously en e s and lea es a sys em. Such
sys ems a e bes analyzed using he concep o a con ol olume bounded by a con ol su ace.
The Fi s Law o The modynamics o a con ol olume combines he p inciples o
conse a ion o mass and conse a ion o ene gy o accoun o all o ms o ene gy ans e
ac oss he con ol su ace.
Fig. 1.22 Fi s law o open sys em.
Conse a ion o Ene gy
Ene gy may c oss he con ol su ace in wo o ms:
1. Hea ans e (Q)
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2. Wo k ans e (W)
Addi ionally, each uni o mass ha en e s o lea es he con ol olume ca ies ene gy in he
o m o :
 In e nal ene gy (𝑢)
 Flow ene gy (p )
 Kine ic ene gy (𝐶2
2)
 Po en ial ene gy (gz)
Thus, he gene al ene gy balance o a con ol olume is:
Ne ene gy c ossing bounda y as hea and wo k + Ene gy ca ied in by mass low -
Ene gy ca ied ou by mass low = Ne change in ene gy con en o he con ol olume
Conside ing a con ol olume wi h mass low ac oss i s bounda y (see Figu e), he ene gy
balance becomes:
𝑄˙−𝑊
˙+∑
in 𝑚˙in (ℎ+𝐶2
2+𝑔𝑧)−∑
ou 𝑚˙ou (ℎ+𝐶2
2+𝑔𝑧)=𝑑𝐸𝐶𝑉
𝑑𝑡
whe e,
 𝑄˙= Ra e o hea ans e o he con ol olume
 𝑊
˙= Ra e o wo k ans e om he con ol olume
 𝑚˙in ,𝑚˙ou = Mass low a es a inle and ou le
 ℎ=𝑢+𝑝𝑣= En halpy (includes in e nal + low ene gy)
 𝐶2
2= Kine ic ene gy pe uni mass
 𝑔𝑧= Po en ial ene gy pe uni mass
 𝑑𝐸𝐶𝑉
𝑑𝑡 = Ra e o change o o al ene gy wi hin he con ol olume
1.15 The S eady-S a e Flow P ocess
In enginee ing applica ions such as u bines, comp esso s, nozzles, boile s, and condense s,
mass and ene gy con inuously low in o and ou o he sys em. When ce ain condi ions a e
sa is ied, he low p ocess is e e ed o as a s eady-s a e low p ocess.
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Condi ions o S eady-S a e Flow
A p ocess is called a s eady low p ocess i :
1. The mass and ene gy con en o he con ol olume emain cons an wi h ime.
2. The s a e and ene gy o he luid a he inle , exi , and e e y poin inside he con ol
olume a e ime-independen .
3. The a e o ene gy ans e in he o m o hea and wo k ac oss he con ol su ace
emains cons an wi h ime.
These condi ions ensu e ha al hough mass and ene gy a e c ossing he sys em bounda y,
he p ope ies inside he con ol olume do no change wi h ime.
Applica ions o he S eady Flow Ene gy Equa ion (SFEE)
The S eady Flow Ene gy Equa ion (SFEE) go e ns he wo king o many he modynamic
de ices used in enginee ing applica ions. These de ices ope a e unde s eady- low
condi ions, whe e mass and ene gy con inuously c oss he sys em bounda y bu condi ions
inside emain cons an wi h ime.
Below is a summa y o he wo king p inciples and go e ning equa ions o key componen s:
1. Tu bines
Tu bines a e de ices used in s eam, gas, and hyd aulic powe plan s o p oduce wo k. As
he luid expands h ough he u bine, i ans e s ene gy o he blades, which o a e a sha
and gene a e mechanical wo k.
Fig. 1.23 Tu bines.
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51
Fo a cons an p essu e p ocess: 𝑑𝑝=0 ⇒ 𝛿𝑄=𝑑𝐻
Thus, 𝑑ℎ=𝐶𝑝𝑑𝑇
Hence, 𝐶𝑝 ela es he change in en halpy o he change in empe a u e.
Impo an Rela ions
1. Di e ence be ween speci ic hea s: 𝐶𝑝−𝐶𝑣=𝑅
whe e 𝑅= gas cons an .
2. Ra io o speci ic hea s (adiaba ic index):
𝛾=𝐶𝑝
𝐶𝑣
3. Since bo h en halpy (h) and in e nal ene gy (u) a e p ope ies:
𝑑ℎ=𝐶𝑝𝑑𝑇,𝑑𝑢=𝐶𝑣𝑑𝑇 ( alid o all p ocesses).
Wo k In e ac ion in a Re e sible S eady Flow P ocess
In a s eady low p ocess, he wo k in e ac ion pe uni mass be ween an open sys em (con ol
olume) and i s su oundings can be exp essed using he i s law o he modynamics in
di e en ial o m.
F om he ene gy balance o a s eady low p ocess:
𝛿𝑞−𝛿𝑤=𝑑ℎ+𝐶𝑑𝐶+𝑔𝑑𝑧
Rea anging o wo k: 𝛿𝑤=𝛿𝑞−(𝑑ℎ+𝐶𝑑𝐶+𝑔𝑑𝑧)
Also, we know: 𝛿𝑞=𝑑𝑢+𝑝𝑑𝑣 (o ) 𝛿𝑞=𝑑ℎ−𝑣𝑑𝑝

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Subs i u ing, 𝛿𝑤=𝑑ℎ−𝑣𝑑𝑝−(𝑑ℎ+𝐶𝑑𝐶+𝑔𝑑𝑧)
𝛿𝑤=−𝑣𝑑𝑝−(𝐶𝑑𝐶+𝑔𝑑𝑧)
Wo k Done in a P ocess
In eg a ing be ween s a es 1 and 2:
𝑊=−∫ 2
1𝑣𝑑𝑝−(𝐶22−𝐶12)
2−𝑔(𝑧2−𝑧1)
Special Case: S a iona y Sys em
Fo a s a iona y sys em (no change in eloci y o ele a ion):
𝑊=−∫ 2
1𝑣𝑑𝑝
1. The wo k in e ac ion in a s eady low p ocess depends on p essu e- olume changes
as well as changes in kine ic and po en ial ene gy.
2. Fo a s a iona y con ol olume wi h negligible kine ic and po en ial ene gy
a ia ions, he wo k educes simply o:
𝑊=−∫ 𝑣𝑑𝑝
which ep esen s he low wo k con ibu ion.
Fi s Law o an Open Sys em unde Uns eady Flow Condi ions
In many p ac ical enginee ing applica ions, he low o mass and ene gy in o and ou o a
sys em is uns eady, meaning he amoun o ene gy and mass wi hin he con ol olume a ies
wi h ime. Unlike s eady low sys ems, in uns eady low sys ems, he p ope ies o he sys em
a e no cons an o e ime.
Examples o Uns eady Flow P ocesses
1. Filling o closed anks wi h gas o liquid.
2. Discha ge o luid om closed essels.
3. Fluid low in ecip oca ing machines (e.g., comp esso s, pumps) du ing each cycle.
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Assump ions o Analysis
To de elop a ma hema ical model o such p ocesses, he ollowing assump ions a e made:
1. The con ol olume emains ixed ela i e o he coo dina e sys em.
2. The s a e o he mass wi hin he con ol olume may change wi h ime, bu a any
ins an , he s a e is uni o m h oughou he con ol olume.
3. The s a e o he mass c ossing each inle and ou le sec ion o he con ol su ace is
uni o m wi h espec o ime, e en hough he mass low a es may a y wi h ime.
Mass Balance o Uns eady Flow
Le he mass o luid inside he con ol olume a he beginning and end o a ime in e al Δ𝑡
be 𝑚1 and 𝑚2, espec i ely.
Applying conse a ion o mass:
(𝑚2−𝑚1)𝐶𝑉=Σ𝑚in −Σ𝑚ou
Whe e:
 Σ𝑚in = mass en e ing he con ol olume du ing Δ𝑡.
 Σ𝑚ou = mass lea ing he con ol olume du ing Δ𝑡.
Ene gy Balance o Uns eady Flow
Applying he i s law o he modynamics o he con ol olume:
[𝑄𝐶𝑉−𝑊𝐶𝑉]+∑
𝑖𝑛  𝑚𝑖𝑛[ℎ+𝐶2
2+𝑍𝑔]−∑
𝑜𝑢𝑡  𝑚𝑜𝑢𝑡[ℎ+𝐶2
2+𝑍𝑔]=Δ𝐸𝐶𝑉
Whe e:
 Δ𝐸𝐶𝑉= Change in ene gy o he con ol olume du ing Δ𝑡.
 𝑄𝐶𝑉= Hea ene gy ans e ed in o he con ol olume.
 𝑊𝐶𝑉= Wo k done by he con ol olume.
 ℎ= Speci ic en halpy o inle /ou le s eams.
 𝐶2
2= Speci ic kine ic ene gy o inle /ou le s eams.
 𝑍𝑔= Speci ic po en ial ene gy o inle /ou le s eams.
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Unlike s eady low, in uns eady low sys ems he ene gy and mass wi hin he con ol olume
a y wi h ime. The go e ning equa ion conside s bo h ansien accumula ion (o deple ion)
o ene gy and he ne ans e o ene gy associa ed wi h mass c ossing he bounda ies.
Such analysis is i al o s udying cha ging and discha ging o anks, s a -up and shu down
o u bines/comp esso s, and ecip oca ing machines.
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CHAPTER -2
SECOND LAW AND AVAILABILITY ANALYSIS
2.1 Hea Rese oi , sou ce and sink
A he mal ene gy ese oi is a hypo he ical concep used in he modynamics o ep esen
a body wi h a e y la ge hea capaci y. Because o his, i s empe a u e emains essen ially
cons an e en when a ini e amoun o hea is added o emo ed.
The hea capaci y (𝐶) o any ma e ial is de ined as:
𝐶=𝑚⋅𝑐
Whe e,
 𝑚= mass o he body
 𝑐= speci ic hea o he ma e ial
F om he i s law o he modynamics:
𝑄=𝑚𝑐Δ𝑇=𝐶Δ𝑇
Fo a ese oi , since 𝐶→∞, any ini e hea ans e 𝑄 esul s in Δ𝑇≈0. Hence, he
empe a u e o he ese oi is conside ed cons an .
Key No e: A he mal ene gy ese oi can in e ac wi h o he sys ems by supplying o
abso bing hea inde ini ely, wi hou expe iencing a measu able change in empe a u e.
Examples o The mal Ene gy Rese oi s
1. Na u al ese oi s: A mosphe e, oceans, la ge i e s, lakes, geo he mal bodies, and he
Sun.
2. Enginee ed ese oi s: La ge u naces, indus ial cooling ponds, powe plan condense s.
3. Phase-change sys ems: Mel ing ice, boiling wa e , o any ma e ial unde going a phase
change a cons an empe a u e. These ac as ese oi s because hey abso b o ejec la ge
amoun s o hea (la en hea ) wi hou empe a u e a ia ion.
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5. E e yday cases: E en smalle sys ems like he ai in a oom abso bing CPU hea can be
ea ed as a ese oi when i s empe a u e change is negligible compa ed o he p ocess unde
s udy.
Why Does he Rese oi ’s Tempe a u e No Va y?
In eali y, any body will expe ience some empe a u e change when hea ans e occu s.
Howe e , in he modynamics, a ese oi is ea ed as an idealized concep . This assump ion
simpli ies analysis by allowing sys ems o exchange hea wi h a cons an - empe a u e body.
1. Fo eal sys ems, sligh a ia ions occu .
2. Fo ideal analysis, we assume ΔT=0, ensu ing accu a e modeling o e e sible cycles like
he Ca no cycle.
Hea Sou ce and Hea Sink
 A hea sou ce is a high- empe a u e ese oi ha supplies ene gy in he o m o hea .
 A hea sink is a low- empe a u e ese oi ha abso bs he ejec ed hea .
No e: Bo h sou ce and sink a e essen ial o he unc ioning o he modynamic de ices. Hea
ans e always occu s om a sou ce a highe empe a u e o a sink a lowe empe a u e.
Applica ions in The modynamic Sys ems
1. Hea Engines (e.g., s eam engines, gas u bines, in e nal combus ion engines):
 Sou ce: Boile o combus ion chambe
 Sink: A mosphe e o condense
2. Re ige a o s & Hea Pumps:
 Sou ce: Cold space o e ige a ed chambe (low- empe a u e ese oi )
 Sink: Su oundings o a mosphe e (high- empe a u e ese oi )
3. Powe Plan s:
 Sou ce: S eam p oduced by bu ning coal, oil, o nuclea uel
 Sink: Cooling wa e om i e s, lakes, o cooling owe s
Wi hou bo h a sou ce and a sink, no cyclic he modynamic de ice can ope a e. I only one
ese oi exis ed, i would iola e he Second Law o The modynamics, which equi es hea
o low om a high- empe a u e body o a low- empe a u e body o p oduce wo k.

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2.2 Hea Engine
A hea engine is a de ice ha ope a es on a he modynamic cycle and p oduces use ul wo k
by ans e ing hea ene gy om a high- empe a u e ese oi o a low- empe a u e ese oi .
In his p ocess, pa o he hea supplied om he ho ese oi is con e ed in o wo k, while
he emaining po ion is ejec ed o he cold ese oi .
Examples o p ac ical hea engines include in e nal combus ion (I.C.) engines, s eam
engines, gas u bines, and boile s. Despi e di e ences in cons uc ion and ope a ion, all
hea engines wo k on he same undamen al p inciple: hea lows om a sou ce (ho
ese oi ) o a sink (cold ese oi ), and a ac ion o his ene gy is con e ed in o mechanical
wo k.
Gene al Rep esen a ion o a Hea Engine
A hea engine ypically in e ac s wi h h ee elemen s:
1. Ho ese oi (sou ce) a empe a u e 𝑇1, which supplies hea 𝑄1.
2. Wo king luid o sys em, which con e s pa o his hea in o wo k ou pu 𝑊.
3. Cold ese oi (sink) a empe a u e 𝑇2, which abso bs he ejec ed hea 𝑄2.
The schema ic diag am o a gene al hea engine is shown in Figu e 2.1.
Fig. 2.1 Hea Engine.
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58
Wo k and E iciency o a Hea Engine
The pe o mance o any hea engine is measu ed in e ms o i s he mal e iciency (𝜂), de ined
as he a io o ne wo k ou pu o he hea inpu supplied o he engine:
𝜂= Ne wo k ou pu
To al hea inpu =𝑊
𝑄1(2.1)
whe e,
 𝑊= Ne wo k p oduced by he engine
 𝑄1= Hea supplied om he ho ese oi a empe a u e 𝑇1
F om he ene gy balance o he cycle: 𝑊=𝑄1−𝑄2(2.2)
whe e,
 𝑄2= Hea ejec ed o he cold ese oi a empe a u e 𝑇2
Subs i u ing equa ion (2.2) in o (2.1), he e iciency becomes:
𝜂=𝑄1−𝑄2
𝑄1=1−𝑄2
𝑄1(2.3)
E iciency in Te ms o Rese oi Tempe a u es
Fo a e e sible hea engine (such as he Ca no engine), he hea ans e a ios a e di ec ly
ela ed o he absolu e empe a u es o he ese oi s:
𝑄2
𝑄1=𝑇2
𝑇1
Hence, he e iciency can be exp essed as:
𝜂=1−𝑇2
𝑇1(2.4)
whe e,
 𝑇1= Tempe a u e o ho ese oi
 𝑇2= Tempe a u e o cold ese oi
This shows ha he e iciency o a hea engine depends only on he empe a u es o he wo
ese oi s.
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59
Obse a ions:
1. E iciency is always less han uni y (η<1):
This means no engine can con e he en i e hea inpu in o wo k. A po ion o he ene gy
mus always be ejec ed o a sink, in acco dance wi h he Second Law o The modynamics.
2. Highe T1 and lowe T2 imp o e e iciency:
Inc easing he sou ce empe a u e o dec easing he sink empe a u e inc eases e iciency.
This is why powe plan s aim o achie e high boile empe a u es and use e icien cooling
sys ems o condense s.
3. Absolu e empe a u es mus be used:
The empe a u es T1 and T2 in he e iciency exp ession a e always measu ed in Kel in.
Signi icance o Hea Engine Analysis
P ac ical insigh : The analysis o hea engines highligh s he ine i able losses in eal sys ems
and he impossibili y o achie ing 100% e iciency.
Design objec i e: Enginee s aim o design sys ems ha ope a e as close as possible o he
Ca no e iciency, which se es as he heo e ical uppe limi .
Applica ions: Hea engine p inciples a e applied in au omo i e engines, ai c a p opulsion
sys ems, s eam and gas powe plan s, and o he ene gy con e sion de ices.
2.3 Re ige a o and I s Pe o mance
A e ige a o is a he modynamic de ice ha ope a es on a cyclic p ocess o emo e hea
om a low- empe a u e egion and ejec i o a high- empe a u e egion. I s main pu pose is
o main ain he empe a u e o a space o body lowe han ha o he su oundings.
In simple e ms, a e ige a o ex ac s hea om a cold ese oi ( he e ige a ed space) and
ejec s i o he wa me su oundings, wi h he aid o ex e nal wo k inpu .
Examples: Ai condi ione s, coole s, domes ic e ige a o s, and eeze s.
Wo king P inciple
As illus a ed in Figu e 2.2, he e ige a o ope a es be ween wo he mal ese oi s:
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1. Low- empe a u e ese oi ( he e ige a ed space), om which hea 𝑄4 is abso bed.
2. High- empe a u e ese oi (su oundings/a mosphe e), o which hea 𝑄3 is ejec ed.
An ex e nal wo k inpu 𝑊 is supplied o main ain he con inuous cycle o ope a ion.
Fig. 2.2 Re ige a o .
Coe icien o Pe o mance (COP) o a Re ige a o
Unlike a hea engine, whe e he measu e o pe o mance is he mal e iciency, he
pe o mance o a e ige a o is exp essed in e ms o he Coe icien o Pe o mance (COP).
The COP o a e ige a o is de ined as he a io o he hea ex ac ed om he low-
empe a u e ese oi o he ne wo k inpu equi ed:
COP e = Hea ex ac ed om cold ese oi
Wo k inpu
COP e =𝑄4
𝑊=𝑄4
𝑄3−𝑄4=𝑇4
𝑇3−𝑇4
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F om he abo e Figu e 2.4:
1. The impossible engine: A de ice ope a ing wi h a single ese oi , deli e ing all he
abso bed hea as wo k ( 𝑊=𝑄1 ), iola es he Kel in-Planck s a emen .
2. The possible engine: A eal engine abso bs hea 𝑄1 om a ho ese oi , con e s pa in o
wo k ( 𝑊=𝑄1−𝑄2), and ejec s he emainde 𝑄2 o a cold ese oi , he eby complying
wi h he second law.
2. Clausius S a emen
The Clausius s a emen may be exp essed as:
“I is impossible o cons uc a de ice ope a ing in a cycle ha p oduces no o he e ec
han he ans e o hea om a colde body o a ho e body.”
In simple e ms, hea canno low spon aneously om a cold ese oi o a ho ese oi
wi hou ex e nal assis ance. Howe e , hea can na u ally low in he opposi e di ec ion om
ho o cold wi hou any aid.
Implica ions:
 Re ige a o s and hea pumps, which ans e hea om low o high empe a u es,
equi e ex e nal wo k inpu o unc ion.
 A spon aneous ans e o hea om cold o ho would iola e he Clausius s a emen .
Fig. 2.5 Clausius S a emen .

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F om he abo e Figu e 2.5:
1. Possible sys em: Hea ans e om ho o cold ese oi wi hou ex e nal wo k is na u al
and allowed.
2. Impossible sys em: Di ec hea ans e om cold o ho ese oi wi hou ex e nal aid is
no possible.
3. Possible sys em wi h wo k inpu : Hea can be made o low om cold o ho ese oi
when assis ed by ex e nal wo k, as in e ige a o s o hea pumps.
Equi alence o he Two S a emen s
Al hough he Kel in–Planck and Clausius s a emen s appea di e en , hey a e equi alen
exp essions o he second law:
 A iola ion o he Kel in–Planck s a emen would imply he cons uc ion o a 100%
e icien hea engine, which could hen be used o d i e a e ige a o wi hou wo k
inpu , iola ing he Clausius s a emen .
 Simila ly, i he Clausius s a emen we e iola ed, a hea pump could ope a e wi hou
wo k inpu , leading o a hea engine wi h comple e con e sion o hea in o wo k,
iola ing he Kel in–Planck s a emen .
Thus, bo h s a emen s ein o ce he impossibili y o pe pe ual mo ion machines o he
second kind (PMM-II).
Signi icance o he Second Law
 I de ines he di ec ion o ene gy ans e p ocesses ( om ho o cold).
 I se s a limi on e iciency o cyclic de ices such as engines, e ige a o s, and hea
pumps.
 I emphasizes ha wo k is a highe -g ade ene gy o m han hea , as hea canno be
comple ely con e ed in o wo k.
Co olla ies o he Second Law o The modynamics
The Second Law o The modynamics es ablishes he di ec ion and limi a ions o ene gy
in e ac ions. Se e al impo an consequences, known as co olla ies, can be de i ed om he
second law wi h he help o e e sible cycles. These co olla ies p o ide deepe insigh s in o
he pe o mance o hea engines, e ige a o s, and hea pumps.
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Co olla y 1: Impossibili y o Hea T ans e om Cold o Ho wi hou Wo k Inpu
I is impossible o cons uc a sys em ha ope a es in a cycle and ans e s hea om a cold
body o a ho body wi hou any ex e nal wo k inpu .
P oo :
Fig. 2.6 Hea pump ope a ing wi h wo k inpu 𝑾=𝟎.
I his we e possible, he sys em would ac like a hea pump ope a ing wi h wo k inpu 𝑊=
0, as shown in Figu e 2.6. I i abso bs 𝑄4 uni s o hea om he cold ese oi , i mus deli e
he same amoun , 𝑄3=𝑄4, o he ho ese oi in o de o sa is y he i s law.
Now conside a hea engine ope a ing be ween he same wo ese oi s. The engine ecei es
𝑄1 uni s o hea om he ho ese oi , p oduces wo k 𝑊, and ejec s 𝑄2 o he cold ese oi .
I he ejec ed hea 𝑄2 is supplied o he hea pump as inpu , he cold ese oi becomes
unnecessa y. The combined sys em would hen ex ac (𝑄1) hea om he ho ese oi and
con e i en i ely in o wo k 𝑊, which is a iola ion o he Kel in-Planck s a emen .
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Hence, his p o es ha hea ans e om a cold o ho ese oi is impossible wi hou wo k
inpu , and Co olla y 1 is ue.
Co olla y 2: E iciency o an I e e sible Engine
No hea engine ope a ing be ween wo gi en hea ese oi s can be mo e e icien han a
e e sible engine wo king be ween he same empe a u e limi s.
This co olla y emphasizes ha e e sible cycles, such as he Ca no cycle, ep esen he
uppe limi o e iciency o any engine.
Co olla y 3: E iciency o Re e sible Engines
All e e sible engines ope a ing be ween he same wo hea ese oi s ha e he same
e iciency, ega dless o he wo king subs ance o cycle de ails.
This means he e iciency depends only on he empe a u es o he ese oi s and no on he
ype o sys em o medium.
Co olla y 4: Engines Ope a ing Be ween Mul iple Rese oi s
The e iciency o a e e sible engine ope a ing be ween mo e han wo ese oi s is always
less han he e iciency o a e e sible engine ope a ing be ween jus wo ese oi s a he
highes and lowes empe a u es o he wo king luid.
This s esses he impo ance o conside ing ex eme empe a u e limi s when e alua ing
pe o mance.
Co olla y 5: Cyclic In eg al o Hea - o-Tempe a u e Ra io
Whene e a sys em unde goes a he modynamic cycle:
∮ 𝛿𝑄
𝑇≤0
 Fo a e e sible cycle, ∮ 𝛿𝑄
𝑇=0
 Fo an i e e sible cycle, ∮ 𝛿𝑄
𝑇<0
This o ms he basis o he Clausius inequali y, which is undamen al o en opy analysis.
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Co olla y 6: En opy o a The mally Isola ed Sys em
The en opy o any closed sys em ha is he mally isola ed om i s su oundings emains
cons an . I he p ocess is e e sible, he en opy emains unchanged; howe e , i he p ocess
is i e e sible, he en opy inc eases.
This is he ounda ion o he p inciple o en opy inc ease.
Pe pe ual Mo ion Machine o he Second Kind (PMM-II)
A PMM-II is a hypo he ical machine ha ecei es hea ene gy om a single ho ese oi
and con e s i en i ely in o an equi alen amoun o wo k, i.e., i would ope a e wi h 100%
e iciency.
 Such a machine is impossible o cons uc because i di ec ly iola es he second law
o he modynamics.
 In o he wo ds, no cyclic de ice can con e all he hea supplied in o wo k
wi hou ejec ing some hea o a sink.
The concep o PMM-II clea ly illus a es he undamen al limi a ions o eal ene gy
con e sion sys ems.
Signi icance o Co olla ies
 They help es ablish he limi s o pe o mance o eal he modynamic de ices.
 They o m he basis o unde s anding en opy, i e e sibili y, and e iciency.
 They con i m he impossibili y o pe pe ual mo ion machines.
 They p o ide p ac ical guidelines in designing engines, e ige a o s, and hea pumps.
2.6 Ca no Cycle and I s Pe o mance
The Ca no cycle, in oduced by Sadi Ca no , is a heo e ical cycle ha se es as he ideal
s anda d o pe o mance o all hea engines. I is also known as he cons an empe a u e
cycle, as wo o i s p ocesses occu a cons an empe a u e.
The Ca no cycle consis s o ou e e sible p ocesses:
1. Two iso he mal (cons an empe a u e) p ocesses
2. Two isen opic ( e e sible adiaba ic) p ocesses
Since all ou p ocesses a e e e sible, he Ca no cycle is i sel a e e sible cycle. The p–V
and T–s diag ams o he Ca no cycle a e shown in Figu e 2.7.
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Fig. 2.7 Ca no cycle.
P ocesses o he Ca no Cycle
P ocess 1-2: Isen opic Comp ession
The wo king luid (ai o gas) is comp essed isen opically om s a e 1 o s a e 2. Du ing his
p ocess, p essu e and empe a u e inc ease om 𝑝1 o 𝑝2 and 𝑇1 o 𝑇2, while he olume
dec eases om 𝑉1 o 𝑉2.
Since he p ocess is isen opic, no hea is ans e ed, and he en opy emains cons an ( 𝑠1=
𝑠2 ).
P ocess 2-3: Iso he mal Hea Addi ion
The wo king luid abso bs hea 𝑄1 a a cons an high empe a u e 𝑇2=𝑇3. Du ing his
p ocess, bo h olume and en opy inc ease ( om 𝑉2 o 𝑉3, and 𝑠2 o 𝑠3 ), while p essu e
dec eases om 𝑝2 o 𝑝3.
Hea supplied: 𝑄1=𝑇3(𝑠3−𝑠2)
P ocess 3-4: Isen opic Expansion
The luid expands isen opically om s a e 3 o s a e 4. Bo h p essu e and empe a u e
dec ease om 𝑝3 o 𝑝4, and 𝑇3 o 𝑇4.
Since he p ocess is adiaba ic and e e sible, en opy emains cons an ( 𝑠3=𝑠4 ). Du ing
his s ep, he sys em pe o ms use ul wo k on he su oundings.

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P ocess 4-1: Iso he mal Hea Rejec ion
Hea is ejec ed a he cons an low empe a u e 𝑇1=𝑇4. Bo h olume and en opy dec ease
om 𝑉4 o 𝑉1, and 𝑠4 o 𝑠1, while p essu e also dec eases.
Hea ejec ed: 𝑄2=𝑇1(𝑠4−𝑠1)
The sys em hen e u ns o i s ini ial s a e, comple ing one ull he modynamic cycle.
Wo k and E iciency o Ca no Cycle
The ne wo k done du ing he cycle is he di e ence be ween he hea abso bed and he hea
ejec ed: 𝑊=𝑄1−𝑄2
The he mal e iciency o he Ca no engine is:
𝜂=𝑊
𝑄1=1−𝑄2
𝑄1
Since hea ans e s in e e sible iso he mal p ocesses a e di ec ly p opo ional o absolu e
empe a u es: 𝑄2
𝑄1=𝑇1
𝑇2
The e o e,
𝜂Ca no =1−𝑇1
𝑇2
whe e:
 𝑇1= Tempe a u e o cold ese oi (minimum empe a u e)
 𝑇2= Tempe a u e o ho ese oi (maximum empe a u e)
Key Fea u es o he Ca no Cycle
1. Re e sibili y: Since all p ocesses a e e e sible, he Ca no cycle ep esen s he uppe
limi o pe o mance o any hea engine.
2. Maximum E iciency: The e iciency depends only on he empe a u e limi s o he
ese oi s, no on he wo king luid o sys em design.
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74
3. Ideal S anda d: No eal engine can exceed he Ca no e iciency; a bes , eal engines
can only app oach i .
4. Benchma king: The Ca no cycle p o ides a e e ence o e alua e ac ual cycles like
O o, Diesel, Rankine, and B ay on cycles.
Signi icance o Ca no Cycle
Es ablishes he heo e ical uppe bound on e iciency o all hea engines. Demons a es he
impo ance o empe a u e di e ence be ween ese oi s: highe T2 o lowe T1 imp o es
e iciency.
Fo ms he basis o he Ca no Theo em, which s a es: No engine ope a ing be ween wo
ese oi s can be mo e e icien han a Ca no engine ope a ing be ween he same ese oi s.
2.7 Re e sed Ca no Cycle and I s Pe o mance
Since all he p ocesses in he Ca no cycle a e e e sible, he cycle can be ope a ed in e e se.
When e e sed, i is called he Re e sed Ca no Cycle, which o ms he heo e ical basis o
e ige a o s and hea pumps.
 In e ige a ion mode, he cycle ex ac s hea om a low- empe a u e body (cold
ese oi ) and ejec s i o a high- empe a u e body (su oundings).
 In hea pump mode, he cycle ex ac s hea om he su oundings (cold ese oi )
and deli e s i o a wa me space (ho ese oi ) o main ain com o able indoo
condi ions.
The cycle consis s o wo iso he mal p ocesses and wo isen opic p ocesses, and i s p–V
and T–s diag ams a e shown in Figu e 2.8.
P ocesses o he Re e sed Ca no Cycle
P ocess 1-2: Isen opic Comp ession (Comp esso )
The wo king luid is comp essed isen opically om s a e 1 o s a e 2. P essu e and
empe a u e bo h inc ease, while en opy emains cons an ( 𝑠1=𝑠2 ). Wo k inpu is equi ed
o his s ep.
P ocess 2-3: Iso he mal Hea Rejec ion (Condense )
A cons an high empe a u e 𝑇3, hea is ejec ed o he ho ese oi (a mosphe e). P essu e
emains cons an while en opy dec eases om 𝑠2 o 𝑠3.
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75
Hea ejec ed: 𝑄3=𝑇3(𝑠2−𝑠3)
Fig. 2.8 Re e sed ca no cycle.
P ocess 3-4: Isen opic Expansion (Expansion Val e/De ice)
The wo king luid expands isen opically om s a e 3 o s a e 4. P essu e and empe a u e
dec ease, while en opy emains cons an ( 𝑠3=𝑠4 ).
P ocess 4-1: Iso he mal Hea Abso p ion (E apo a o )
A cons an low empe a u e 𝑇4, hea is abso bed om he cold ese oi . En opy inc eases
om 𝑠4 o 𝑠1.
Hea abso bed (use ul e ec o e ige a ion):
𝑄4=𝑇4(𝑠1−𝑠4)
The luid hen e u ns o i s ini ial s a e, comple ing one cycle.
Wo k and COP o he Re e sed Ca no Cycle
The ne wo k inpu is he di e ence be ween hea ejec ed and hea abso bed:
𝑊=𝑄3−𝑄4=(𝑇3−𝑇4)(𝑠1−𝑠4)
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Coe icien o Pe o mance (COP) o Re ige a o
The pe o mance o a e ige a o is exp essed by COP, de ined as:
COPRe = Hea abso bed om cold body
Wo k inpu
COPRe =𝑄4
𝑊=𝑇4
𝑇3−𝑇4
whe e:
 𝑇3= High empe a u e (ho ese oi )
 𝑇4= Low empe a u e (cold ese oi )
Thus, COP o a e ige a o depends only on he empe a u e limi s.
Coe icien o Pe o mance (COP) o Hea Pump
When ope a ed as a hea pump, he use ul e ec is he hea ejec ed o he high- empe a u e
ese oi :
COP𝐻𝑃= Hea deli e ed o ho body
Wo k inpu
COP𝐻𝑃 =𝑄3
𝑊=𝑇3
𝑇3−𝑇4
Rela ion be ween COP o Re ige a o and Hea Pump
Fo he same empe a u e limi s, COP𝐻𝑃=COP𝑅𝑒𝑓+1
This shows ha a hea pump always has a COP g ea e han ha o a e ige a o ope a ing
be ween he same ese oi s.
Signi icance o Re e sed Ca no Cycle
1. P o ides he ideal s anda d o pe o mance o all e ige a o s and hea pumps.
2. Demons a es ha COP depends only on he empe a u e limi s (𝑇3,𝑇4) and no on he
wo king luid.
3. Shows ha highe COP is ob ained when he empe a u e di e ence be ween
ese oi s is smalle .
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 In Figu e 2.10 (b), a p ocess be ween s a es 1 and 2 is shown. The shaded a ea unde
he cu e 1→2 co esponds o he hea ans e ed du ing he p ocess:
𝑄1−2, e =A ea(1−2−𝑠2−𝑠1−1)
Thus, he T-s diag am p o ides a di ec and con enien means o measu ing and isualizing
hea ans e in e e sible p ocesses.
Special Fea u es
1. Isen opic P ocesses: Shown as e ical lines (s=cons an s).
2. Iso he mal P ocesses: Shown as ho izon al lines (T=cons an ).
3. Re e sible Hea T ans e : A ea unde he cu e di ec ly gi es he hea ans e ed.
4. I e e sible P ocesses: De ia ions om ideal e ical/ho izon al lines highligh losses and
en opy gene a ion.
Applica ions o T–s Diag am
1. Hea T ans e E alua ion:
 Since hea ans e equals he a ea unde he cu e, T–s diag ams allow enginee s o
e alua e hea in e ac ions wi hou sol ing complex equa ions.
2. Cycle Rep esen a ion:
 The modynamic cycles (such as Ca no , Rankine, O o, Diesel, and B ay on cycles)
a e o en ep esen ed on T–s diag ams.
 The enclosed a ea in a cycle on a T–s diag am co esponds o he ne wo k ou pu o
he cycle.
3. En opy Change Visualiza ion:
 En opy changes a e ep esen ed as ho izon al displacemen s along he sss-axis.
 Isen opic p ocesses appea as e ical lines (cons an en opy).
 Iso he mal p ocesses appea as ho izon al lines (cons an empe a u e).
4. Pe o mance Analysis:
 In powe plan s and e ige a ion sys ems, T–s diag ams help in iden i ying
i e e sibili ies, ene gy losses, and e iciency imp o emen s.

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2.11 En opy Rela ions: Tds Equa ions
En opy (s) is a he modynamic p ope y ha can be exp essed as a unc ion o di e en se s
o independen a iables such as empe a u e (T), p essu e (p), and speci ic olume ( ). The
ela ionships be ween en opy and hese a iables lead o he well-known Tds equa ions,
which a e undamen al in he modynamics.
These equa ions a e de i ed using he i s and second laws o he modynamics, along wi h
Maxwell ela ions.
En opy as a Func ion o 𝑇 and 𝑝
Conside en opy exp essed as: 𝑠=𝑓(𝑇,𝑝)
The o al di e en ial is:
𝑑𝑠=(𝜕𝑠
𝜕𝑇)𝑝𝑑𝑇+(𝜕𝑠
𝜕𝑝)𝑇𝑑𝑝
F om he de ini ion o speci ic hea a cons an p essu e:
𝐶𝑝=𝑇(𝜕𝑠
𝜕𝑇)𝑝⇒(𝜕𝑠
𝜕𝑇)𝑝=𝐶𝑝
𝑇
F om Maxwell's ela ion:
(𝜕𝑠
𝜕𝑝)𝑇=−(𝜕𝑣
𝜕𝑇)𝑝
Subs i u ing hese in o he di e en ial en opy exp ession:
𝑑𝑠=𝐶𝑝
𝑇𝑑𝑇−(𝜕𝑣
𝜕𝑇)𝑝𝑑𝑝
Mul iplying h ough by :
𝑇𝑑𝑠=𝐶𝑝𝑑𝑇−𝑇(𝜕𝑣
𝜕𝑇)𝑝𝑑𝑝
This is known as he Fi s Tds Equa ion o Fi s Fo m o he En opy Equa ion.
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En opy as a Func ion o 𝑇 and 𝑣
Now conside en opy as a unc ion o empe a u e and speci ic olume:
𝑠=𝑓(𝑇,𝑣)
The o al di e en ial is:
𝑑𝑠=(𝜕𝑠
𝜕𝑇)𝑣𝑑𝑇+(𝜕𝑠
𝜕𝑣)𝑇𝑑𝑣
F om he de ini ion o speci ic hea a cons an olume:
𝐶𝑣=𝑇(𝜕𝑠
𝜕𝑇)𝑣⇒(𝜕𝑠
𝜕𝑇)𝑣=𝐶𝑣
𝑇
F om Maxwell's ela ion:
(𝜕𝑠
𝜕𝑣)𝑇=(𝜕𝑝
𝜕𝑇)𝑣
Subs i u ing in o he en opy exp ession:
𝑑𝑠=𝐶𝑣
𝑇𝑑𝑇+(𝜕𝑝
𝜕𝑇)𝑣𝑑𝑣
Mul iplying h ough by :
𝑇𝑑𝑠=𝐶𝑣𝑑𝑇+𝑇(𝜕𝑝
𝜕𝑇)𝑣𝑑𝑣
This is known as he Second Tds Equa ion o Second Fo m o he En opy Equa ion.
En opy as a Func ion o 𝑝 and 𝑣
En opy can also be exp essed as a unc ion o p essu e and speci ic olume:
𝑠=𝑓(𝑝,𝑣)
The o al di e en ial is:
𝑑𝑠=(𝜕𝑠
𝜕𝑝)𝑣𝑑𝑝+(𝜕𝑠
𝜕𝑣)𝑝𝑑𝑣
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Mul iplying h ough by :
𝑇𝑑𝑠=𝑇(𝜕𝑠
𝜕𝑝)𝑣𝑑𝑝+𝑇(𝜕𝑠
𝜕𝑣)𝑝𝑑𝑣
F om Maxwell ela ions,
(𝜕𝑠
𝜕𝑣)𝑝=(𝜕𝑝
𝜕𝑇)𝑣,(𝜕𝑠
𝜕𝑝)𝑣=−(𝜕𝑣
𝜕𝑇)𝑝
By combining hese ela ionships and applying he modynamic iden i ies, one can simpli y
and de i e al e na i e use ul o ms.
Applica ions o Tds Equa ions
1. En opy Change Calcula ions: Use ul o e alua ing en opy changes in p ocesses
in ol ing ideal gases, eal gases, and apo s.
2. The modynamic P ope y Rela ions: P o ide links be ween measu able p ope ies
(T,p, ) and en opy.
3. Cycle Analysis: Widely applied in analyzing powe cycles (Rankine, B ay on) and
e ige a ion cycles.
4. I e e sibili y Measu emen : Help in en opy gene a ion s udies and e iciency
e alua ions.
2.12 En opy Change o Ideal Gas
En opy is a key he modynamic p ope y ha helps measu e he i e e sibili y o p ocesses
and he a ailabili y o ene gy o doing use ul wo k. Fo an ideal gas, en opy change can
be de i ed om he i s law o he modynamics and exp essed in e ms o measu able
p ope ies like empe a u e, p essu e, and olume.
Conside an ideal gas being hea ed om s a e 1 o s a e 2, wi h i s empe a u e ising om 𝑇1
o 𝑇2, as shown in Figu e 2.11.
Fo a e e sible p ocess:
𝑑𝑠=𝛿𝑄𝑟𝑒𝑣
𝑇
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F om he Fi s Law o The modynamics:
𝛿𝑄=𝑑𝑈+𝛿𝑊=𝑚𝐶𝑣𝑑𝑇+𝑝𝑑𝑉
Fig. 2.11 An ideal gas being hea ed om s a e 1 o s a e 2, wi h i s empe a u e ising
om 𝑻𝟏 o 𝑻𝟐.
Since o an ideal gas, 𝑝𝑉=𝑚𝑅𝑇, we can w i e:
𝛿𝑄
𝑇 =𝑚𝐶𝑣𝑑𝑇
𝑇+𝑝𝑑𝑉
𝑇
𝑑𝑆 =𝑚𝐶𝑣𝑑𝑇
𝑇+𝑚𝑅𝑑𝑉
𝑉
In eg a ing be ween s a es 1 and 2:
Δ𝑆=𝑆2−𝑆1=𝑚𝐶𝑣ln (𝑇2
𝑇1)+𝑚𝑅ln (𝑉2
𝑉1)
This is he gene al en opy change exp ession in e ms o empe a u e and olume.
En opy Change in Te ms o Tempe a u e and P essu e
F om he ideal gas equa ion: 𝑝1𝑉1
𝑇1=𝑝2𝑉2
𝑇2
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88
Rea anging, 𝑉2
𝑉1=𝑝1
𝑝2⋅𝑇2
𝑇1
Subs i u ing his in o he gene al en opy exp ession:
Δ𝑆=𝑚𝐶𝑣ln (𝑇2
𝑇1)+𝑚𝑅ln (𝑝1
𝑝2⋅𝑇2
𝑇1)
Simpli ying:
Δ𝑆=𝑚𝐶𝑝ln (𝑇2
𝑇1)−𝑚𝑅ln (𝑝2
𝑝1)
Thus, en opy change in e ms o empe a u e and p essu e is:
Δ𝑆=𝑚𝐶𝑝ln (𝑇2
𝑇1)+𝑚𝑅ln (𝑝1
𝑝2)
En opy Change in Te ms o P essu e and Volume
F om he ideal gas law: 𝑝1𝑉1
𝑇1=𝑝2𝑉2
𝑇2
Rea anging: 𝑇2
𝑇1=𝑝2
𝑝1⋅𝑉2
𝑉1
Subs i u ing his in o he gene al en opy exp ession:
Δ𝑆=𝑚𝑅ln (𝑉2
𝑉1)+𝑚𝐶𝑣ln (𝑝2
𝑝1⋅𝑉2
𝑉1)
Simpli ying:
Δ𝑆=𝑚𝐶𝑝ln(𝑉2
𝑉1)+𝑚𝐶𝑣ln(𝑝2
𝑝1)

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89
Key Obse a ions
1. The en opy change o an ideal gas depends only on i s end s a es (since en opy is a
p ope y) and no on he pa h aken.
2. En opy inc eases when he gas is hea ed o expanded.
3. Fo e e sible adiaba ic p ocesses, en opy emains cons an (ΔS=0).
4. These exp essions a e ex emely use ul in cycle analysis (O o, Diesel, Rankine, and
e ige a ion cycles).
2.13 En opy Change o Di e en P ocesses
1. En opy Change in Cons an Volume P ocess
A he modynamic p ocess in which he olume emains cons an h oughou is known as a
cons an olume p ocess o isocho ic p ocess. Since he e is no change in olume, he wo k
done by he sys em is ze o ( 𝑊=𝑝Δ𝑉=0 ). The hea supplied o he sys em is he e o e
en i ely used o inc ease he in e nal ene gy.
A sys em unde going a cons an olume p ocess om s a e 1 o s a e 2 is shown in he 𝐩−𝐕
and 𝐓−𝐬 diag ams in Figu e 2.12.
Fig. 2.12 Cons an olume p ocess.
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90
En opy Change De i a ion
F om he gene al en opy change exp ession o an ideal gas:
Δ𝑆=𝑚𝑅ln (𝑉2
𝑉1)+𝑚𝐶𝑣ln (𝑇2
𝑇1)
Fo a cons an olume p ocess:
𝑉1=𝑉2⇒ln (𝑉2
𝑉1)=0
Thus, en opy change educes o:
Δ𝑆=𝑚𝐶𝑣ln (𝑇2
𝑇1)
Since o an ideal gas, 𝑇2
𝑇1=𝑝2
𝑝1
he en opy change can also be exp essed as:
Δ𝑆=𝑚𝐶𝑣ln (𝑝2
𝑝1)
G aphical Rep esen a ion
 p-V Diag am (Figu e 2.12a): The p ocess is ep esen ed by a e ical line since
olume is cons an while p essu e dec eases om 𝑝1 o 𝑝2.
 T-s Diag am (Figu e 2.12b): The p ocess appea s as a cu e ising om 𝑇1 o 𝑇2. The
a ea unde he cu e be ween en opies 𝑠1 and 𝑠2 ep esen s he hea ans e du ing
he p ocess.
Key Fea u es o Cons an Volume P ocess
1. Wo k Done: 𝑊=∫ 𝑝𝑑𝑉=0
No wo k is done since olume emains ixed.
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91
2. Hea T ans e : 𝑄=Δ𝑈=𝑚𝐶𝑣(𝑇2−𝑇1)
The hea supplied is comple ely u ilized in aising he in e nal ene gy.
3. En opy Change:
Δ𝑆=𝑚𝐶𝑣ln (𝑇2
𝑇1)=𝑚𝐶𝑣ln (𝑝2
𝑝1)
4. P ac ical Applica ion:
 This p ocess occu s du ing he comp ession and expansion in closed combus ion
chambe s (e.g., spa k igni ion engines du ing combus ion).
 Use ul o analyzing cons an - olume hea addi ion in he O o cycle.
2. En opy Change in Cons an P essu e P ocess
A he modynamic p ocess in which he p essu e emains cons an h oughou is known as a
cons an p essu e p ocess o isoba ic p ocess. In his case, he sys em unde goes a change in
olume and empe a u e while main aining cons an p essu e. Such p ocesses a e e y
common in p ac ical he modynamic cycles- o example, in boile s whe e hea is supplied a
cons an p essu e.
A sys em unde going a cons an p essu e p ocess om s a e 1 o s a e 2 is ep esen ed in he
𝐩−𝐕 and 𝐓−𝐬 diag ams shown in Figu e 2.13.
Fig. 2.13 Cons an p essu e p ocess.
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92
En opy Change De i a ion
F om he gene al en opy change exp ession o an ideal gas:
Δ𝑆=𝑚𝑅ln (𝑉2
𝑉1)+𝑚𝐶𝑣ln (𝑇2
𝑇1)
Fo a cons an p essu e p ocess, he ela ion be ween empe a u e and olume is:
𝑇2
𝑇1=𝑉2
𝑉1
Subs i u ing in o he abo e equa ion:
Δ𝑆=𝑚(𝐶𝑝−𝐶𝑣)ln (𝑉2
𝑉1)+𝑚𝐶𝑣ln (𝑉2
𝑉1)
Δ𝑆=𝑚𝐶𝑝ln (𝑉2
𝑉1)
Since a cons an p essu e 𝑉2
𝑉1=𝑇2
𝑇1,
Δ𝑆=𝑚𝐶𝑝ln (𝑇2
𝑇1)
Thus, en opy change in a cons an p essu e p ocess depends only on he a io o inal o ini ial
empe a u es.
G aphical Rep esen a ion
 p-V Diag am (Figu e 2.13a): The p ocess appea s as a ho izon al line since p essu e
emains cons an while olume inc eases om 𝑉1 o 𝑉2. The a ea unde his line
ep esen s he wo k done du ing he p ocess.
 T-s Diag am (Figu e 2.13b): The p ocess is ep esen ed by a ising cu e om 𝑇1 o
𝑇2, wi h en opy inc easing om 𝑠1 o 𝑠2. The shaded a ea unde he cu e gi es he
hea ans e o he sys em.
Key Fea u es o Cons an P essu e P ocess
1. Wo k Done: 𝑊=𝑝(𝑉2−𝑉1)
The wo k is equal o he p oduc o cons an p essu e and change in olume.
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99
Di iding h ough by empe a u e :
𝑑𝑆=(𝛾−𝑛
𝛾−1)𝑚𝑅𝑑𝑉
𝑉
In eg a ing om s a e 1 o s a e 2 gi es:
𝑆2−𝑆1=(𝛾−𝑛
𝛾−1)𝑚𝑅ln (𝑉2
𝑉1)
This is one o he s anda d en opy ela ions o a poly opic p ocess.
Al e na i e De i a ions
Using gas laws and he modynamic iden i ies, he change in en opy can also be w i en as:
𝑑𝑆=𝑚[𝛾−𝑛
𝛾−1]𝐶𝑣ln (𝑝1
𝑝2)
O ,
𝑑𝑆=𝑚𝐶𝑣(𝛾−𝑛)
𝑛ln (𝑝1
𝑝2)
These al e na i e exp essions a e use ul in cases whe e p essu e and olume a e known
ins ead o empe a u e.
G aphical Rep esen a ion
Fig. 2.16 Poly opic p ocess.

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100
 p-V diag am: Shows a cu ed pa h depending on he alue o 𝑛. Fo 𝑛=1, i educes
o an iso he mal p ocess; o 𝑛=𝛾, i becomes an adiaba ic p ocess.
 T-s diag am: Illus a es ha en opy inc eases when hea is abso bed and dec eases
when hea is ejec ed.
Special Cases o Poly opic Index
 𝑛=0 : Cons an p essu e p ocess
 𝑛=1 : Iso he mal p ocess
 𝑛=𝛾 : Re e sible adiaba ic (isen opic) p ocess
 𝑛=∞ : Cons an olume p ocess
Thus, he poly opic p ocess se es as a gene alized o m o he modynamic p ocesses,
making i an essen ial ool in he analysis o p ac ical cycles like comp esso s, u bines, and
engines.
2.14 P inciple o inc ease in en opy
The concep o en opy is cen al o he second law o he modynamics. Fo a e e sible
p ocess, he change in en opy is gi en by:
𝑑𝑠=𝑑𝑄
𝑇
This ela ion indica es ha en opy change can be di ec ly e alua ed om he hea ans e a
a gi en absolu e empe a u e. Howe e , in eal sys ems, p ocesses a e no always e e sible.
The e o e, i is essen ial o ex end he p inciple o i e e sible p ocesses.
En opy in I e e sible P ocesses
Conside a he modynamic sys em unde going a change o s a e om poin 1 o poin 2 by a
e e sible p ocess ( 1−A−2 ), and hen e u ning o s a e 1 ei he h ough an in e nally
e e sible p ocess ( 2−B−1 ) o h ough an i e e sible p ocess (2-C-1), as illus a ed in
Figu e 2.17.
Fo he e e sible cycle 1-A-2-B-1, he Clausius equali y applies:
∫
2𝐴
1𝐴  𝑑𝑄
𝑇+∫
1𝐵
2𝐵  𝑑𝑄
𝑇=0 (2.5)
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101
Fig. 2.17 En opy in i e e sible p ocess.
Fo he i e e sible cycle 1-A-2-C-1, he Clausius inequali y holds:
∫
2𝐴
1𝐴  𝑑𝑄
𝑇+∫
1𝐶
2𝐶  𝑑𝑄
𝑇≤0 (2.6)
De i a ion o En opy Inequali y
Sub ac ing equa ion (2.5) om (2.6), we ge :
∫
1𝐶
2𝐶  𝑑𝑄
𝑇−∫
1𝐵
2𝐵  𝑑𝑄
𝑇≤0 (2.7)
Re e sing limi s and ea anging:
∫
2𝐶
1𝐶  𝑑𝑄
𝑇≥∫
2𝐵
1𝐵  𝑑𝑄
𝑇(2.8)
Since he pa h 2−𝐵−1 is e e sible, he en opy change along i can be w i en as:
𝑑𝑠=𝑑𝑄
𝑇
Subs i u ing in o equa ion (2.8):
∫ 2
1𝑑𝑠≥∫
2𝐶
1𝐶 𝑑𝑄
𝑇
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102
o
𝑑𝑠≥𝑑𝑄
𝑇(2.9)
In e p e a ion o he P inciple
Equa ion (2.9) es ablishes he P inciple o Inc ease o En opy, which s a es:
 Fo a e e sible p ocess, 𝑑𝑠=𝑑𝑄
𝑇
 Fo an i e e sible p ocess, 𝑑𝑠>𝑑𝑄
𝑇
 Fo an impossible p ocess, 𝑑𝑠<𝑑𝑄
𝑇
This p inciple implies ha i e e sibili y always inc eases en opy in a sys em. In o he wo ds,
en opy is a measu e o ene gy deg ada ion o he endency o sys ems o mo e owa d
diso de .
En opy o an Isola ed Sys em
Fo an isola ed sys em, no hea o mass in e ac ion occu s wi h he su oundings. The e o e:
𝑑𝑆≥0
 I he p ocess is e e sible, en opy emains cons an .
 I he p ocess is i e e sible, en opy inc eases.
 En opy can ne e dec ease in an isola ed sys em.
2.15 Applica ions o II Law: A ailable Ene gy and Una ailable
Ene gy
A ailable Ene gy (A.E.)
A ailable ene gy is de ined as he po ion o he ene gy supplied as hea ha can be e ec i ely
con e ed in o use ul wo k by a e e sible engine. In he modynamics, his concep plays a
c ucial ole in de e mining he p ac ical u iliza ion o hea ene gy.
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103
Conside a Ca no engine ope a ing be ween he empe a u e limi s 𝑇1 and 𝑇2, as illus a ed
in Figu e 2.18. Acco ding o he second law o he modynamics, he ec angula a ea 1−2−
3−4 on he T−s diag am ep esen s he use ul ene gy. Howe e , he a ea 2−3−5−6
co esponds o he ene gy los o he su oundings due o i e e sibili ies, such as ic ion,
u bulence, and o he uncon ollable ac o s.
Fig. 2.18 T-s diag am.
The p ima y objec i e o enginee ing design is o minimize hese ene gy losses. One e ec i e
me hod is o educe he empe a u e o hea ejec ion, 𝑇2, close o he ambien o su ounding
empe a u e 𝑇0. As he ejec ion empe a u e dec eases, he use ul ene gy ha can be
con e ed in o wo k inc eases, he eby educing he unp oduc i e ene gy loss.
I is impo an o no e ha , as pe he Ca no heo em, no eal o ideal engine can e e su pass
he e iciency o a Ca no engine ope a ing be ween he same empe a u e limi s. This ac
es ablishes he heo e ical bounda y o he con e sion o a ailable ene gy in o wo k.
The e iciency o he Ca no engine is gi en by:
𝜂max=1−𝑇2
𝑇1
Thus, he use ul ene gy ou pu becomes:
𝑊=(1−𝑇2
𝑇1)𝑄
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104
Fo a ailable ene gy:
𝐴.𝐸=(1−𝑇0
𝑇1)𝑄
whe e 𝑇0 is he empe a u e o he su oundings.
By he en opy p inciple:
Δ𝑆=𝑄
𝑇0
Hence, 𝐴.𝐸=𝑄−𝑇0Δ𝑆
Una ailable Ene gy (U.A.E.)
Una ailable ene gy is de ined as he po ion o he ene gy supplied as hea ha canno be
con e ed in o use ul wo k. This loss is una oidable because o i e e sibili ies such as
ic ion, hea ans e ac oss ini e empe a u e di e ences, and en opy gene a ion.
Ma hema ically, una ailable ene gy is exp essed as:
𝑈⋅𝐴⋅𝐸=𝑄−𝐴⋅𝐸
Subs i u ing he ela ion o a ailable ene gy:
𝑈⋅𝐴⋅𝐸=𝑄−[𝑄−𝑇0Δ𝑆]
𝑈⋅𝐴⋅𝐸=𝑇0Δ𝑆
Thus, he una ailable ene gy is di ec ly ela ed o en opy gene a ion and he su ounding
empe a u e.
No e:
Una ailable ene gy can also be iewed as:
 The loss in a ailable ene gy,
 A measu e o i e e sibili y, o
 The consequence o he p inciple o en opy gene a ion.

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105
Dec ease in A ailable Ene gy Th ough a Fini e Tempe a u e Di e ence
In p ac ical hea ans e p ocesses, ene gy is seldom ans e ed a an in ini esimal
empe a u e di e ence. Ins ead, hea lows h ough a ini e empe a u e di e ence, which
ine i ably esul s in a loss o a ailable ene gy. This concep can be illus a ed using he T-s
diag am shown in Figu e 2.19.
Fig. 2.19 T-s diag am.
Ideal Case: Re e sible Hea T ans e
Conside a e e sible hea engine ope a ing be ween a high- empe a u e ese oi a 𝑇1 and a
low empe a u e ese oi a 𝑇0.
 Hea supplied om he sou ce: 𝑄1=𝑇1Δ𝑆
 Hea ejec ed o he sink: 𝑄2=𝑇0Δ𝑆
 Wo k ou pu , which ep esen s he a ailable ene gy (A.E.):
𝑊=𝑄1−𝑄2=(𝑇1−𝑇0)Δ𝑆
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106
In his ideal case, he wo k ou pu is maximized because he p ocess is ully e e sible, and
he e a e no losses due o ini e empe a u e g adien s.
P ac ical Case: Hea T ans e Th ough a Fini e Tempe a u e Di e ence
In eali y, when hea 𝑄1 is ans e ed o he hea engine, i does no each he engine a he
ese oi empe a u e 𝑇1. Ins ead, due o ini e empe a u e esis ance, he e ec i e
empe a u e a which he hea en e s he engine is sligh ly lowe , deno ed as 𝑇1′. The high-
empe a u e ese oi emains a 𝑇1, bu he wo king luid o he engine ecei es hea a 𝑇1′.
 Hea supplied o he engine: 𝑄1′=𝑇1Δ𝑆=𝑇1′Δ𝑆′
 Hea ejec ed o he sink a 𝑇0 : 𝑄2′=𝑇0Δ𝑆′
 Ac ual wo k ou pu : 𝑊′=𝑄1′−𝑄2′=(𝑇1′−𝑇0)Δ𝑆′
Clea ly, he ac ual wo k 𝑊′ is less han he ideal wo k 𝑊, since 𝑇1′<𝑇1 and Δ𝑆′>Δ𝑆.
Dec ease in A ailable Ene gy
The dec ease in a ailable ene gy is caused by he excess hea ejec ed o he sink:
Δ𝑊=𝑊−𝑊′=𝑄2′−𝑄2
Thus, he loss in a ailable ene gy di ec ly depends on he di e ence be ween 𝑇1 and 𝑇1′.
 I he empe a u e di e ence ( 𝑇1−𝑇1′ ) is small, he dec ease in a ailable ene gy is
minimal.
 I he empe a u e di e ence is la ge, he dec ease in a ailable ene gy becomes
signi ican .
2.16 Concep o I e e sibili y (I)
In he modynamics, i e e sibili y is a measu e o he loss o wo k po en ial in a p ocess due
o he p esence o non-ideali ies such as ic ion, un es ained expansion, mixing o di e en
subs ances, hea ans e h ough a ini e empe a u e di e ence, and o he dissipa i e e ec s.
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107
I can be o mally de ined as he di e ence be ween he maximum possible wo k ( e e sible
wo k) and he ac ual wo k ob ained in a eal p ocess.
𝐼=𝑊max−𝑊ac
Whe e:
 𝑊max = Maximum wo k ob ainable i he p ocess we e comple ely e e sible.
 𝑊ac = Ac ual wo k ob ained in he eal, i e e sible p ocess.
Exp ession o I e e sibili y
By applying he second law o he modynamics, i e e sibili y can also be exp essed in e ms
o en opy gene a ion. Fo a p ocess ha exchanges hea wi h su oundings a ambien
empe a u e 𝑇0 : 𝐼=𝑇0Δ𝑆
He e,
 𝑇0 is he empe a u e o he su oundings (dead s a e),
 Δ𝑆 is he en opy gene a ed du ing he p ocess.
Thus, i e e sibili y quan i ies he ene gy los o he su oundings ha canno be con e ed
in o use ul wo k.
Physical Signi icance
 In an ideal e e sible p ocess, i e e sibili y is ze o, since no en opy is gene a ed and
all a ailable ene gy can be con e ed in o use ul wo k.
 In eal p ocesses, i e e sibili y is always posi i e, because en opy gene a ion is
una oidable.
 A highe deg ee o i e e sibili y means g ea e ene gy deg ada ion, educing he
e iciency o he sys em.
Examples o Sou ces o I e e sibili y
1. Mechanical i e e sibili y: F ic ion in mo ing pa s, inelas ic de o ma ion.
2. The mal i e e sibili y: Hea ans e ac oss a ini e empe a u e di e ence.
3. Chemical i e e sibili y: Combus ion, mixing o gases.
4. Elec ical i e e sibili y: Resis ance hea ing, eddy cu en s.
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108
2.17 Exp essions o Ene gy o a Closed Sys ems in Te ms o
A ailabili y and Second Law E iciency
In he modynamics, he analysis o closed sys ems is o signi ican impo ance, pa icula ly
when s udying he use ul po ion o ene gy and he associa ed losses. The concep s o
a ailabili y (exe gy), una ailable ene gy (ane gy), and second law e iciency a e i al o
quan i ying he ue e ec i eness o ene gy u iliza ion.
The o al ene gy supplied o a sys em is ne e ully con e ed in o use ul wo k due o
i e e sibili ies and en opy gene a ion. Hence, he second law o he modynamics guides us
o dis inguish be ween he use ul (a ailable) and he was ed (una ailable) pa s o ene gy.
Fo any closed sys em unde going a p ocess:
Hea T ans e : 𝑄=(𝛾−𝑛
𝛾−1)⋅𝑝1𝑉1−𝑝2𝑉2
𝑛−1 o 𝑄=(𝛾−𝑛
𝛾−1)⋅𝑚𝑅(𝑇1−𝑇2)
𝑛−1
Change in En opy:
Δ𝑆=𝐶𝑝ln (𝑇2
𝑇1)−𝑅ln (𝑝2
𝑝1) o Δ𝑆=𝐶𝑣ln (𝑇2
𝑇1)+𝑅ln (𝑉2
𝑉1)
A ailabili y (Maximum Wo k): 𝑊max=𝑄−𝑇0Δ𝑆
I e e sibili y: 𝐼=𝑊max−𝑊=𝑇0Δ𝑆
Second Law E iciency: 𝜂𝐼𝐼=𝑊ac
𝑊max
Case S udies
(a) Cons an Volume P ocess
When ai is hea ed a cons an olume om 𝑇1 o 𝑇2 wi h su oundings a empe a u e 𝑇0 :
Hea supplied: 𝑄=𝑚𝐶𝑣(𝑇2−𝑇1)
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En opy Balance
The concep o en opy balance plays a undamen al ole in he modynamics, as i accoun s
o he ans e and gene a ion o en opy wi hin a sys em and i s su oundings. Acco ding o
he second law o he modynamics, he en opy change o any sys em is always g ea e han
o equal o he en opy ans e ed o i , he di e ence being he en opy gene a ed wi hin he
sys em due o i e e sibili ies. This gene a ion o en opy is he eason o he imbalance
be ween en opy ans e and en opy change.
Ma hema ically, he en opy balance equa ion can be exp essed as:
(En opy en e ing he sys em) + (En opy gene a ion wi hin he sys em) = (En opy lea ing
he sys em) + (En opy change o he su ounding
This ela ion can be ew i en as:
𝑆in +𝑆gen =𝑆ou +Δ𝑆nu
𝑆gen =(𝑆ou −𝑆in )+Δ𝑆nu
Since (𝑆ou −𝑆in )=Δ𝑆sys em , he exp ession becomes:
𝑆gen =Δ𝑆syp em +Δ𝑆su (2.10)
Fo uni mass, his en opy balance educes o:
𝑠gen −Δ𝑠o g een +Δ𝑠gu (2.11)
In e p e a ion o he En opy Balance
The en opy balance equa ion (2.10) is uni e sal in na u e and applies o any sys em
unde going any he modynamic p ocess, whe he e e sible o i e e sible. I highligh s ha
he en opy gene a ion in a p ocess is equal o he combined en opy changes o he sys em
and i s su oundings.
Fo a e e sible p ocess:
En opy gene a ion is ze o, i.e., 𝑆gen =0. In his case, he en opy change o he sys em is
exac ly balanced by he en opy ans e o o om he su oundings.
Fo an i e e sible p ocess:
En opy gene a ion is always posi i e, i.e., 𝑆𝑔𝑒𝑛>0. This indica es ha en opy inc eases
because o i e e sibili ies such as ic ion, un es ained expansion, mixing o luids, and hea
ans e ac oss a ini e empe a u e di e ence.

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Fo an impossible p ocess:
I en opy gene a ion is nega i e, i.e., 𝑆𝑔𝑒𝑛<0, he p ocess iola es he second law o
he modynamics and is he e o e physically impossible.
P ac ical Impo ance
The en opy balance p o ides a powe ul ool o e alua ing he pe o mance and easibili y
o he modynamic sys ems. I allows enginee s o:
 Quan i y i e e sibili ies in eal p ocesses.
 Assess he e iciency o sys ems like u bines, comp esso s, and hea exchange s.
 E alua e he deg ada ion o ene gy quali y h ough en opy gene a ion.
 Apply he p inciple o en opy balance o designing ene gy-e icien sys ems by
minimizing en opy p oduc ion.
2.20 Fi s Law and Second Law E iciencies
In he modynamics, he pe o mance o a sys em can be e alua ed using wo dis inc measu es
o e iciency: he Fi s Law E iciency and he Second Law E iciency. While bo h a e
ela ed o ene gy u iliza ion, hey di e signi ican ly in e ms o wha hey measu e and how
hey e lec he quali y o ene gy con e sion.
Fi s Law E iciency ( 𝜼𝟏 )
The Fi s Law E iciency is based on he p inciple o ene gy conse a ion, i.e., he Fi s Law
o The modynamics. I is de ined as he a io o he ne wo k ou pu o he sys em o he o al
hea supplied o i . Ma hema ically, i is exp essed as:
𝜂1= Ne wo k ou pu
Hea supplied
This e iciency indica es how e ec i ely he supplied ene gy is con e ed in o use ul wo k.
Howe e , i does no accoun o he quali y o ene gy o he i e e sibili ies p esen in he
p ocess. Fo ins ance, wo p ocesses may ha e he same i s law e iciency, bu one may
in ol e g ea e losses due o i e e sibili y, which is no e lec ed by his measu e.
Second Law E iciency ( II)
The Second Law E iciency is based on he Second Law o The modynamics and conside s
no only he amoun o ene gy bu also he quali y and a ailabili y o ene gy. I is de ined as
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117
he a io o he change in a ailable ene gy o he sys em o he change in a ailable ene gy o
he sou ce. Al e na i ely, i can be exp essed as he a io o he a ailabili y o he ou pu o
he a ailabili y o he inpu .
Ma hema ically:
𝜂𝐼𝐼= Change in a ailable ene gy o he sys em
Change in a ailable ene gy o he sou ce
o ,
𝜂𝐼𝐼=𝐴ou
𝐴in
Compa ison and P ac ical Insigh
 Fi s Law E iciency (𝜼𝟏) ocuses only on ene gy conse a ion and does no
dis inguish be ween use ul and was ed ene gy. I p o ides a basic measu e o
pe o mance bu o e looks i e e sibili ies and deg ada ion o ene gy.
 Second Law E iciency ( 𝜂II ) goes u he by e alua ing how e ec i ely he sys em
u ilizes he a ailable ene gy (exe gy). I accoun s o i e e sibili ies, such as ic ion,
mixing, and hea ans e h ough ini e empe a u e di e ences, which educe he
use ul ene gy ha can be ex ac ed.
Enginee ing Signi icance
 𝜂1 is o en used in simple pe o mance analysis, such as in engines, boile s, and powe
cycles, whe e ene gy conse a ion is he main conce n.
 𝜂 II is mo e meaning ul in ad anced sys em e alua ions, as i highligh s he gap
be ween ac ual pe o mance and he ideal e e sible p ocess. I allows enginee s o
pinpoin losses, op imize sys em design, and mo e owa d ene gy-e icien and
sus ainable solu ions.
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CHAPTER -3
PROPERTIES OF PURE SUBSTANCE AND
STEAM POWER CYCLE
3.1 Fo ma ion o S eam and I s The modynamic P ope ies
When a pu e subs ance such as wa e is hea ed unde a cons an p essu e, i unde goes dis inc
phase changes be o e eaching he s a e o supe hea ed s eam. To illus a e, conside 1 kg o
wa e in a closed essel main ained a a cons an p essu e o 1.01325 ba (a mosphe ic
p essu e) and an ini ial empe a u e o –20°C. The a ious s ages o hea ing a e ep esen ed
in Figu e 3.1, which shows he empe a u e–hea added ela ionship.
Fig. 3.1 Fo ma ion o s eam.
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119
(a) Hea ing o Ice (Line 1-2)
Ini ially, as hea is supplied, he empe a u e o ice ises om −20∘C o he eezing poin o
wa e (0∘C). Du ing his s age, he ice emains in solid o m, and he ise in empe a u e is
p opo ional o he hea inpu .
The en halpy change in his s age is gi en by:
ℎ=𝑚𝐶𝑝𝑖𝑐𝑒(𝑇2−𝑇1)
whe e 𝐶𝑝ice is he speci ic hea o ice.
(b) Mel ing o Ice (Line 2-3)
Once he empe a u e eaches 0∘C, any u he hea supplied does no inc ease he empe a u e
bu is ins ead used o con e solid ice in o liquid wa e . This p ocess is known as usion o
mel ing.
The hea equi ed o con e ice a 0∘C in o wa e a 0∘C is called he la en hea o usion o
la en hea o ice. Du ing his s age, bo h ice and wa e coexis in equilib ium un il he en i e
ice has mel ed.
(c) Hea ing o Wa e (Line 3-4)
A e mel ing, he liquid wa e is hea ed om 0∘C o i s boiling o sa u a ion empe a u e,
which is 100∘C a a mosphe ic p essu e. The hea supplied in his p ocess is called he
sensible hea o wa e and is deno ed by ℎ𝑓.
A his s age:
 The empe a u e a which boiling s a s ( o a gi en p essu e) is he sa u a ion
empe a u e 𝑇sa .
 The p essu e co esponding o his empe a u e is called he sa u a ion p essu e 𝑝sa .
Bo h 𝑇sa and 𝑝sa a e dependen on each o he .
The en halpy change can be exp essed as:
ℎ𝑓=𝑚𝐶𝑝uu e (𝑇sa −𝑇ini ial )
(d) Vapo iza ion (Line 4-5)
Once he wa e eaches he sa u a ion empe a u e, u he hea addi ion does no inc ease he
empe a u e bu con e s he liquid wa e in o apo . Ini ially, s eam con ains wa e pa icles
in suspension, o ming a mix u e known as we s eam.
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The hea supplied du ing his cons an - empe a u e phase change is called he la en hea o
apo iza ion (o en halpy o apo iza ion), deno ed by ℎ𝑓𝑔.
The o al en halpy o d y sa u a ed s eam is exp essed as:
ℎ𝑔=ℎ𝑓+ℎ𝑓𝑔
Fo we s eam, he en halpy is calcula ed using he d yness ac ion ( x ):
ℎ𝑤𝑒𝑡=ℎ𝑓+𝑥⋅ℎ𝑓𝑔
whe e 0≤𝑥≤1.
He e,
 𝑥=0→ sa u a ed liquid (all wa e ),
 𝑥=1→ d y sa u a ed s eam (no wa e d ople s).
A a mosphe ic p essu e, ℎ𝑓≈419 kJ/kg and ℎ𝑓𝑔≈2257 kJ/kg.
(e) D y Sa u a ed S eam (Poin 5)
When all he wa e has comple ely e apo a ed, he s eam is said o be d y sa u a ed s eam. A
his s age, he s eam exis s a sa u a ion empe a u e and p essu e, and no liquid phase emains
in suspension. The en halpy o d y sa u a ed s eam is:
ℎ𝑔=ℎ𝑓+ℎ𝑓𝑔
( ) Supe hea ing o S eam (Line 5-6)
I u he hea is supplied a e d y sa u a ion, he empe a u e o he s eam ises abo e he
sa u a ion empe a u e. This s eam is called supe hea ed s eam, and he p ocess is e e ed o
as supe hea ing.
The addi ional hea supplied is known as he hea o supe hea o supe hea en halpy, deno ed
by ℎsup . I is exp essed as: ℎsup =ℎ𝑔+𝐶𝑝(𝑇sup −𝑇sa )
whe e 𝐶𝑝 is he speci ic hea o supe hea ed s eam, and 𝑇𝑠𝑢𝑝 is he supe hea ed empe a u e.
Supe hea ed s eam is pa icula ly use ul in powe gene a ion cycles because i educes
mois u e con en in u bines, minimizes blade e osion, and inc eases he mal e iciency.

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121
3.2 The modynamic P ope ies
1. D yness F ac ion
The d yness ac ion o s eam is a undamen al p ope y ha desc ibes he quali y o we
s eam. I is de ined as he a io o he mass o he d y s eam ac ually p esen o he o al mass
o he s eam mix u e (which consis s o bo h d y s eam and wa e d ople s in suspension). I
is deno ed by he symbol 𝐱.
𝑥= 𝑚𝑔
𝑚𝑓+𝑚𝑔
whe e:
 𝑚𝑔= Mass o d y s eam (kg)
 𝑚𝑓= Mass o wa e d ople s in suspension (kg)
This e m is applicable only o we s eam because d y s eam con ains no suspended wa e
pa icles.
 Fo d y sa u a ed s eam, 𝑚𝑓=0, hence:
𝑥=1
Thus, he d yness ac ion a ies be ween 0 and 1:
 𝑥=0→ sa u a ed liquid (all wa e )
 𝑥=1→ d y sa u a ed s eam (no mois u e p esen )
 0<𝑥<1→ we s eam
When exp essed in pe cen age, he d yness ac ion is called he quali y o s eam:
Quali y o s eam =100×𝑥%
This pa ame e is e y impo an in powe plan s, as he p esence o mois u e in s eam educes
u bine e iciency and causes blade e osion. Hence, highe alues o d yness ac ion a e
desi able o e icien ope a ion.
2. We ness F ac ion
The we ness ac ion is a complemen a y p ope y o he d yness ac ion. I is de ined as he
a io o he mass o suspended wa e d ople s o he o al mass o he s eam mix u e.
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Ma hema ically,
We ness ac ion =𝑚𝑓
𝑚𝑓+𝑚𝑔
Since 𝑥= 𝑚𝑔
𝑚𝑓+𝑚𝑔, he we ness ac ion can be w i en as:
We ness ac ion =1−𝑥
Thus, he we ness ac ion is simply he mois u e con en o s eam. Fo example:
 I 𝑥=0.9 (d yness ac ion), he we ness ac ion =0.1, i.e. 10% mois u e con en .
When exp essed as a pe cen age, he we ness ac ion is some imes e e ed o as p iming.
High we ness ac ion in s eam is undesi able as i leads o u bine blade wea , co osion, and
e iciency losses. Hence, s eam is o en supe hea ed o elimina e mois u e be o e being
expanded in u bines.
3. Phase Rule
The beha io o mul i-componen , mul i-phase sys ems is go e ned by he Gibbs Phase Rule,
which es ablishes he numbe o independen in ensi e a iables equi ed o comple ely
de ine he s a e o a sys em a equilib ium. The ule is exp essed as:
𝑛=𝐶−𝜙+2
whe e:
 𝑛= Numbe o independen a iables (deg ees o eedom)
 𝐶= Numbe o componen s
 𝜙= Numbe o phases in equilib ium
Applica ion Examples:
1. Two-Phase, Single-Componen Sys em
Fo wa e (𝐶=1) exis ing in wo phases (say, liquid + apo , so =2 ):
𝑛=1−2+2=1
This means ha only one independen p ope y (ei he empe a u e o p essu e) is su icien
o de ine he s a e. The o he p ope y is au oma ically ixed, as p essu e and empe a u e a e
ela ed h ough he sa u a ion condi ion.
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2. T iple Poin o Wa e
A he iple poin , wa e exis s in h ee phases simul aneously ( 𝜙=3 ) and =1 :
𝑛=1−3+2=0
Thus, he iple poin has no deg ee o eedom. Nei he empe a u e no p essu e can be
changed; bo h a e ixed uniquely a he iple poin .
3. Single-Phase, Single-Componen Sys em
Fo wa e exis ing en i ely in one phase (say, liquid only o apo only):
𝑛=1−1+2=2
This implies ha wo independen in ensi e p ope ies (e.g., p essu e and empe a u e, o
empe a u e and speci ic olume) a e equi ed o ix he s a e o he sys em.
Signi icance o he Phase Rule
 The phase ule is a powe ul ool in he modynamics and physical chemis y o
unde s and equilib ium s a es.
 Fo pu e subs ances, i simpli ies p ope y calcula ions since ewe a iables a e
needed.
 Fo enginee ing applica ions like boile s, condense s, and u bines, he phase ule
p o ides cla i y on how many p ope ies mus be speci ied o de e mine he sys em's
condi ion.
3.3 p– Diag am o Pu e Subs ances
A p– diag am ep esen s he ela ionship be ween he speci ic olume ( ) o a subs ance,
plo ed along he X-axis, and he p essu e (p), plo ed along he Y-axis. I is a undamen al
diag am in he modynamics used o desc ibe he phase-change p ocesses o pu e subs ances.
When a pu e subs ance is g adually hea ed o cooled a cons an p essu e, i unde goes a se ies
o s a e changes ha can be ep esen ed on he p– diag am. Figu es 3.2 and 3.3 show wo
ypical p– diag ams:
 Figu e 3.2 – Fo subs ances ha con ac du ing eezing (mos subs ances).
 Figu e 3.3 – Fo subs ances ha expand du ing eezing (wa e is he mos no able
example).
The di e ence be ween hese wo diag ams lies p ima ily in he slope o he solid–liquid
equilib ium line.
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124
Fig. 3.2 p- diag am o a subs ance du ing con ac ion on eezing.
Fig. 3.3 p- diag am o a subs ance du ing expansion on eezing.
Regions o he p– Diag am
1. Solid Region:
To he le o he sa u a ed solid line, he subs ance exis s en i ely in he solid s a e.
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131
 Cons an quali y (x = 0.2, 0.4, 0.6, e c.) lines a e d awn o show he condi ion o s eam
wi hin his egion.
3. Supe hea ed Region (Righ o D y S eam Line)
The egion o he igh o he sa u a ed apou line co esponds o supe hea ed s eam.
He e, s eam exis s a empe a u es highe han he sa u a ion empe a u e o a gi en p essu e.
C i ical Poin
As empe a u e and p essu e inc ease, he sa u a ed liquid line and sa u a ed apou line
app oach each o he and mee a he c i ical poin .
A his poin , he liquid is con e ed di ec ly in o apou wi hou o ming a wo-phase
mix u e.
Fo wa e , he c i ical empe a u e is 374.15°C and he co esponding c i ical p essu e is 221.2
ba . Beyond his s a e, he e is no dis inc ion be ween liquid and apou , and he subs ance
exis s as a supe c i ical luid.
Rep esen a ion o The modynamic P ocesses
The T–s diag am is pa icula ly aluable because di e en he modynamic p ocesses appea
as simple cu es o s aigh lines:
1. Iso he mal P ocess: A p ocess a cons an empe a u e appea s as a ho izon al line.
2. Isen opic P ocess: A e e sible adiaba ic p ocess (cons an en opy) appea s as a
e ical line. This p ope y is especially use ul o analysing expansion and comp ession
p ocesses in u bines and comp esso s.
3. Cons an P essu e Lines: In he supe hea ed egion, cons an p essu e lines a e d awn.
These lines slope upwa d o he igh , e lec ing he inc ease in en opy wi h empe a u e a
cons an p essu e.
4. Cons an Volume Lines: In he we egion, cons an speci ic olume lines can also be
ep esen ed. These a e use ul o calcula ing changes in speci ic olume du ing phase change
p ocesses.
Applica ions
The T–s diag am is widely used in s eam powe cycle analysis (e.g., Rankine cycle, ehea
cycle, egene a i e cycle).

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132
I p o ides a clea isual ep esen a ion o hea addi ion, hea ejec ion, expansion, and
comp ession p ocesses.
By eading alues di ec ly om he cha , enginee s can quickly de e mine p ope ies like
en opy, d yness ac ion, and en halpy di e ences.
3.6 h-s diag am o Mollie cha
The h–s diag am, mo e commonly known as he Mollie cha , is a g aphical ep esen a ion
o he he modynamic p ope ies o s eam. In his diag am:
 The e ical axis (o dina e) ep esen s he en halpy (h), exp essed in kJ/kg.
 The ho izon al axis (abscissa) ep esen s he en opy (s), exp essed in kJ/kg·K.
This cha is an in aluable ool o sol ing p oblems in s eam powe enginee ing, as i allows
quick and di ec de e mina ion o he modynamic p ope ies wi hou leng hy calcula ions.
Regions o he h–s Diag am
1. We Region (Below D y S eam Line)
The egion below he sa u a ed apou line (d y s eam line) ep esen s we s eam, whe e
s eam exis s as a mix u e o wa e and apou .
 D yness ac ion lines a e d awn pa allel o he sa u a ed apou line, helping o
de e mine he quali y o s eam.
 Fo example, a d yness ac ion o 0.8 indica es ha he mix u e consis s o 80% d y
s eam and 20% suspended wa e .
2. Supe hea ed Region (Abo e D y S eam Line)
The a ea abo e he d y s eam line ep esen s supe hea ed s eam.
 In his egion, s eam exis s a a empe a u e highe han he sa u a ion empe a u e o
a gi en p essu e.
 Cons an empe a u e cu es a e plo ed, which slope upwa d o he igh , indica ing
en opy inc ease wi h empe a u e.
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3. C i ical Poin
A he c i ical p essu e (221.2 ba ), he sa u a ed liquid line and sa u a ed apou line mee .
Beyond his poin , he dis inc ion be ween liquid and apou phases disappea s, and s eam
beha es as a supe c i ical luid.
Fig. 3.7 Mollie cha .
Rep esen a ion o The modynamic P ocesses
The Mollie cha is pa icula ly use ul because a ious he modynamic p ocesses can be
easily ep esen ed:
1. Isen opic (Re e sible Adiaba ic) P ocess:
Since en opy emains cons an , an isen opic p ocess appea s as a e ical line.
Example: Expansion o s eam in a u bine.
2. Th o ling P ocess:
In h o ling, en halpy emains cons an . The e o e, he p ocess is ep esen ed as a ho izon al
line.
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Example: Expansion h ough a h o le al e in e ige a ion o calo ime e
expe imen s.
3. Cons an P essu e P ocess:
In he we egion, cons an p essu e lines appea s aigh , while in he supe hea ed egion,
hey a e cu ed.
4. Cons an Tempe a u e P ocess:
These a e shown as sloping lines in he supe hea ed egion.
5. Cons an Volume P ocess:
Such p ocesses can also be aced using he p e-d awn lines in he cha .
Enginee ing Signi icance
 The Mollie cha is ex ensi ely used o s eam u bine analysis, since i allows he
en halpy d op (hea d op) du ing adiaba ic expansion o be di ec ly measu ed as he
e ical dis ance be ween wo poin s.
 I educes he e o o consul ing de ailed s eam ables, making i con enien o
p ac ical calcula ions in powe plan s.
 P ocesses like comp ession, expansion, hea ing, cooling, and h o ling can all be
quickly isualized.
3.7 p- -T su ace
In he modynamics, he beha iou o a pu e subs ance can be desc ibed using h ee impo an
he modynamic p ope ies: p essu e (p), speci ic olume ( ), and empe a u e (T). When
hese h ee a iables a e plo ed in a h ee-dimensional coo dina e sys em, he esul ing plo
is known as he p– –T su ace.
In his ep esen a ion:
 Speci ic olume ( ) and empe a u e (T) a e aken as he independen a iables
( o ming he ho izon al plane).
 P essu e (p) is aken as he dependen a iable ( ep esen ed on he e ical axis).
Thus, e e y poin on he su ace co esponds o a unique equilib ium s a e o he subs ance.
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135
Cha ac e is ics o he p– –T Su ace
1. Single-Phase Regions:
The single-phase egions (solid, liquid, o apou ) appea as con inuous cu ed su aces on
he p– –T plo .
2. Two-Phase Regions:
The egions whe e wo phases coexis in equilib ium (solid–liquid, liquid– apou , solid–
apou ) appea as su aces pe pendicula o he p–T plane. These ep esen sa u a ion
condi ions.
3. T iple Poin Line:
The line whe e he h ee phases (solid, liquid, and apou ) coexis is ep esen ed as he iple
poin line on he su ace.
 Fo wa e , his co esponds o a empe a u e o 273.16 K and a p essu e o 0.6113
kPa.
 A his line, speci ic olume changes, bu empe a u e and p essu e emain ixed.
4. C i ical Poin :
A he end o he sa u a ed liquid and apou su aces lies he c i ical poin , beyond which
he dis inc ion be ween liquid and apou phases disappea s.
Subs ances Expanding and Con ac ing on F eezing
1. Figu e 3.8 (a) – Wa e (Expands on F eezing):
Fo wa e and simila subs ances, eezing causes expansion due o he open c ys al la ice o
ice. This is e lec ed in he slope o he solid–liquid equilib ium su ace.
2. Figu e 3.8 (b) – CO₂ (Con ac s on F eezing):
Fo subs ances like ca bon dioxide, eezing causes con ac ion, and he solid–liquid su ace
has an opposi e slope compa ed o wa e .
This dis inc ion be ween con ac ion and expansion on eezing is a c i ical p ope y o
ma e ial beha iou unde a ying p essu es and empe a u es.
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136
Fig. 3.8 p- -T su ace o wa e and CO2.
Rela ion wi h Two-Dimensional Diag ams
The commonly used he modynamic diag ams such as p– , p–T, and T– diag ams a e
simply wo-dimensional p ojec ions o he comple e p– –T su ace on o hei espec i e
coo dina e planes:
 The p– diag am is ob ained by p ojec ing on o he p– plane.
 The p–T diag am is a p ojec ion on o he p–T plane.
 The T– diag am is a p ojec ion on o he T– plane.
Al hough he p– –T su ace p o ides he mos comp ehensi e desc ip ion o subs ance
beha iou , in p ac ice, wo-dimensional diag ams a e used mo e equen ly since hey a e
simple and con enien o enginee ing applica ions.
Enginee ing Impo ance
 The p– –T su ace p o ides a comple e he modynamic map o a pu e subs ance.

The modynamics
137
 I helps explain he in e ela ion be ween di e en p ope y diag ams used in
p ac ice.
 Unde s anding his su ace is essen ial o analysing phase changes, loca ing he
iple poin , and in e p e ing he c i ical poin beha iou .
 While he su ace o e s a weal h o in o ma ion, enginee s ypically ely on simpli ied
2D diag ams o s eam ables o p ac ical calcula ions.
3.8 S eam Tables
In he modynamics, i is o en edious and imp ac ical o calcula e s eam p ope ies such as
p essu e, empe a u e, speci ic olume, en halpy, and en opy using heo e ical equa ions
alone.
To simpli y his, he p ope ies o wa e and s eam ha e been expe imen ally de e mined
and sys ema ically a anged in abula o m. These abula ions a e collec i ely known as
S eam Tables.
S eam ables p o ide he he modynamic p ope ies o 1 kg o s eam, usually unde di e en
condi ions o sa u a ion o supe hea ing. Fo we s eam, he equi ed p ope ies can be
ob ained wi h he help o he d yness ac ion in combina ion wi h he s eam ables.
S eam ables a e b oadly di ided in o h ee main pa s:
1. Sa u a ed Wa e Table (P essu e Scale)
This able p esen s he p ope ies o s eam a di e en sa u a ion p essu es. The key p ope ies
lis ed include:
 Sa u a ion empe a u e (T_sa )
 Speci ic olume o liquid wa e (𝑣𝑓) and d y sa u a ed s eam (𝑣𝑔)
 En halpy o sa u a ed liquid (ℎ𝑓), la en hea o apo isa ion (ℎ𝑓𝑔), and d y sa u a ed
s eam (ℎ𝑔)
 En opy o sa u a ed liquid (𝑠𝑓), e apo a ion (𝑠𝑓𝑔), and d y sa u a ed s eam (𝑠𝑔)
I he equi ed p essu e is no exac ly lis ed, he alues a in e media e p essu es can be
ob ained by in e pola ion.
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138
P ess
u e
in
kPa
Sa u a
ion
empe
a u e
in ∘C
Spec
i ic
olu
me
𝑣𝑓 (
m3/
kg )
Spec
i ic
olu
me
𝑣𝑔 (
m3/
kg )
En h
alpy
ℎ𝑓
(kJ/k
g)
En h
alpy
ℎ𝑓𝑔
(kJ/k
g)
En h
alpy
ℎ𝑔
(kJ/k
g)
En o
py 𝑠𝑓
(kJ/k
g•K)
En
opy
𝑠𝑓𝑔 (
kJ/
kg⋅
K )
En
opy
𝑠𝑔 (
kJ/
kg⋅
K )
10.0
45.81
1.01
0
14.6
7
191.8
3
2392.
8
2584.
7
0.649
3
7.50
09
8.15
02
15.0
53.97
1.04
0
10.0
2
225.9
4
2373.
1
2599.
1
0.754
9
7.25
36
8.00
85
20.0
60.06
1.01
7
7.64
9
251.4
0
2358.
3
2609.
7
0.832
0
7.07
65
7.90
85
Table. 3.1 Sa u a ed Wa e Table (P essu e Scale).
2. Sa u a ed Wa e Table (Tempe a u e Scale)
This able p o ides he same se o p ope ies bu a anged acco ding o sa u a ion
empe a u e ins ead o p essu e.
Since o e e y p essu e he e is only one unique sa u a ion empe a u e, his o m o he able
is pa icula ly use ul when he empe a u e o s eam is known.
Like he p essu e-based able, p ope ies include speci ic olume, en halpy, and en opy
alues o liquid, apou , and mix u es.
Sa u a i
on
empe a
u e in
°C
P ess
u e in
kPa
Speci
ic
olu
me
( )
(m³/k
g)
Speci
ic
olu
me
( g)
(m³/k
g)
En ha
lpy
(h )
(kJ/kg
)
En ha
lpy
(h g)
(kJ/kg
)
En ha
lpy
(hg)
(kJ/kg
)
En o
py (s )
(kJ/kg
·K)
En o
py
(s g)
(kJ/kg
·K)
En o
py (sg)
(kJ/kg
·K)
70
31.19
1.023
5.042
292.98
2333.8
2626.8
0.9549
6.8761
7.8310
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139
75
38.58
1.026
4.131
313.93
2321.4
2635.3
1.0155
6.6669
7.6824
80
47.39
1.029
3.407
334.91
2308.8
2643.7
1.0753
6.5369
7.6122
Table. 3.2 Sa u a ed Wa e Table (Tempe a u e Scale).
3. Supe hea ed S eam Table
The supe hea ed s eam able lis s he p ope ies o s eam a empe a u es abo e he
sa u a ion empe a u e o a gi en p essu e. The abula ed p ope ies include:
 Speci ic olume ( )
 En halpy (h)
 En opy (s)
The da a a e gi en o di e en supe hea ed empe a u es (e.g., 100°C, 200°C, 300°C, e c.)
and co esponding p essu es.
This able is especially use ul in s eam u bine analysis, whe e supe hea ed s eam is widely
employed o imp o e e iciency and educe mois u e con en a u bine exhaus .
Temp. (°C)
Speci ic Volume (m³/kg)
En halpy (kJ/kg)
En opy (kJ/kg·K)
100
17.20
2687.5
8.449
150
19.51
2783.1
8.689
200
21.83
2879.6
8.905
250
24.14
2977.4
9.101
300
26.45
3076.6
9.282
350
28.75
3177.3
9.450
400
31.06
3279.6
9.608
500
35.68
3489.1
9.898
600
40.30
3705.5
10.162
Table. 3.3 Supe hea ed S eam Table.
Va ia ion o P ope ies
F om he s udy o s eam ables, he ollowing ends a e obse ed:
 As p essu e inc eases, he sensible hea (h ) g adually inc eases.
 The la en hea o apo isa ion (h g) dec eases wi h p essu e.
 The en halpy o d y sa u a ed s eam (hg) ini ially inc eases wi h p essu e, eaching
a maximum a app oxima ely 33.5 ba , and hen begins o dec ease.
These a ia ions a e o g ea impo ance in he design and analysis o boile s, condense s,
and s eam u bines.
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140
Enginee ing Applica ions o S eam Tables
 Used in Rankine cycle analysis o e alua e hea addi ion, hea ejec ion, u bine
wo k, and pump wo k.
 Essen ial o de e mining s eam quali y (d yness ac ion) in powe plan s.
 P o ides quick e e ence o p ope y e alua ion wi hou sol ing complex
he modynamic equa ions.
 Used in bo h labo a o y expe imen s and indus ial applica ions o accu a e and
con enien p ope y de e mina ion.
3.9 De e mina ion o d yness ac ion
The d yness ac ion (x) o s eam indica es he p opo ion o apou p esen in a we s eam
mix u e. I is a c i ical pa ame e in s eam enginee ing, as he e iciency and pe o mance o
s eam powe plan s la gely depend on he s eam quali y.
The d yness ac ion can be expe imen ally measu ed by using di e en ypes o s eam
calo ime e s. The commonly used calo ime e s a e:
1. Bucke o Ba el Calo ime e
2. Th o ling Calo ime e
3. Sepa a ing Calo ime e
4. Combined Sepa a ing and Th o ling Calo ime e
1. Bucke o Ba el Calo ime e
In his me hod, he calo ime e is placed inside an insula ed essel illed wi h a known mass
o wa e . S eam om he main line is passed in o he calo ime e h ough a s eam pipe and
bubbled in o he wa e .
The s eam condenses, ans e ing i s la en hea (and pa o i s sensible hea ) o he wa e ,
he eby aising i s empe a u e. By measu ing he empe a u e ise o wa e and knowing he
mass o wa e and condensed s eam, he d yness ac ion can be es ima ed.
Limi a ion: This me hod is simple bu no e y accu a e, as some hea is los o he
su oundings and he measu emen does no accoun o exac ene gy ans e .
2. Th o ling Calo ime e
This calo ime e is bes sui ed o s eam wi h a high d yness ac ion (low mois u e
con en ). I wo ks on he p inciple o he h o ling p ocess, whe e s eam expands h ough a
h o ling al e o o i ice.
The modynamics
243
F om he cha (a 100 kPa ):
 En halpy a Poin 1: ℎ1=16.5 kJ/kg d y ai
 En halpy a Poin 2: ℎ2=28 kJ/kg d y ai
 Humidi y a io a Poin 2: 𝜔2=0.003 kg/kg d y ai
 Humidi y a io a Poin 3: 𝜔3=0.012 kg/kg d y ai
S ep 2: Mass low a e o d y ai
Use ideal-gas ela ion o he d y-ai s eam:
𝑚𝑎=𝑝𝑉
˙
𝑅𝑎𝑇1=100×(45/60)
0.287×283 =0.923 kg/s
S ep 3: Hea added in hea ing sec ion (𝟏→𝟐)
𝑄
˙=𝑚𝑎(ℎ2−ℎ1)=0.923(28−16.5)=10.615 kJ/s
S ep 4: Mois u e added in humidi ying sec ion ( 𝟐→𝟑 )
Humidi y inc ease:
Δ𝜔 =𝜔3−𝜔2=0.012−0.003=0.009 kg apou /kg d y ai

The modynamics
244
S eam mass low:
Δ𝜔 = 𝑚˙𝑣
𝑚𝑎⇒𝑚˙𝑣=Δ𝜔𝑚𝑎=0.009×0.923=0.0083 kg/s
5.8 Psych ome ic P ocesses
In ai -condi ioning and en i onmen al con ol sys ems, i is o en necessa y o al e he
he modynamic s a e o mois ai o mee speci ic equi emen s o com o o p ocess needs.
These ans o ma ions o mois ai a e known as psych ome ic p ocesses. Each p ocess
in ol es a change in one o mo e psych ome ic p ope ies, such as empe a u e, humidi y
a io, en halpy, o ela i e humidi y.
The main psych ome ic p ocesses a e:
1. Sensible hea ing
2. Sensible cooling
3. Humidi ica ion and dehumidi ica ion
4. Cooling and dehumidi ica ion
5. Cooling wi h adiaba ic humidi ica ion
6. Cooling and humidi ica ion by wa e injec ion (e apo a i e cooling)
7. Hea ing and humidi ica ion
8. Humidi ica ion by s eam injec ion
9. Adiaba ic chemical dehumidi ica ion
10. Adiaba ic mixing o wo ai s eams
Each p ocess can be ep esen ed on he psych ome ic cha and analyzed ma hema ically
o de e mine hea and mois u e ans e s.
1. Sensible Hea ing
Sensible hea ing e e s o hea ing ai wi hou changing i s speci ic humidi y (i.e., no addi ion
o emo al o mois u e). This is achie ed by passing ai o e a ho su ace such as a hea ing
coil.
On he psych ome ic cha , sensible hea ing is ep esen ed by a ho izon al line mo ing o
he igh , since he d y-bulb empe a u e inc eases while he humidi y a io emains
cons an . The inal ai empe a u e is always less han he coil su ace empe a u e, since ull
he mal equilib ium is no eached.
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245
This p ocess is commonly used in win e ai -condi ioning, p ehea ing o en ila ion ai , and
d ying sys ems.
Fig. 5.4 Psych ome ic p ocess.
2. Sensible Cooling
Sensible cooling is he e e se o sensible hea ing, whe e ai is cooled wi hou changing i s
speci ic humidi y. This is usually achie ed by passing ai o e a cooling coil wi h a su ace
empe a u e abo e he dew-poin o he en e ing ai , ensu ing ha condensa ion does no
occu .
On he psych ome ic cha , sensible cooling is ep esen ed by a ho izon al line mo ing o
he le , as he d y-bulb empe a u e dec eases bu he mois u e con en emains
unchanged.
This p ocess is used in summe ai -condi ioning whe e cooling is equi ed bu
dehumidi ica ion is no necessa y.
3. Humidi ica ion and Dehumidi ica ion
Humidi ica ion is he p ocess o adding mois u e o ai wi hou changing i s d y-bulb
empe a u e. This inc eases bo h he speci ic humidi y and ela i e humidi y. On he
psych ome ic cha , he p ocess is shown as a e ical upwa d line, since mois u e inc eases
bu empe a u e emains cons an .
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246
Dehumidi ica ion, on he o he hand, emo es mois u e om ai a cons an d y-bulb
empe a u e, dec easing bo h he speci ic humidi y and ela i e humidi y. On he cha , i is
ep esen ed as a e ical downwa d line.
These p ocesses a e essen ial o con olling com o condi ions and o indus ial ope a ions
such as ex ile and pape manu ac u ing.
4. Cooling and Dehumidi ica ion
This p ocess is widely used in summe ai -condi ioning o educe bo h he empe a u e and
humidi y o mois ai . I occu s when ai is passed o e a cooling coil wi h a su ace
empe a u e below he dew-poin o he incoming ai .
As ai cools, i s d y-bulb empe a u e dec eases, and once he dew poin is eached,
condensa ion begins, educing he humidi y a io. On he psych ome ic cha , his is
ep esen ed by a sloping line mo ing downwa d o he le .
The concep o Appa a us Dew Poin (ADP) is impo an he e. The ADP is he e ec i e
su ace empe a u e o he cooling coil, and dehumidi ica ion occu s only when he coil
su ace empe a u e is below he dew poin o he incoming ai .
5. Cooling wi h Adiaba ic Humidi ica ion
This p ocess in ol es passing ai h ough a chambe con aining sp ays o eci cula ed wa e .
The sp ay wa e empe a u e is lowe han he d y-bulb empe a u e bu highe han he dew-
poin empe a u e o he en e ing ai .
Since no ex e nal hea is added o emo ed (adiaba ic p ocess), he ai app oaches he
condi ion o adiaba ic sa u a ion. On he psych ome ic cha , he p ocess ollows a line o
cons an we -bulb empe a u e o nea ly cons an en halpy.
In p ac ice, he inal s a e o ai is no ully sa u a ed (poin 3 on he cha ) bu lies somewhe e
along he line (poin 2), depending on he e ec i eness o he sys em. This p ocess is
commonly used in cooling owe s and e apo a i e coole s.
6. Cooling and Humidi ica ion by Wa e Injec ion (E apo a i e Cooling)
In his p ocess, wa e is di ec ly injec ed in o he ai s eam. As he wa e e apo a es, he ai
is bo h cooled and humidi ied. The inal condi ion depends on he ex en o e apo a ion.
When he wa e is injec ed a a empe a u e equal o he we -bulb empe a u e o he en e ing
ai , he p ocess ollows a cons an we -bulb line on he cha . This is he p inciple o
e apo a i e cooling, widely used in ho and d y clima es whe e cooling is needed bu
e ige a ion is imp ac ical.
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247
7. Hea ing and Humidi ica ion
This p ocess is ypical o win e ai -condi ioning, whe e cold, d y ou doo ai mus be
wa med and humidi ied o p o ide com o indoo s. The ai is passed h ough a humidi ie
wi h sp ay wa e a a empe a u e highe han he d y-bulb empe a u e o he en e ing ai .
On he psych ome ic cha , he p ocess is shown as a diagonal upwa d line o he igh ,
indica ing ha bo h empe a u e and humidi y a io inc ease simul aneously. The inal
ela i e humidi y may be highe o lowe han he ini ial, depending on he ex en o hea ing
and mois u e addi ion.
The modynamics
248
Fig. 5.5 Psych ome ic p ocess-II.
8. Humidi ica ion by S eam Injec ion
In his p ocess, s eam is injec ed di ec ly in o he ai o inc ease i s humidi y a io. The d y-
bulb empe a u e changes e y li le, since he la en hea o s eam is abso bed while i s
sensible hea con ibu ion is minimal.
On he psych ome ic cha , he p ocess is ep esen ed by a e ical upwa d mo emen ,
simila o humidi ica ion, bu wi h a sligh empe a u e ise. This is commonly used in ex ile
indus ies, whe e high humidi y le els mus be main ained o ab ic p ocessing.
9. Adiaba ic Chemical Dehumidi ica ion
This p ocess is mainly used in indus ial ai -condi ioning sys ems ha equi e low humidi y
le els o low dew-poin empe a u es. In his me hod, ai is passed o e chemicals (such as
silica gel o li hium chlo ide) ha ha e a high a ini y o mois u e.

The modynamics
249
As ai passes o e he chemicals, wa e apo is abso bed, educing he speci ic humidi y.
A he same ime, he la en hea eleased du ing condensa ion is con e ed in o sensible hea ,
he eby inc easing he d y-bulb empe a u e.
On he psych ome ic cha , he p ocess ollows a line o nea ly cons an en halpy o we -
bulb empe a u e, bu mo ing downwa d in humidi y and upwa d in empe a u e.
10. Adiaba ic Mixing o Two Ai S eams
When wo ai s eams o di e en condi ions mix adiaba ically, he inal s a e o he mix u e
depends on he en halpy, humidi y a io, and mass low a e o each s eam.
Le :
 𝑚1,ℎ1,𝑊1= mass low, en halpy, and humidi y a io o s eam 1
 𝑚2,ℎ2,𝑊2= mass low, en halpy, and humidi y a io o s eam 2
 𝑚3,ℎ3,𝑊3= co esponding p ope ies o he mix u e
The ene gy and mass balance gi es:
𝑚1
𝑚2=ℎ3−ℎ2
ℎ1−ℎ3=𝑊3−𝑊2
𝑊1−𝑊3
On he psych ome ic cha , he inal s a e (poin 3 ) lies on he s aigh line connec ing he
wo s a es (poin s 1 and 2). I s exac loca ion depends on he mass a io o he mixing s eams.
This p ocess is impo an in en ila ion sys ems, whe e ou doo and eci cula ed ai s eams
a e mixed o achie e desi ed indoo condi ions.