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Javed, M. A., Rüther, M., Baumhögger, E., & Vrabec, J. (2020). Density and Thermodynamic Speed of
Sound of Liquid Vinyl Chloride. Journal of Chemical & Engineering Data, 65(5), 2495–2504.
https://doi.org/10.1021/acs.jced.9b01133
Muhammad Ali Javed, Moritz Rüther, Elmar Baumhögger, Jadran Vrabec
Density and Thermodynamic Speed of
Sound of Liquid Vinyl Chloride
Accepted manuscript (Postprint)Journal article |
Density and thermodynamic speed of sound of
liquid vinyl chloride
Muhammad Ali Javed,
†
Moritz Rüther,
‡
Elmar Baumhögger,
‡
and Jadran
Vrabec
∗
,
†
†
Thermodynamics and Process Engineering, Technical University of Berlin, 10623 Berlin,
Germany
‡
Thermodynamics and Energy Technology, University of Paderborn, 33098 Paderborn,
Germany
E-mail: vrabec@tu-berlin.de
Abstract
Vinyl chloride is one of the world's most important industrially synthesized sub-
stances, but due to its physico-chemical nature comparably little is known about its
thermodynamic behavior. Accurate density and thermodynamic speed of sound data of
vinyl chloride in the liquid state are measured along nine isotherms, covering the tem-
perature range from 283 K to 362 K up to a pressure of 91 MPa. Data are presented
with a maximum expanded uncertainty (
k= 2
) of 0.15% for the density and 0.16%
for the speed of sound. They are compared with all available literature sources and
a preliminary equation of state. Present density data are in good agreement with the
literature data and have a maximum deviation of 1.5% from the equation of state. How-
ever, no experimental speed of sound data are available in the literature for comparison
and the equation of state diverges up to -12.4% from the present data.
keywords:
Density, speed of sound, densimeter, pulse-echo technique, vinyl chloride.
1
1 Introduction
Vinyl chloride, a common name for chloroethene, chloroethylene, ethylene monochloride or
monochloroethylene, is under ambient conditions a colorless and combustible gas with a
mildly sweet odor. It is one of the world's most important industrial commodity chemicals,
but it can also be formed in the environment, when chlorinated solvents are broken down by
soil microorganisms.
1,2
Vinyl chloride is toxic for humans, since acute or short-term exposure
during respiration damages the central nervous system, while long-term exposure results in
liver cancer.
1,3
The global production of vinyl chloride monomer was 49 million metric tons in 2018
and it is expected to reach 53 million metric tons by 2023.
4
Northeast Asia is currently the
largest consumer of vinyl chloride, utilizing more than half of its total production. China
is the biggest player in the vinyl chloride industry, consuming about 40% of its total yield,
while the United States is in the second place.
5
Vinyl chloride was commercially produced for the rst time in the 1930s. Currently,
it is synthesised by direct chlorination or oxychlorination of ethylene. As a result of both
processes, 1,2-dichloroethane is obtained, which is subjected to a pressure of about 3 MPa
at a temperature of 550
◦
C. This causes 1,2-dichloroethane to undergo pyrolysis or thermal
cracking, forming vinyl chloride monomer and hydrogen chloride, from which vinyl chloride
is isolated.
1,6
Almost 99% of the total production of vinyl chloride is used for making polyvinyl chloride
(PVC), which contains repeating units of vinyl chloride monomer in long chains. This
polymer is commonly utilized with great exibility to make end products, including pipes
and ttings, proles and tubes, siding, wire coating, housewares and automotive parts. The
vinyl chain, containing ethylene dichloride, vinyl chloride monomer and polyvinyl chloride,
is a main component of the petrochemical and thermoplastic industry.
5
Vinyl chloride is also
used to produce methyl chloroform and copolymers with vinyl acetate, vinyl stearate and
2
vinylidene chloride.
1
In the past, vinyl chloride was used as a refrigerant, propellant in spray
cans and in some cosmetics, but these practices have been ocially banned since the 1970s.
1
Because vinyl chloride has critical health and re hazards and can easily undergo poly-
merization reactions,
15
very limited experimental data for the density and no data for the
speed of sound have been reported in the literature, cf. Table 1. Eight authors have mea-
sured the density in the liquid phase, covering the temperature range from 213 K to 423 K up
to a maximum pressure of 4.2 MPa, cf. Figure 1. However, most have measured only along
the vapor pressure line. Cullick and Ely
12
as well as Zerfa and Brooks
14
have investigated
higher pressures, but the latter have reported only a single data point.
Density and the speed of sound data, covering wide temperature and pressure ranges, are
necessary for the development and parameterization of Helmholtz energy equations of state.
16
As the global demand for vinyl chloride is increasing rapidly,
5
a precise equation of state
is benecial for the design and optimization of industrial chemical processes. However, the
currently available literature data for vinyl chloride are insucient to properly parameterize
such models. Nonetheless, a preliminary Helmholtz energy equation of state of Thol and
Span
17
exists.
In the present work, an apparatus was built to simultaneously measure the density and
speed of sound of vinyl chloride. To suppress the risk of polymerization, copper wires were
avoided and hydroquinone was placed in the rig as a stabilizer.
18
The measurements were
performed in the liquid phase, covering the temperature range from 283 K to 362 K up to
a pressure of 91 MPa. The density was measured with an Anton Paar densimeter (DMA-
HPM) with a maximum expanded uncertainty of 0.15% (
k= 2
). The speed of sound
was investigated by employing a double path length pulse-echo technique with a maximum
expanded uncertainty of 0.16% (
k= 2
). The obtained results were compared with the
available literature data and the preliminary Helmholtz energy equation of state of Thol and
Span.
17
3
2 Experiment
2.1 Materials
The specications of the materials and details of their suppliers are provided in Table 2.
They were purchased under high purity and studied without any further purication, except
for degassing the liquid water sample.
2.2 Apparatus
An apparatus was developed to simultaneously sample the density and the speed of sound
of vinyl chloride. For this purpose, a densimeter and an acoustic cell were combined. The
schematic of the experimental rig is presented in Figure 2. To specify a temperature, both
measurement devices were connected to a thermostat (Huber CC415). Therein, water was
circulated as a heat transfer medium to regulate and maintain the temperature of the sample
uid within 0.01 K. The temperature was varied between 283 K and 362 K, remaining about
11 K below the normal boiling point of water to prevent excessive evaporation and to protect
the circulating pump and electric circuits from damage caused by moisture. A hand pump
(HIP 50-6-15) was employed to impose a pressure of up to 91 MPa that was measured by a
pressure transducer (Keller-PAA-33X).
Vinyl chloride is a highly unstable monomer and undergoes rapid polymerization reac-
tions to form polyvinyl chloride (PVC) by heating and under the inuence of air, sunlight
and contact with strong oxidizers and metals, i.e. copper and aluminum.
15
It is a gas under
ambient conditions and its mixture with air forms peroxide, which may explode.
19
More-
over, in the presence of moisture, vinyl chloride reacts with iron or steel. To mitigate this
risk, the copper quantity in the apparatus was reduced to a minimum level and crystalline
hydroquinone was used to prevent spontaneous polymerization.
18
As this stabilizer is not
soluble in vinyl chloride, almost 5 g of it was placed in a container with a porous lid behind
4
Figure 1: State points where (a) density and (b) speed of sound of vinyl chloride were
measured:
this work,
×
experimental literature data. The solid line is the vapor pressure
curve.
5
one of the reectors, cf. Figure 3. The diameter of the lid pores was smaller than the crystal
size of hydroquinone, keeping it in the container. The acoustic cell with the container was
screwed into the ceiling of the pressure vessel. The cell was suspended in the sample uid
and to uniformly ll it, reectors with cavity spacers were used.
2.3 Density measurement
The density of vinyl chloride was measured with an Anton Paar densimeter (DMA-HPM).
Therein, a U-shaped metallic vibrating tube is connected to an interface module, which
generates an oscillation and measures its period and temperature of the tube containing
the sample uid. The oscillation period is a function of density, temperature and pressure.
To accurately determine the density of vinyl chloride, the densimeter was calibrated with
propane and water on the basis of reference quality Helmholtz energy equations of state by
Lemmon et al.
20
and Wagner and Pruÿ
21
that are available for these substances.
22
These
uids were chosen since they envelop the density range of vinyl chloride.
For calibration, the density of propane and water at dierent state points was tted as
a function of the measured oscillation period, temperature and pressure.
16
A third order
Legendre polynomial containing ten coecients was used for this purpose
ρ=a+b1T+c1p+d1s+b23T2−1
2+d2
(3s2−1)
2
+b1d1Ts +b1d2T(3s2−1)
2+c1d2
(3s2−1)
2
+b1c1d1Tps.
(1)
Therein,
T
,
p
and
s
are scaled parameters used to enhance the performance of the polynomial,
dened by
y=y−y
δy .
(2)
6
degasing
outlet
sample
p
exhaust/
vacuum
oscillation
period
temperature
pressure
transducer
densimeter
hand
pump
thermostat
switch
in / out
burst
in
sync
signal
out
computer
data
aqusition
switchable
inductivity
func.
generator
oscilloscope
PT-100
Figure 2: Schematic of the apparatus for measuring density and speed of sound along with
the instruments for control and analysis.
7
Table 1: Experimental density and the speed of sound data for vinyl chloride, where
N
is the
number of measured data points,
T
min
−T
max
the temperature range and
p
max
the maximum
pressure.
author year
N T
min
-
T
max
/K
p
max
/MPa
Uρ
/(kg m
−3
)
Uw
/(m s
−1
)
densityDana et al.
7
1927 7 260 - 333 vapor pressure 0.7
−
Mizutani and Yamashita
8
1950 27 222 - 259 vapor pressure
− −
Dreisbach
9
1952 - 1955 3 243 - 253 vapor pressure
− −
Anonymous
10
1965 1 260 vapor pressure
− −
Hannaert et al.
11
1967 2 213 - 233 vapor pressure 8.3
−
Cullick and Ely
12
1982 68 281 - 337 4.2 0.4
−
de Loos et al.
13
1983 16 273 - 423 vapor pressure 1.4
−
Zerfa and Brooks
14
1996 1 328 0.9
− −
this work 2019 107 283.3 - 362.2 91.07 1.1
−
speed of sound
this work 2019 109 283.97 - 361.1 91.06
−
1.1
Table 2: Specication of the materials and their suppliers.
chemical name CAS number source purity/% purication method
hydroquinone 123-31-9 Sigma-Aldrich 100.00 none
propane 74-98-6 Gerling Holz & Co. 99.50 none
vinyl chloride 75-01-4 Sigma-Aldrich 99.96 none
water 7732-18-5 Merck 99.99 none
l1 ≈ 20 mm
reflector 2
first echo
second echo
delay in
time of flight
quartz
l2 ≈ 30 mm
reflector 1
hydroquinone
container
porous lid
cavity
Figure 3: Working principle of the speed of sound measurement.
8
The parameters of the calibration equation (1) are listed in Table 3. A comparison of the
calibration measurements with the reference equations of state for propane and water is pre-
sented in Figure 4. In the liquid region, these equations of state have very low uncertainties of
0.01% for propane and 0.003% for water. It is convincing that the calibration measurements
are in very good agreement with the equations of state, exhibiting a maximum deviation of
less than 0.04% for propane and about 0.01% for water. Also at elevated pressures, present
measurements are consistent with the reference equations.
Table 3: Parameters of the calibration equation (1) for the density measurement.
parameter value unit
a750.0756 −
b1−359.6746 −
c1−4.9587 −
d1767.7276 −
b2−2.7453 −
d21.4900 −
b1d1−14.0967 −
b1d22.0918 −
c1d2−3.6169 −
b1c1d14.2310 −
T57.077 ◦
C
δT 80 ◦
C
p46.059
MPa
δp 47.0
MPa
s2646.468 µ
s
δs 60 µ
s
2.4 Speed of sound measurement
The thermodynamic speed of sound was measured with a double path length pulse-echo tech-
nique.
2326
To bring this method into practice, an 8 MHz gold plated piezoelectric quartz
crystal was placed symmetrically between two metallic reectors of unequal lengths. The
quartz was excited electrically with a functional generator (Agilent 33220A). Consequently,
two sound waves emerged, traveled in opposite directions, and after reection, were received
back by the quartz at dierent time instances. These echoes were analyzed with an oscil-
9
Figure 4: Comparison of the calibration measurements for density as a function of pressure
along isotherms:
298 K,
⊕
323 K,
362 K; (a) propane, where the baseline is the equation
of state by Lemmon et al.;
20
(b) water, where the baseline is the equation of state by Wagner
and Pruÿ.
21
10
loscope (Agilent DSO1022A) and, neglecting diraction and dispersion eects, the speed of
sound was calculated by
w=2∆L
∆t,
(3)
where
∆L
is the path length dierence between the two reectors and
∆t
is the delay in
time of ight of the two echoes.
The path length dierence
∆L(T0, p0)
= 9.99 mm at
T0
= 300 K and
p0
= 1 MPa was
determined from calibration measurements with water. In order to achieve this, the equation
of state by Wagner and Pruÿ
21
was employed, which has an uncertainty of 0.005% for the
speed of sound calculation at the selected state point. Thermal expansion and pressure
compression of the acoustic cell, fabricated from stainless steel (type 1.4571) were considered
by
∆L(T, p) = ∆L(T0, p0)1 + α−1
E(1 −2ν) (p−p0).
(4)
Therein,
ν= 0.3
is the Poisson number, provided by the steel supplier. The integral thermal
expansion coecient
α
was calculated by
α=n0(T−T0) + n1
2T2−T2
0+n2
3T3−T3
0
+n3
4T4−T4
0+n4
5T5−T5
0,
(5)
where
n0= 4.7341 ·10−6
K
−1
,
n1= 7.1518 ·10−8
K
−2
,
n2=−1.5273 ·10−10
K
−3
,
n3=
1.5864 ·10−13
K
−4
and
n4=−6.1342 ·10−17
K
−5
.
27
The temperature dependent modulus of
elasticity
E
contributed with a rst order polynomial
E=a+b(T),
(6)
where
a= 219711.07
MPa
−1
and
b=−79.8
K
−1
MPa
−1
.
27
11
To measure the delay in time of ight, a peak-to-peak measurement method, which
considers the time dierence between maximum amplitudes of both echoes, and a correlation
approach, were adapted. For the correlation method, a time domain analysis was performed,
in which two data cuts were made for both echoes and the delay in time of ight was
determinded by applying a correlation function. Details were recently described by Javed
et al.
28
Figure 5: Comparison of the calibration measurements for speed of sound with the equation
of state by Wagner and Pruÿ.
21
Experimental data: this work,
298 K,
⊕
323 K,
361
K; Lin and Trusler,
29
4
303 K,
♦
323 K,
5
373 K; Al Ghafri et al.,
30
+
306 K,
×
358 K;
Wilson,
31
N
303 K,
H
364 K; Yebra et al.,
32
303 K,
F
323 K; Benedetto et al.,
33
•
303
K,
364 K.
A comparison of the calibration measurements with the equation of state by Wagner and
Pruÿ
21
and the experimental literature data is shown in Figure 5. The literature data have a
maximum uncertainty of about 0.04%. It should be noted that the calibration measurements
of this work are in very good agreement with the equation of state, exhibiting a maximum
deviation of 0.02% for the entire measured temperature and pressure range.
12
3 Results and discussion
Vinyl chloride was delivered in a metal ask as a saturated liquid at ambient temperature and
0.4 MPa pressure. To measure its density and speed of sound, the apparatus was evacuated
for about 2 h and the system temperature was reduced to 283 K. Subsequently, vinyl chloride
was imbibed into the apparatus and a pressure was specied with the hand pump. Density
and speed of sound were measured along nine isotherms between 283 K and 362 K with an
increment of 10 K up to a pressure of 91 MPa. The sample uid was given an equilibration
time of about 1.25 h, before measuring the next state point.
3.1 Density
The numerical density data for vinyl chloride together with their uncertainties are listed in
Table 4. The overall expanded uncertainty at a condence level of 95% was calculated by
considering the individual uncertainties of temperature
uT
, pressure
up
, oscillation period
us
, calibration
u
cal
and impurities
u
imp
Uρ=k"∂ρ
∂T 2
p,s
u2
T+∂ρ
∂p2
T,s
u2
p+∂ρ
∂s2
T,p
u2
s+u2
cal
+u2
imp
#1/2
,
(7)
with the coverage factor
k= 2
. The partial derivatives of density with respect to temperature
and pressure were calculated with the Helmholtz energy equation of state by Thol and
Span.
17
The partial derivative with respect to oscillation period was obtained from equation
(1). A detailed uncertainty budget for the density measurement is provided in Table 5. It
should be noted that the major contribution to the overall uncertainty, i.e. 0.109%, is due
to calibration, which also includes reproducibility of the data and aging of the densimeter.
The graphical presentation of experimental uncertainty as a function of pressure along
dierent isotherms is provided in Figure 6. The uncertainty varies between 0.11% to 0.15%
for the entire measured temperature and pressure range. The maximum uncertainty is at
13
Figure 6: Experimental uncertainty of the density of vinyl chloride as a function of pressure
along dierent isotherms:
4
283 K,
293 K,
⊕
303 K,
313 K,
♦
323 K,
×
333 K,
+
343
K,
5
352 K,
F
362 K.
262 K and 5.8 MPa.
Table 4: Density of vinyl chloride with its expanded experimental uncertainty for varying
temperature
T
and pressure
p
1
.
T
/K
p
/MPa
ρ
/(kg m
−3
)
Uρ
/(kg m
−3
)
T
/K
p
/MPa
ρ
/(kg m
−3
)
Uρ
/(kg m
−3
)
283.3 0.44 927.8 1.1 322.8 10.69 877.4 1.1
283.3 0.83 928.4 1.1 322.9 20.78 898.4 1.1
283.3 2.27 931.1 1.1 322.9 30.62 915.7 1.1
283.3 5.98 937.6 1.1 322.9 49.89 943.5 1.1
283.3 6.95 939.2 1.1 322.9 70.36 967.7 1.1
283.3 10.76 945.4 1.1 322.9 90.68 988.1 1.1
283.3 20.97 960.4 1.1 332.7 1.03 830.6 1.1
283.3 31.91 974.6 1.1 332.7 1.61 832.6 1.1
283.3 51.01 996.1 1.1 332.8 2.4 835.3 1.1
14
Table 4 : (Continued)
T
/K
p
/MPa
ρ
/(kg m
−3
)
Uρ
/(kg m
−3
)
T
/K
p
/MPa
ρ
/(kg m
−3
)
Uρ
/(kg m
−3
)
283.3 73 1017 1.1 332.8 5.24 844.3 1.1
283.3 90.77 1031.9 1.1 332.7 6.95 849.4 1.1
293.2 0.96 910.5 1.1 332.7 10.02 857.8 1.1
293.2 2.4 913.4 1.1 332.7 14.4 868.7 1.1
293.2 4.6 917.8 1.1 332.7 20.56 882.2 1.1
293.2 5.31 919.1 1.1 332.7 26.77 894.3 1.1
293.2 10.5 928.5 1.1 332.7 31.05 902 1.1
293.2 11.45 930.2 1.1 332.7 50.18 931.3 1.1
293.2 20.89 945.2 1.1 332.7 70.92 957 1.1
293.2 31.77 960.3 1.1 332.7 91.07 977.9 1.1
293.2 37.25 967.1 1.1 342.6 1.28 808.6 1.1
293.2 51.02 983.2 1.1 342.6 2.15 812.1 1.1
293.2 70.5 1002.8 1.1 342.6 3 815.5 1.1
293.2 90.71 1020.6 1.1 342.6 5.17 823.5 1.1
303.1 0.52 890.6 1.1 342.6 7.43 831 1.1
303.1 0.98 891.7 1.1 342.5 13.31 848.2 1.1
303.1 2.09 894.2 1.1 342.6 20.72 866.4 1.1
303.2 5.56 901.6 1.1 342.6 22.8 871 1.1
303.1 8.52 907.9 1.1 342.6 30.32 886.1 1.1
303.1 11.08 912.8 1.1 342.6 50.28 918.8 1.1
303.1 20.08 928.5 1.1 342.5 69.08 943.4 1.1
303.1 30.52 944.3 1.1 342.5 90.25 966.7 1.1
303.2 46.93 965.5 1.1 352.4 2.27 788.8 1.1
303.1 51.59 971 1.1 352.4 5.25 802 1.1
15
Table 4 : (Continued)
T
/K
p
/MPa
ρ
/(kg m
−3
)
Uρ
/(kg m
−3
)
T
/K
p
/MPa
ρ
/(kg m
−3
)
Uρ
/(kg m
−3
)
303.2 70.65 991.1 1.1 352.4 6.81 808.2 1.1
303.2 90.72 1009.5 1.1 352.4 7.68 811.4 1.1
313.0 0.67 871.5 1.1 352.4 9.33 817.3 1.1
313.0 1.54 873.7 1.1 352.4 20.25 849 1.1
313.0 2.58 876.5 1.1 352.4 30.6 872 1.1
313.0 5.13 882.6 1.1 352.4 49.71 905.4 1.1
313.0 7.13 887.2 1.1 352.4 70.97 934.4 1.1
313.0 8.96 891.3 1.1 352.4 90.4 956.4 1.1
313.0 10.88 895.4 1.1 362.3 5.8 781 1.1
313.0 14.47 902.7 1.1 362.3 7.24 787.6 1.1
313.0 20.92 914.5 1.1 362.2 8.28 792.5 1.1
313.0 30.6 930.2 1.1 362.2 10.7 802.1 1.1
313.0 49.8 956.3 1.1 362.2 21.95 836.9 1.1
313.0 66.99 975.9 1.1 362.2 29.87 855.8 1.1
313.0 88.11 996.6 1.1 362.2 36.77 869.9 1.1
322.8 1.26 852.8 1.1 362.3 40.28 876.5 1.1
322.8 2.31 855.9 1.1 362.2 50.5 894.1 1.1
322.8 5.02 863.4 1.1 362.2 70.57 922.8 1.1
322.8 7.6 870.1 1.1 362.2 90.22 946.1 1.1
322.8 8.46 872.1 1.1
1
Uρ
is the expanded uncertainty of the density at a condence level of 95%
(k= 2)
,
composed of standard uncertainties of temperature
uT= 0.1
K, pressure
up= 0.002
MPa, oscillation period
us= 0.015 µ
s, calibration
u
cal
= 0.5
kg m
−3
and impurities
u
imp
= 0.2
kg m
−3
.
16
Figure 7: Density of vinyl chloride as a function of pressure (a) and deviation of the density
data from the equation of state by Thol and Span
17
(b):
4
283 K,
293 K,
⊕
303 K,
313 K,
♦
323 K,
×
333 K,
+
343 K,
5
352 K,
F
362 K.
17
The density of vinyl chloride as a function of pressure along the measured isotherms
is depicted in Figure 7(a). The density ranges from 781.0 kg m
−3
to 1031.9 kg m
−3
and
increases with falling temperature or rising pressure. Deviations of the density data from
the Helmholtz energy equation of state by Thol and Span
17
are shown in Figure 7(b). It
can be noted that performance of the equation of state is much better at low temperature
and low pressure, were the deviations converge to -0.15%. At high pressures, the isotherms
systematically diverge from the equation of state. The maximum deviation is 1.5% at the
state point 362.2 K and 90.22 MPa. The experimental data at elevated temperatures and
pressures indicate that the equation of state should be improved.
A comparison of the present density data with the experimental literature data is provided
in Figure 8 and the base line is calculated with the equation of state of Thol and Span.
17
Cullick and Ely
12
as well as Zerfa and Brooks
14
have measured the density of vinyl chloride
above its vapor pressure, where the latter authors have measured only a single data point.
This point has a deviation of -0.18% from the equation of state. Cullick and Ely
12
have
reported the density along six isotherms, covering the temperature range between 281 K and
337 K with a pressure of up to 4.2 MPa. These data are in good agreement with the present
work and show a similar trend. Their measurements exhibit a systematic behavior, where
all isotherms cross the base line at a pressure between 2 MPa to 4 MPa with a maximum
deviation of 0.1%, except for the isotherm 337 K, which has a noticeably dierent slope with
a maximum deviation of about 1.6%.
Table 5: Detailed uncertainty budget for the density measurement of vinyl chloride.
source type measuring
range standard
uncertainty density
derivative
a
relative expanded
uncertainty
a
temperature
− −
0.1 K 1.5 kg m
−3
K
−1
0.016%
pressure Keller-PAA-33X <100 MPa 0.02 MPa 0.2 kg m
−3
MPa
−1
0.003%
oscillation period
− −
0.015
µ
s 1.3 10
−7
kg m
−3
s
−1
0.028%
calibration
− −
0.5 kg m
−3−
0.109%
impurities
− −
0.2 kg m
−3−
0.044%
a
Uncertainty value at a typical state point of
T= 322.87
K and
p= 30.62
MPa for the present density
measurement of vinyl chloride.
18
Figure 8: Deviation of the density data from the equation of state by Thol and Span
17
in
a region where other experimental data were available: this work;
4
283 K,
293 K,
⊕
303 K,
313 K,
♦
323 K,
×
333 K,
+
343 K,
5
352 K,
F
362 K: experiment literature
data; Cullick and Ely
12
N
281 K,
•
289 K,
•
295 K,
306 K,
318 K,
H
337 K; Zerfa and
Brooks
14
328 K.
19
3.2 Speed of sound
Speed of sound data for vinyl chloride at dierent temperatures and pressures with uncer-
tainty values are numerically listed in Table 6. The overall expanded uncertainty of the
speed of sound at a condence level of 95% (
k= 2
) consists of standard uncertainties of
temperature
uT
, pressure
up
, delay in time of ight
u∆t
and path length dierence
u∆L
measurement
Uw=k"∂w
∂T 2
p,∆L,∆t
u2
T+∂w
∂p 2
T,∆L,∆t
u2
p+∂w
∂∆L2
T,p,∆t
u2
∆L+∂w
∂∆t2
T,p,∆L
u2
∆t#1/2
.
(8)
The partial derivatives of speed of sound with respect to temperature and pressure were
calculated with the equation of state for vinyl chloride,
17
while the derivatives with respect
to delay in time of ight and path length dierence were calculated from equation (3). A
detailed uncertainty budget for the speed of sound measurement at a typical state point
is provided in Table 7. The expanded uncertainties of temperature, pressure and timing
are below 0.02%. The largest contribution to the overall uncertainty is due to path length
calibration, i.e. 0.08%, which includes a margin for reproducability of the calibration data at
elevated temperatures and pressures. A graphical representation of the uncertainties shows
that the overall expanded uncertainties are below 0.16% for the entire measured data set, cf.
Figure 9. At pressures above 20 MPa, the uncertainties are below 0.1% throughout. As with
the density data, uncertainties are large at high temperatures and low pressures because the
speed of sound changes signicantly in this region, cf. Figure 10(a).
The speed of sound of vinyl chloride as a function of pressure along nine isotherms is
shown in Figure 10(a). It was measured over a wide span from 550.9 m s
−1
to 1336.2 m s
−1
.
A comparison of the present experimental data with the preliminary equation of state by
Thol and Span
17
is shown in Figure 10(b). It should be noted that no experimental caloric
data, e.g., speed of sound or heat capacity, were available in the literature when the equation
20
Figure 9: Experimental uncertainty of the speed of sound of vinyl chloride as a function of
pressure along isotherms:
4
284 K,
294 K,
⊕
303 K,
313 K,
♦
323 K,
×
333 K,
+
342
K,
5
351 K,
F
361 K.
of state of Thol and Span
17
was developed. As a consequence, the equation of state deviates
by up to
−
12.4% from the present experimental data. The divergence is high at low pressures
for all isotherms. However, at high pressures, all isotherms are systematically approaching
the equation of state with a minimum deviation of
−
7.5%.
Table 6: Speed of sound of vinyl chloride with its expanded experimental uncertainty for
varying temperature
T
and pressure
p
1
.
T
/K
p
/MPa
w
/(m s
−1
)
Uw
/(m s
−1
)
T
/K
p
/MPa
w
/(m s
−1
)
Uw
/(m s
−1
)
283.96 0.45 935.3 1.0 322.48 8.46 817.3 0.9
283.82 0.83 938.4 1.0 322.49 10.69 835.6 0.9
283.97 2.27 948.1 1.0 322.61 20.78 907.9 0.9
283.85 5.98 973.3 1.0 322.62 30.62 968.1 0.9
283.92 6.96 979.5 1.0 322.64 49.89 1066.7 1.0
283.86 10.77 1003.2 1.0 322.64 70.35 1153.5 1.0
21
Table 6 : (Continued)
T
/K
p
/MPa
w
/(m s
−1
)
Uw
/(m s
−1
)
T
/K
p
/MPa
w
/(m s
−1
)
Uw
/(m s
−1
)
283.87 20.97 1060.5 1.0 322.64 90.67 1228.0 1.1
283.86 31.90 1114.8 1.0 332.33 1.03 697.8 0.9
283.87 51.01 1197.1 1.1 332.33 1.61 704.5 0.9
283.95 73.00 1278.1 1.1 332.35 2.40 713.4 0.9
283.95 90.77 1336.2 1.2 332.33 5.24 743.4 0.8
293.75 0.49 888.2 0.9 332.12 6.95 760.5 0.8
293.53 0.97 891.4 0.9 332.12 10.02 788.6 0.8
293.52 2.40 903.0 0.9 332.13 14.40 824.9 0.8
293.50 4.61 919.3 0.9 332.13 20.56 870.5 0.9
293.52 5.31 924.3 0.9 332.20 26.77 911.4 0.9
293.76 7.84 940.1 0.9 332.18 31.05 937.6 0.9
293.51 10.50 959.4 1.0 332.20 50.18 1038.8 0.9
293.52 11.45 965.5 1.0 332.21 70.92 1129.2 1.0
293.53 20.89 1021.6 1.0 332.22 91.06 1204.5 1.1
293.53 31.77 1078.3 1.0 341.91 1.28 649.9 0.9
293.63 37.25 1104.4 1.0 341.93 2.15 661.1 0.9
293.54 51.02 1164.7 1.1 341.92 2.99 671.9 0.8
293.63 70.49 1239.5 1.1 341.94 5.17 697.2 0.8
293.65 90.70 1307.8 1.2 341.93 7.43 721.5 0.8
303.22 0.52 840.6 0.9 341.82 13.32 776.7 0.8
303.28 0.98 844.2 0.9 341.84 20.72 835.7 0.8
303.30 2.08 853.5 0.9 341.84 22.80 850.9 0.8
303.36 5.59 881.1 0.9 341.85 30.31 900.7 0.9
303.22 8.52 903.1 0.9 341.86 50.27 1010.8 0.9
22
Table 6 : (Continued)
T
/K
p
/MPa
w
/(m s
−1
)
Uw
/(m s
−1
)
T
/K
p
/MPa
w
/(m s
−1
)
Uw
/(m s
−1
)
303.23 11.08 921.1 0.9 341.87 69.07 1095.7 1.0
303.23 20.07 978.5 0.9 341.88 90.24 1177.5 1.0
303.24 30.52 1036.5 1.0 351.50 2.27 612.1 0.9
303.34 46.93 1115.0 1.0 351.51 5.25 652.1 0.8
303.26 51.59 1135.3 1.0 351.49 6.81 670.9 0.8
303.35 70.65 1210.7 1.1 351.51 7.68 680.8 0.8
303.36 90.72 1280.4 1.1 351.49 9.34 698.9 0.8
313.08 0.67 792.9 0.9 351.52 20.26 797.5 0.8
312.84 1.54 801.7 0.9 351.46 30.59 871.0 0.8
313.08 2.57 810.4 0.9 351.48 49.70 980.3 0.9
312.86 5.13 833.2 0.9 351.50 70.98 1078.5 1.0
312.86 7.13 849.6 0.9 351.53 90.39 1154.6 1.0
312.85 8.96 863.9 0.9 361.21 1.89 550.9 0.9
312.86 10.88 878.4 0.9 361.17 5.80 611.6 0.8
312.89 14.47 903.8 0.9 361.10 7.24 631.0 0.8
312.91 20.92 945.9 0.9 361.04 8.27 644.0 0.8
312.91 30.59 1002.2 0.9 361.05 10.71 672.1 0.8
312.92 49.80 1096.6 1.0 361.07 21.95 776.4 0.8
312.92 66.99 1168.2 1.0 361.08 29.86 835.3 0.8
312.91 88.10 1245.1 1.1 361.05 36.77 880.1 0.8
322.73 0.82 745.5 0.9 361.11 40.28 901.4 0.8
322.48 1.27 750.4 0.9 361.08 50.50 957.7 0.9
322.49 2.31 761.0 0.9 361.10 70.56 1052.6 0.9
322.50 5.02 787.0 0.9 361.13 90.22 1131.4 1.0
23
Table 6 : (Continued)
T
/K
p
/MPa
w
/(m s
−1
)
Uw
/(m s
−1
)
T
/K
p
/MPa
w
/(m s
−1
)
Uw
/(m s
−1
)
322.49 7.59 810.0 0.9
1
Uw
is the expanded uncertainty of speed of sound at a condence level of 95%
(k= 2)
,
composed of standard uncertainties of temperature
uT= 0.05
K, pressure
up= 0.02
MPa, delay in time of ight
u∆t= 0.002 µ
s and path length dierence
u∆L= 7 µ
m.
Table 7: Detailed uncertainty budget for the speed of sound measurement of vinyl chloride.
source type measuring
range standard
uncertainty speed of sound
derivative
a
relative expanded
uncertainty
a
temperature PT-100 84 - 693 K 0.05 K 4.2 m s
−1
K
−1
0.017%
pressure Keller-PAA-33X <100 MPa 0.02 MPa 0.6 m s
−1
MPa
−1
0.012%
time oscilloscope
Agilent DSO1022A
−
0.002
µ
s
4.7·107
m s
−2
0.019%
path length
− −
7
µ
m
4.8·104
s
−1
0.080%
a
Uncertainty value at a typical state point of
T= 322.62
K and
p= 30.6
MPa for the present speed of
sound measurement of vinyl chloride.
4 Conclusions
An apparatus was built to simultaneously measure the density and speed of sound of vinyl
chloride. An Anton Paar densimeter was employed for the density measurement and was
calibrated with propane and water. The maximum deviation of the density calibration
measurements was 0.04% from the reference quality equation of state for propane by Lemmon
et al.
20
and 0.01% from the reference quality equation of state for water by Wagner and
Pruÿ.
21
For the speed of sound measurements, a double path length pulse-echo technique was
implemented and the acoustic cell was calibrated with water. The calibration measurements
have a maximum deviation of 0.02% from the equation of state by Wagner and Pruÿ.
21
Density and speed of sound of vinyl chloride were investigated over a wide temperature
range from 283 K to 362 K up to a pressure of 91 MPa. A detailed experimental uncertainty
analysis was carried out. The maximum expanded uncertainty, at a condence level of 95%
24
Figure 10: Speed of sound of vinyl chloride (a) and deviation of the present data from the
equation of state by Thol and Span
17
(b):
4
284 K,
294 K,
⊕
303 K,
313 K,
♦
323 K,
×
333 K,
+
342 K,
5
351 K,
F
361 K.
25
(
k= 2
), is 1.1 kg m
−3
for the density and 1.2 m s
−1
for the speed of sound measurements.
Present results for the density of vinyl chloride were compared with the available literature
data and the preliminary equation of state by Thol and Span.
17
Only two authors have
reported the density above the vapor pressure, i.e. Cullick and Ely
12
as well as Zerfa and
Brooks.
14
Present data are in a good agreement with these literature data and have a maxi-
mum deviation of 1.5% from the equation of state. However, for the speed of sound of vinyl
chloride, no literature data were found and the preliminary equation of state of Thol and
Span
17
diverges up to
−
12.4% from the present data. Therefore, the preliminary equation
of state for vinyl chloride should be rened on the basis of the present data.
5 Acknowledgement
The rst author would like to thank the DAAD/HEC Pakistan scholarship program for
nancing this study.
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29
Cl
C
H
C
HH
For Table of Contents Only
30
