Speed of Sound Measurements and a Fundamental Equation of State

Article pubs.acs.org/jced

Speed of Sound Measurements and a Fundamental Equation of State for Cyclopentane Holger Gedanitz,† Maria J. Davila,§,† and Eric W. Lemmon*,‡ †

Thermodynamics, Ruhr-Universität Bochum, D-44780 Bochum, Germany Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, United States

‡

ABSTRACT: The speed of sound in liquid cyclopentane has been measured in the temperature range from (258 to 353) K at pressures up to 30 MPa (42 data points) using a pulse-echo method with a double path type sensor. The expanded overall uncertainty (k = 2) in the speed of sound measurements is estimated to be 0.2 %. A function for the speed of sound with inputs of temperature and pressure has been fitted to the experimental results. The new speed of sound data along with available literature data were used to develop a fundamental Helmholtz equation of state for cyclopentane. Typical expanded uncertainties of properties calculated using the new equations are 0.2 % in density in the liquid phase, 1 % in heat capacity, 0.2 % in liquid-phase sound speed, and 0.5 % in vapor pressure. The equation of state is valid from the triple-point temperature, 179.7 K, to temperatures of 550 K with pressures to 250 MPa.

1. INTRODUCTION This work characterizes the properties of cyclopentane (C5H10, CAS no. 287-92-3). Cyclopentane is mainly used as a foamblowing agent in the manufacture of polyurethane insulating foam in order to replace environmentally damaging chlorofluorocarbons. Thus, cyclopentane is found in the insulation in most refrigerators and freezers. The thermodynamic properties of fluids can be depicted through the use of equations that cover the liquid, vapor, and supercritical phases of the compound. Modern, high-accuracy equations of state for pure-fluid properties are fundamental equations explicit in the Helmholtz energy as a function of density and temperature.1 All single-phase thermodynamic properties can be calculated as derivatives of the Helmholtz energy. The location of the saturation boundaries requires an iterative solution of the physical constraints on saturation (the Maxwell criterion, i.e., equal pressures and Gibbs energies at constant temperature during phase changes), as is required with any form of an equation of state for thermodynamic consistency. The speed of sound plays a major role in establishing these equations because, in the limit of small amplitudes and low frequency, the speed of sound is a thermodynamic state variable and connects the thermal and caloric properties.2 In this work, the speeds of sound in cyclopentane have been measured in the temperature range from (258 to 353) K at pressures up to 30 MPa using a pulse-echo method. With these data and several other available properties, a fundamental equation of state was developed.

without further purification. According to the supplier, the mass purity of the substance was 0.988, with a main mass impurity of 0.008 2,2-dimethylbutane. Prior to measurements, the sample was dried over 0.4 nm molecular sieves and degassed in an ultrasonic cleaner. 2.2. Methods and Apparatus. The apparatus used to determine the speed of sound has been previously described in detail;4,5 therefore, only a brief description will be given here. The apparatus employs a pulse-echo technique. The main component is a double-path-length type sensor, in which a quartz transducer is placed at an unequal distance between two reflectors. The transducer operates at its resonant frequency of 8 MHz. The ultrasonic sensor was housed within a pressure vessel and immersed in a thermostated liquid bath. The temperature was measured by a Rosemount Aerospace 162CE Pt 25 sensor (with a temperature-range from 200 to 661 K) with ITS-90 calibration at the height of the quartz crystal. The standard uncertainty u(T) of the temperature measurement is 3 mK over the temperature range of the instrument operation. The pressure measurements were made by two pressure transducers, Paroscientific models 1000-500A and 1000-6K, operative, respectively, up to 3 and 40 MPa. Both were checked against a Degrange and Huot 5200 pressure balance. The pressure transducers are coupled by a differential pressure indicator Rosemount 3051S to communicate the pressure to the measuring cell. Moreover, a correction to the measured pressure has to be applied, taking into account the hydrostatic pressure

2. EXPERIMENTAL SECTION 2.1. Material. The cyclopentane sample measured in this work was obtained from Sigma-Aldrich (Germany)3 and used

Received: November 9, 2014 Accepted: April 7, 2015

© XXXX American Chemical Society

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DOI: 10.1021/je5010164 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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carried out close to the vapor pressure. The experimental results are given in Table 1. Unfortunately a low overall uncertainty as achieved with other fluids could not be obtained in the present measurements because of the relatively high quantity of impurities (as given in section 2.1), which dominates the uncertainty budget. Mixture models built on equations of state can be used (with software such as explained in section 4) to determine the change that might occur with various impurities. For example, a mixture of mostly cyclopentane with 0.008 mass fraction of 2,2dimethylbutane and 0.004 mass fraction of other similar hydrocarbons shows that the changes in the speed of sound would be around 0.1 % to 0.2 %. Thus, the relative expanded (k = 2) uncertainty of the speed of sound Ur(w) in cyclopentane is estimated to be 0.2 %. The experimental data have been fitted by a least-squares analysis to a double polynomial equation suggested by Sun et al.7 of the form

differences from the location of the pressure transducers and the ultrasonic cell. The local densities required in this correction are taken from the equation of state of the substance under investigation. In the present case, a preliminary equation for cyclopentane was used (with an uncertainty of about 0.2 % in density, which is nearly negligible for this correction). The standard uncertainties u(p) of the pressure measurements were estimated to be 0.21 kPa for pressures below 3 MPa and 2.39 kPa up to 30 MPa. The acoustic path length of the sensor was calibrated with degassed (with ultrasound) water of HPLC quality (supplied by J.T. Baker). The calibration was carried out in the temperature range from (274.15 to 353.15) K at atmospheric pressure. More details of the calibration procedure can be found elsewhere.4,6 The reproducibility of measured speeds of sound measured in this device is better than 1·10−5. The relative standard uncertainty ur(w) of the speed of sound measurements was estimated to be 0.003 %, and consists of the length calibration and the time measurements (for further explanation see ref 4). The contribution from sample purity is not included in this estimate. With this design of the apparatus and the calibration procedure over a wide temperature range, very low relative expanded (k = 2) uncertainties Ur(w) can be achieved, especially in gases; for example, uncertainties of 0.011 % for nitrogen4 and less than 0.014 % for argon6 are reported elsewhere.

3

p − p0 =

2

∑ ∑ aij(w − wp0)i T j (1)

i=1 j=0

where aij are the coefficients, T is the temperature, w is the speed of sound at pressures above 0.1 MPa, and wp0 is the speed of sound at p0 = 0.1 MPa calculated with the coefficients bj from the equation 3

wp0 =

3. MEASUREMENT RESULTS The speed of sound in cyclopentane has been measured over the temperature range between (258 and 353) K in intervals of about 20 K. For each isotherm, data were taken up to 30 MPa in steps of about 5 MPa. The lowest pressure was normally 0.1 MPa, except for at T = 333 K and T = 353 K, where the measurements were

p/MPa

w/(m·s−1)

T/K

p/MPa

w/(m·s−1)

258.151 258.151 258.151 258.151 258.151 258.151 258.151 273.149 273.149 273.149 273.149 273.150 273.150 273.150 293.149 293.149 293.149 293.148 293.149 293.148 293.148

0.100 5.072 10.244 15.262 20.158 25.083 30.141 0.100 5.169 10.059 15.219 20.251 25.184 30.227 0.105 5.059 10.088 15.198 20.121 25.192 30.134

1419.058 1446.070 1473.008 1498.119 1521.653 1544.511 1567.131 1336.626 1366.736 1394.32 1422.015 1447.913 1472.273 1496.252 1230.093 1262.962 1294.375 1324.591 1352.283 1379.573 1404.980

313.150 313.150 313.149 313.149 313.149 313.149 313.149 333.151 333.151 333.151 333.151 333.151 333.151 333.151 353.149 353.149 353.149 353.149 353.149 353.149 353.149

0.107 5.113 10.058 15.132 20.097 25.098 30.162 0.149 5.035 10.139 15.108 20.13 25.152 30.170 0.261 5.019 10.069 15.107 20.063 25.009 30.157

1126.831 1164.014 1198.273 1231.306 1261.807 1290.997 1319.175 1026.636 1067.634 1106.967 1142.542 1176.238 1207.969 1238.041 929.399 974.633 1018.218 1058.051 1094.384 1128.301 1161.490

(2)

j=0

Equation 1 represents the experimental speeds of sound with an average absolute deviation of 0.008 %. The resulting coefficients for aij and bj are presented in Table 2. The fitted polynomial given in eq 1 was used to compare the measurement results with literature data. To the best of our knowledge, the data set of Takagi et al.8 is the only set that exists for speeds of sound at elevated pressures. In the Takagi paper, speeds of sound were measured over the temperature range from (283.15 to 343.15) K up to 20 MPa, with a quoted uncertainty of < 0.2 %. Comparisons with the present data show good agreement (AAD: 0.12 %). In the temperature range from (283.15 to 303.15) K the agreement is even much better (AAD: 0.03 %), but the deviations increase with increasing temperature. The maximum absolute deviation in the last isotherm (343.15 K) measured by Takagi et al. is 0.38 %.

Table 1. Experimental Speeds of Sound w for Cyclopentane at Pressures p and Temperatures Ta T/K

∑ bjT j

4. FUNDAMENTAL EQUATION OF STATE 4.1. Critical and Triple Points. The critical temperature for cyclopentane was taken as an average of the five sources available: Alekhin et al.,9 Ambrose and Grant,10 Christou,11 Kay,12 and Kay and Hissong.13 The critical density was determined during the fitting of the equation of state to experimental data in all phases and for multiple properties. The critical pressure was determined from the final equation of state as a calculated property at the critical temperature and density. The values are Tc = 511.72 K ± 0.15 K ρc = 3.92 mol/dm 3 ± 0.1 mol/dm 3 pc = 4.5828 MPa ± 0.07 MPa

a

Standard uncertainties u are u(T) = 3 mK, u(p) = 0.21 kPa for p < 3 MPa, and u(p) = 2.39 kPa for p > 3 MPa, and the relative expanded uncertainty Ur is Ur(w) = 0.2% with a level of 95% confidence (k = 2).

These values of the critical parameters should be used for all property calculations from the equations of state reported here. B



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Table 2. Coefficients bj of eq 2 in (m·s−1·K−j) and Coefficients aij of eq 1 in (MPa·m−i·si·K−j) j

bj

a1j

a2j

a3j

0 1 2 3

3.4231448·103 −1.0754431·101 1.4691989·10−2 −1.2028079·10−5

5.4119297·10−1 −1.8244133·10−3 1.6264598·10−6

6.2949373·10−4 −2.6830251·10−6 3.4786647·10−9

−2.3988544·10−6 1.5101010·10−8 −2.3265412·10−11

Table 3. Coefficients and Exponents of the Equation of State k

Nk

tk

dk

lk

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.0630928 1.50365 −2.37099 −0.484886 0.191843 −0.835582 −0.435929 0.545607 −0.209741 −0.0387635 0.677674 −0.137043 −0.0852862 −0.128085 −0.00389381

1.0 0.29 0.85 1.185 0.45 2.28 1.8 1.5 2.9 0.93 1.05 4.0 2.33 1.5 1.0

4 1 1 2 3 1 3 2 2 7 1 1 3 3 2

0 0 0 0 0 2 2 1 2 1

The value of the critical pressure differs by 40 kPa from the two other available values from the group of Kay, and is based in part on the vapor pressure data of Shah et al.14 Additional measurements of the vapor pressure at temperatures near the critical point are needed to reduce the uncertainty given above. The selected triple-point temperature is 179.7 K, as reported by Douslin and Huffman15 and Aston et al.16 The molar mass is 70.1329 g/mol, which was calculated from the atomic weights of the elements given by Wieser and Berglund.17 4.2. Equation of State. The equation of state expressed in a fundamental form explicit in the Helmholtz energy has become the most widely used method for calculating thermodynamic properties with high accuracy for many fluids. The independent variables in the functional form are density and temperature, a ( ρ , T ) = a 0 (ρ , T ) + a r (ρ , T )

α0 =

γk

εk

0.86 0.85 0.86 1.53 5.13

0.63 2.8 0.5 0.95 0.23

1.22 0.32 0.22 1.94 1.21

0.684 0.7 0.77 0.625 0.42

h00τ s0 δτ τ − 0 − 1 + ln 0 − RTc R δ0τ R

∫τ

τ

cp0

0

cp0 τ2

dτ

dτ

τ

0

∫τ

τ

(6)

T0, ρ0, h00,

where δ0 = ρ0/ρc, τ0 = Tc/T0, and and are used to define an arbitrary reference state point. The equation (developed here) for the ideal-gas heat capacity is given by cp0 R

4

= c0 +

s00

exp(uk /T ) ⎛ uk ⎞2 ⎜ ⎟ ⎠ T [exp(uk /T ) − 1]2

∑ vk⎝ k=1

(7)

where the molar gas constant, R, is 8.3144621 J·mol−1·K−1. The coefficients of eq 7 are c0 = 4.0, v1 = 1.34, v2 = 13.4, v3 = 17.4, v4 = 6.65, u1 = 230 K, u2 = 1180 K, u3 = 2200 K, and u4 = 5200 K. A more convenient form of the ideal-gas Helmholtz energy, derived from the integration of eq 6 and the application of a reference state with zero enthalpy and entropy at the normal boiling point for the saturated liquid, is

(3)

α 0 = a1 + a 2τ + ln δ + (c0 − 1) ln τ 4

+

2

∑ vk ln[1 − exp(−ukτ /Tc)] k=1

(4)

(8)

where a1 = −0.3946233253 and a2 =2.4918910143. The functional form for the residual Helmholtz energy is

In practical applications, the functional form is the dimensionless Helmholtz energy α as a function of a dimensionless density and temperature, a(ρ , T ) = α(δ , τ ) = α 0(δ , τ ) + α r(δ , τ ) RT

βk

1 + R

where a is the Helmholtz energy, a0 is the ideal-gas contribution to the Helmholtz energy, and ar is the residual Helmholtz energy that results from intermolecular forces. All thermodynamic properties can be calculated as derivatives of the Helmholtz energy. For example, the pressure derived from this expression is ⎛ ∂a ⎞ p=ρ ⎜ ⎟ ⎝ ∂ρ ⎠T

ηk

5

α r(δ , τ ) =

10

∑ Nkδ d τ t k

k=1

k

+

∑ Nkδ d τ t k

k

exp( − δ lk)

k=6 15

(5)

+

where δ = ρ/ρc and τ = Tc/T. The ideal-gas Helmholtz energy is given in a dimensionless form by

∑

Nkδ dkτ tk exp(− ηk (δ − εk)2 − βk (τ − γk)2 )

k = 11

(9)

The coefficients and exponents of eq 9 are given in Table 3. C



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Table 4. Summary and Comparisons of Experimental Data reference PVT Brazier and Freeman (1969) Garcia Baonza et al. (1993) Kuss and Taslimi (1970) Second Virial Coefficientsc Ewing et al. (1970) Garcia Baonza et al. (1993) Marsh (1970) McCullough et al. (1959) Saturated-Liquid Density other data sets Garcia Baonza et al. (1993) Harris et al. (2004) Khalilov (1962) Pereiro et al. (2004) Vapor Pressure other data sets Aston et al. (1943) Machat and Boublik (1985) Marsh (1970) Mokbel et al. (1995) Shah et al. (1991) Willingham et al. (1945) Heat of Vaporization Aston et al. (1943) McCullough et al. (1959) Ideal-Gas Isobaric Heat Capacity McCullough et al. (1959) Isobaric Heat Capacity Aston et al. (1943) Douslin and Huffman (1946) Jacobs and Parks (1934) McCullough et al. (1959) Szasz et al. (1947) Speed of Sound this work Pereiro et al. (2004) Romero et al. (2006) Takagi et al. (1957) c

pressure range (MPa)

density range (mol·dm−3)

AAD (%)

10.5 to 13 10.6 to 12.3 9.81 to 12

0.72 0.06 0.34

no. points

temp. range (K)

10 199 24

303 193 to 298 298 to 353

3 32 3 3

288 to 308 193 to 353 291 to 308 298 to 322

140 38 5 16 5

175 to 322 189 to 302 278 to 298 293 to 514 293 to 313

81 11 9 3 23 15 11

193 to 374 226 to 287 281 to 320 291 to 308 205 to 343 277 to 493 289 to 323

3 3

295 298 to 322

2.33 0.03

3

329 to 463

0.36

19 16 15 6 13

184 to 291 186 to 300 186 to 294 329 to 463 180 to 299

0.101 0.101 0.101 0.042 to 0.101 0.101

0.65 0.10 0.67 0.12 0.12

42 5 3 142

258 to 353 293 to 313 283 to 313 283 to 343

0.1 to 30.2

0.01 0.17 0.19 0.12

0.1 to 450 0.07 to 104 0.098 to 196

0.96 37.9 0.74 5.0 10.2 to 12.1 10.5 to 12 10.6 to 10.8 5.13 to 10.7 10.3 to 10.6 0 to 0.421 0.001 to 0.027 0.02 to 0.093 0.032 to 0.062 0 to 0.192 0.017 to 3.53 0.029 to 0.104

0.549 to 19.7

0.13 0.05 0.05 3.65 0.13 0.91 0.77 0.06 0.01 0.32 0.75 0.05

The AAD for the second virial coefficients is given in cm3·mol−1.

The functions used for calculating pressure, compressibility factor, internal energy, enthalpy, entropy, Gibbs energy, isochoric heat capacity, isobaric heat capacity, and the speed of sound from eq 5 are given in a number of various publications, such as Span1 and Lemmon et al.,18 and will not be repeated here. These publications also give the derivatives of the Helmholtz energy equation of state required to calculate these thermodynamic properties. This new equation for cyclopentane will be implemented in the Refprop program, and will replace the preliminary formulation available in version 9.1.19

5. EXPERIMENTAL DATA AND COMPARISONS TO THE EQUATIONS OF STATE

Figure 1. Comparisons of ideal-gas isobaric heat capacities cp0 calculated with the equation of state to experimental and predicted data as a function of temperature T.

The units adopted for this work are Kelvin (ITS-90) for temperature, megapascal for pressure, and moles per cubic decimeter for density. Units of the experimental data were converted as necessary from those of the original publications to these units. Where necessary, temperatures reported on IPTS-68

and IPTS-48 were converted to the International Temperature Scale of 1990 (ITS-90).20 D



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Figure 2. Comparisons of densities ρ calculated with the equation of state to experimental data as a function of pressure p. Figure 5. Comparisons of vapor pressures pσ calculated with the equation of state to experimental data as a function of temperature T.

Figure 3. Comparisons of second virial coefficients B calculated with the equation of state to experimental data as a function of temperature T. Figure 6. Comparisons of isobaric heat capacities cp calculated with the equation of state to experimental data as a function of temperature T.

Figure 4. Comparisons of saturated-liquid densities ρ′ calculated with the equation of state to experimental data as a function of temperature T.

Figure 7. Comparisons of speeds of sound w calculated with the equation of state to experimental data as a function of temperature T.

Often, only selected data from among the available data are used in fitting, although comparisons are made to all available experimental data, including those not used in the development of the equation of state, to estimate the uncertainties in the equations (where the uncertainties can be considered as estimates of a combined expanded uncertainty with a coverage factor of 2). These values are determined by statistical comparisons of property values calculated from the equation of state to experimental data. The deviation in any property X is defined here as ⎛ X − Xcalc ⎞ %ΔX = 100⎜ data ⎟ Xdata ⎝ ⎠

AAD =

1 n

n

∑ |%ΔXi| i=1

(11)

where n is the number of data points. The AAD between experimental data and the equation of state are given in Table 4. The deviations between the equation of state and the experimental data are given in Figures 1 to 7. Data points shown at the upper or lower vertical limits of the graph indicate that the point is off scale. Much of the data reported here was obtained from the Thermodynamic Data Engine (TDE) program (Frenkel et al.21) available from the Thermodynamic Research Center (TRC) of NIST. There are approximately 160 additional data sets, each of

(10)

and the average absolute deviation is defined as E



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Table 5. Calculated Values of Properties from the Equation of State To Verify Computer Code T/K

p/MPa

ρ/(mol·dm−3)

cv/(J·mol−1·K−1)

cp/(J·mol−1·K−1)

w/(m·s−1)

330 330 530 512 520

0.02720379 75.55974 3.240235 4.601539 6.522373

0.01 11.0 1.0 4.0 6.0

86.25843 100.6003 156.4924 161.5786 159.2304

94.88857 130.5568 187.7243 22857.91 276.7530

205.6768 1471.842 195.4293 113.0171 234.2660

0.25 % above 240 K. Below 240 K, the scatter in the available data, including Aston et al. and Mokbel et al.,32 increases quickly due to the values of the low vapor pressures for this fluid. Fitting these data caused the errors in the values of cp and cp0 to increase, and they were thus not included in the fit. The data of Shah et al.14 are the only data above 340 K, but are scattered and were not much help in the development of the equation of state. Four data sets are available for the isobaric heat capacity in the liquid phase, as shown in Figure 6. These data of Jacobs and Parks,33 Szasz et al.,34 and Douslin and Huffman15 are quite consistent. The equation fits all but the data of Aston et al.16 and Jacob and Parks to within 0.5%. The Aston et al. data agree on average within 1%. In the vapor phase, only the data of McCullough et al.22 are available, with an agreement of 0.3% as compared to the equation of state. Only two of the data sets for speed of sound extend to pressures greater than 1 bar. These are the data reported here and those of Takagi et al.8 Our measurements were fitted to within 0.035 %, with an AAD of 0.011 %. The data of Takagi et al. agree at the lower temperature end as shown in Figure 7, but the differences increase at higher temperatures with a maximum of 0.38 %. The equation deviates from the low pressure data of Pereiro et al. and Romero et al.35 by 0.15 %.

which reports only one to three data points; these data were not included in this work unless the points were important to the development of the equation of state. However, these extra measurements are shown in the figures and are labeled as “Other data sets”. Estimated values for the ideal-gas heat capacities, obtained from the TRC database with expanded uncertainties of 1 %, were used to fit the initial cp0 equation because experimental data were not available. During the fitting process (which fitted cp0 and αr simultaneously), the available liquid-phase heat-capacity and speed of sound data could be fitted well only if the estimated ideal-gas heat-capacity values were given low weights, resulting in deviations of about 1.5% in cp0 at 300 K and a maximum of 2.4 % at 250 K, as shown in Figure 1. The ideal-gas heat-capacity data from McCullough et al.22 were located after the fit was finished, and these data confirmed the larger deviations in the estimated cp0 values from the TRC database between (200 and 500) K. There are three available sets of pressure−density−temperature data available for cyclopentane that cover a wide range of pressure, as shown in Figure 2. The data of Garcia Baonza et al.23 cover the largest area, from temperatures of (193 to 298) K with pressures to 104 MPa. These data were fitted to within 0.1 % in density. The data of Kuss and Taslimi24 overlap the Garcia Baonza et al. data at 298 K and extend the measurements up to 353 K. At 298 K, the data sets agree at 40 MPa (the lower limit of the Kuss and Taslimi data), but differ with increasing deviations as the pressure increases. Near this same temperature, data from Brazier and Freeman25 differ by + 0.25 % up to + 1 %. Figure 3 shows comparisons with the second virial coefficients and the wide range of differences between the various data sets. The fit shows good agreement with the data of Ewing et al.26 Additional data for the saturated-liquid phase of cyclopentane further helped to verify the validity of the data from Garcia Baonza et al. A significant amount of data as shown in Figure 4 between (270 and 315) K shows extremely good agreement with the equation of state, generally within 0.05 %, such as the data of Harris et al.,26 and to a lesser extent the data of Pereiro et al.27 Two additional sets extend outside this temperature range. The data of Garcia Baonza et al. extend down to 190 K with deviations within 0.1 %. The data of Khalilov28 are in sharp disagreement with other data (greater than 1 %) where the data overlap, and the deviations from the equation of state rise quickly as the temperature increases to the critical point. The upper temperature limit of these saturated data is 3 K above the critical point of cyclopentane. Data for the saturated-vapor phase are not available. Figure 5 shows the six data sets with more than three data points available for the vapor pressure of cyclopentane, in addition to other points available from TRC. The most consistent data are those from Willingham et al.,29 Machat and Boublik,30 Marsh,31 and the additional data from TRC. In the region where these data overlap, from (280 to 323) K, the data and the equation of state all agree to within about 0.05 %. The data of Aston et al.16 at lower temperatures show deviations of

6. CONCLUSIONS The expanded uncertainties in density of the equation of state reported here range from 0.2 % in the liquid (for temperatures up to 300 K) to 1% or more above the critical temperature. The upper uncertainty value needs to be validated by new measurements of the density. The uncertainty in heat capacities is 1 %, and the uncertainty in vapor pressure is 0.5 % (possibly as low as 0.1% between (290 and 323) K). The low uncertainty in the speed of sound in the liquid phase is 0.2 % at temperatures from (258 to 353) K due to new measurements presented in this work. In the critical region, the uncertainties are higher for all properties except vapor pressure. The equation of state is valid from the triple-point temperature of 179.7 K to temperatures of 550 K with pressures to 250 MPa. The upper temperature limit is most likely within the region where cyclopentane begins to decompose (Ambrose and Grant13), and far above all measured values, but the equation should extrapolate well due to multiple constraints used in fitting to control the derivatives of various constant-property lines. As an aid to computer implementation, calculated values of properties from the equation of state are given in Table 5. The number of digits displayed does not indicate the accuracy in the values but is given only for validation of computer code.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

§ M.J.D.: Department of Geology, Faculty of Biology, University of Duisburg-Essen, Universitätsstraße 5, 45141 Essen, Germany.

F



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Temperatures from the Melting Line to 650 K and Pressures up to 1000 MPa. J. Chem. Eng. Data 2009, 54, 3141−3180. (19) Lemmon, E. W.; Huber, H. L.; McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, version 9.1. National Institute of Standards and Technology, Standard Reference Data Program: Gaithersburg, MD, 2013. (20) Preston-Thomas, H. The International Temperature Scale of 1990 (ITS-90). Metrologia 1990, 27, 3−10. (21) Frenkel, M.; Chirico, R. D.; Diky, V.; Muzny, C. D.; Kazakov, A. F.; Lemmon, E. W. NIST Standard Reference Database 103b: ThermoData Engine (TDE), version 3.0. National Institute of Standards and Technology, Standard Reference Data Program: Gaithersburg, MD, 2008. (22) McCullough, J. P.; Pennington, R. E.; Smith, J. C.; Hossenlopp, I. A.; Waddington, G. Thermodynamics of Cyclopentane, Methylcyclopentane and 1,cis-3-Dimethylcyclopentane + Verification of the Concept of Pseudorotation. J. Am. Chem. Soc. 1959, 81, 5880−5883. (23) Garcia Baonza, V.; Caceres Alonso, M.; Nunez Delgado, J. Study of the Equation of State of Liquid 2,3-Dimethylbutane at High Pressures. J. Phys. Chem. 1993, 97, 2002−2008. (24) Kuss, E.; Taslimi, M. p,V,T-Measurements on Twenty Organic Liquids. Chem. Ing. Technol. 1970, 42, 1073−1081. (25) Brazier, D. W.; Freeman, G. R. The Effects of Pressure on the Density, Dielectric Constant, and Viscosity of Several Hydrocarbons and Other Organic Liquids. Can. J. Chem. 1969, 47, 893−899. (26) Harris, K. R.; Newitt, P. J.; Woolf, L. A. Temperature and Density Dependence of the Viscosity of Cyclopentane. J. Chem. Eng. Data 2004, 49, 138−142. (27) Pereiro, A. B.; Rodriguez, A.; Canosa, J.; Tojo, J. Density, Viscosity, and Speed of Sound of Dialkyl Carbonates with Cyclopentane and Methyl Cyclohexane at Several Temperatures. J. Chem. Eng. Data 2004, 49, 1392−1399. (28) Khalilov, Kh. M. Viscosity of Isooctane, Cyclohexane, Cyclopentane and their Saturated Vapor-Pressures. Russ. J. Phys. Chem. 1962, 36, 1341−1342. (29) Willingham, C. B.; Taylor, W. J.; Pignocco, J. M.; Rossini, F. D. Vapor Pressures and Boiling Points of Some Paraffin, Alkylcyclopentane, Alkylcyclohexane, and Alkylbenzene Hydrocarbons. J. Res. Natl. Bur. Stand. 1945, 35, 219−244. (30) Machat, V.; Boublik, T. Vapour−Liquid Equilibrium and Excess Molar Volume of (Trans-1,2-dichloroethene + Cyclopentane) at 293.15 K. J. Chem. Thermodyn. 1985, 17, 887−891. (31) Marsh, K. N. Enthalpies of Mixing and Excess Gibbs Free Energies of Mixtures of Octamethylcyclotetrasiloxane + Cyclopentane at 291.15, 298.15, and 308.15 K. J. Chem. Thermodyn. 1970, 2, 359−365. (32) Mokbel, I.; Rauzy, E.; Loiseleur, H.; Berro, C.; Jose, J. Vapor Pressures of 12 Alkylcyclohexanes, Cyclopentane, Butylcyclopentane and Trans-Decahydronaphthalene down to 0.5 Pa. Experimental Results, Correlation and Prediction by an Equation of State. Fluid Phase Equilib. 1995, 108, 103−120. (33) Jacobs, C. J.; Parks, G. S. Thermal Data on Organic Compounds. XIV. Some Heat Capacity, Entropy and Free Energy Data for Cyclic Substances. J. Am. Chem. Soc. 1934, 56, 1513−1517. (34) Szasz, G. J.; Morrison, J. A.; Pace, E. L.; Aston, J. G. Thermal Properties of Cyclopentane and Its Use as a Standard Substance in Low Temperature Thermal Measurements. J. Chem. Phys. 1947, 15, 562− 564. (35) Romero, C. M.; Guzman, C.; Gascon, I.; Cea, P.; Lopez, M. C. Speeds of Sound and Isentropic Compressibilities for Binary Mixtures of a Cyclic Diether with a Cyclic Compound at Three Temperatures. Int. J. Thermophys. 2006, 27, 760−776.

The authors are grateful to the Ministerio de Educación y Ciencia (Spain) for the financial support granted to M. J. Dávila and to R. Span. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Mostafa Salehi aided us in the retrieval and entry of data obtained from the literature and used in this work to fit the equation of state.

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REFERENCES

(1) Span, R. Multiparameter Equations of StateAn Accurate Source of Thermodynamic Property Data; Springer: Berlin, 2000. (2) Trusler, J. P. M. Physical Acoustic and Metrology of Fluids; Adam Hilger: Bristol, 1991. (3) Certain trade names and products are identified only to document the experimental equipment and procedure. This does not constitute a recommendation or endorsement of these products, nor does it imply that the products are necessarily the best available for the purpose. (4) Gedanitz, H.; Dávila, M. J.; Baumhögger, E.; Span, R. An Apparatus for the Determination of Speeds of Sound in Fluids. J. Chem. Thermodyn. 2010, 42, 478−483. (5) Gedanitz, H. Schallgeschwindigkeits- und Dichtemessungen in Fluiden. (Sound velocity and density measurements in fluids.) Ph.D. Dissertation, Ruhr-Universität Bochum, 2010. (6) Meier, K.; Kabelac, S. Speed of Sound Instrument for Fluids with Pressures up to 100 MPa. Rev. Sci. Instrum. 2006, 77, 123903. (7) Sun, T.; Schouten, J. A.; Biswas, S. N. Determination of the Thermodynamic Properties of Liquid Ethanol from 193 to 263 K and up to 280 MPa from Speed of Sound Measurements. Int. J. Thermophys. 1991, 12, 381−395. (8) Takagi, T.; Sakura, T.; Guedes, H. J. R. Speed of Sound in Liquid Cyclic Alkanes at Temperatures between (283 and 343) K and Pressures up to 20 MPa. J. Chem. Thermodyn. 2002, 34, 1943−1957. (9) Alekhin, A. D.; Krupskii, N. P.; Minchenko, Yu. B. Temperature Dependence of the Isothermal Compressibility of Cyclopentane near the Liquid−Vapor Critical Point (in Russian). Ukr. Fiz. Zh. (Russ. Ed.) 1970, 15, 509−10. (10) Ambrose, D.; Grant, D. G. The Critical Temperatures of Some Hydrocarbons and Pyridine Bases. Trans. Faraday Soc. 1957, 53, 771− 778. (11) Christou, G. Critical Properties of Binary Mixtures. Ph.D. Dissertation, University of Melbourne, Australia, 1988. (12) Kay, W. B. Vapor Pressures and Saturated Liquid and Vapor Densities of Cyclopentane, Methylcyclopentane, Ethylcyclopentane and Methylcyclohexane. J. Am. Chem. Soc. 1947, 69, 1273−1277. (13) Kay, W. B.; Hissong, D. W. The Critical Properties of Hydrocarbons I. Simple Mixtures. Proc. Am. Pet. Inst., Div. Refin. 1967, 47, 653−722. (14) Shah, N. N.; Zollweg, J. A.; Streett, W. B. Vapor−Liquid Equilibrium in the System Carbon Dioxide + Cyclopentane from 275 to 493 K at Pressures to 12.2 MPa. J. Chem. Eng. Data 1991, 36, 188−192. (15) Douslin, D. R.; Huffman, H. M. The Heat Capacities, Heats of Transition, Heats of Fusion and Entropies of Cyclopentane, Methylcyclopentane, and Methylcyclohexane. J. Am. Chem. Soc. 1946, 68, 173−176. (16) Aston, J. G.; Fink, H. L.; Schumann, S. C. The Heat Capacity and Entropy, Heats of Transition, Fusion and Vaporization and the Vapor Pressures of Cyclopentane. Evidence for a Non-planar Structure. J. Am. Chem. Soc. 1943, 65, 341−346. (17) Wieser, M. E.; Berglund, M. Atomic Weights of the Elements 2007. Pure Appl. Chem. 2009, 81, 2131−2156. (18) Lemmon, E. W.; McLinden, M. O.; Wagner, W. Thermodynamic Properties of Propane. III. A Reference Equation of State for G


Speed of Sound Measurements and a Fundamental Equation of State

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