Thermodynamic Properties of R-227ea, R-365mfc ... - ACS Publications

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Thermodynamic Properties of R‑227ea, R‑365mfc, R‑115, and R-13I1 Eric W. Lemmon*,† and Roland Span‡ †

Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, United States ‡ Thermodynamics, Ruhr-Universität Bochum, Universitätsstraße 150, 44801 Bochum, Germany S Supporting Information *

ABSTRACT: Equations of state are presented for the refrigerants 1,1,1,2,3,3,3-heptafluoropropane (R-227ea) and 1,1,1,3,3-pentafluorobutane (R-365mfc). For R-227ea, the uncertainties in densities are 0.05 % in the liquid region up to 360 K, 0.3 % in the vapor phase, and 0.5 % in the supercritical region. For vapor pressures, the uncertainties are 0.1 % above 270 K and 0.4 % between 240 K and 270 K (with the higher value at the lower temperature). The uncertainty in heat capacities is 1 % (with increasing uncertainties in the critical region and at high temperatures). For sound speeds, the uncertainties are 0.05 % in the vapor phase up to pressures of 0.5 MPa and 0.03 % in the liquid phase between 280 K and 420 K. For R-365mfc, the uncertainties in densities of the equation of state range from 0.1 % in the liquid to 1 % near the critical point, and the uncertainty in the speeds of sound is 0.05 %. The uncertainty in heat capacities is 2 %, and the uncertainty in vapor pressures is 0.25 % at temperatures between 280 K and 360 K. In the critical region, the uncertainties are higher for all properties. Equations of state for trifluoroiodomethane (R-13I1) and chloropentafluoroethane (R-115) are also given in an appendix for applications where systems using these banned substances are being upgraded or replaced with modern refrigerants, and properties of the old working fluids are needed in the design of the new system.

1. INTRODUCTION The equations for 1,1,1,2,3,3,3-heptafluoropropane (R-227ea, CAS no. 431-89-0) and 1,1,1,3,3-pentafluorobutane (R-365mfc, CAS no. 406-58-6) presented here are part of a larger project to develop equations of state for a wide number of industrial fluids. The work of Lemmon and Span1 presented equations based on a fixed functional form for acetone, carbon monoxide, carbonyl sulfide, decane, hydrogen sulfide, 2-methylbutane (isopentane), 2,2-dimethylpropane (neopentane), 2-methylpentane (isohexane), krypton, nitrous oxide, nonane, sulfur dioxide, toluene, xenon, hexafluoroethane (R-116), 1,1-dichloro-1-fluoroethane (R-141b), 1-chloro-1,1-difluoroethane (R-142b), octafluoropropane (R-218), 1,1,1,3,3-pentafluoropropane (R-245fa), and fluoromethane (R-41). A preliminary equation for R-227ea was originally developed as part of that work, but a significant amount of data was available to allow for a functional form with more fluid specific terms and increased accuracy, and thus the equation no longer resided in the scope of that work and will be presented here. For R-365mfc, data became available after the publication of that work, although they are still limited in range. The appendix gives equations of state for trifluoroiodomethane (R-13I1, CAS no. 2314-97-8) and chloropentafluoroethane (R-115, CAS no. 76-15-3). (An appendix is used because these substances are now banned and are not generally in use in new equipment.) All of the experimental data available for these fluids are given in refs 2−66. © 2015 American Chemical Society

The four equations presented have been available since version 8.0 of the REFPROP program [the current version is 9.1 (Lemmon et al.67)], but do not have a formal publication that explains the details of the equation. This work gives those details and reports the coefficients of the equations as given in versions 8.0, 9.0, and 9.1 of REFPROP. There are still applications where R-115 or R-13I1 are used, and properties are needed to either upgrade systems or to design new systems with more environmentally friendly fluids that are now available, but with similar properties as those of the older fluids. The thermodynamic properties of fluids can be modeled through the use of equations that cover the liquid, vapor, and supercritical regions of the compound, as well as states in the 2-phase region. 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. All single-phase thermodynamic properties can be calculated as functions of temperature and density from these equations by combining derivatives of the Helmholtz energy. The calculation of saturation boundaries requires an iterative solution of the physical constraints on saturation (the Maxwell criterion, i.e., Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: August 10, 2015 Accepted: November 5, 2015 Published: November 30, 2015 3745

DOI: 10.1021/acs.jced.5b00684 J. Chem. Eng. Data 2015, 60, 3745−3758

Journal of Chemical & Engineering Data

Article

vary widely between sources. The critical density is particularly difficult to determine accurately by experiment because of the infinite compressibility at the critical point. The values of the critical parameters below must be used for all property calculations from the equations of state reported here. The critical temperature for R-227ea was taken from Fröba et al.19 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 for R-227ea are

equal pressures and Gibbs energies at constant temperature during phase changes), as is required with any form of the equation of state for thermodynamic consistency. Iterative solutions are also required in cases in which different independent variables, for example, temperature and pressure or pressure and entropy, are used. Over the past 20 years, many of the older industrial equations of state for fluids such as nitrogen, carbon dioxide, R-134a, and water (about 30 in total) have been replaced with high-accuracy fundamental equations of state developed from fitting state-ofthe-art experimental measurements for density, vapor pressure, heat capacities, and speed of sound. The most recent of these fluids available at the time of development of the equations for the fluids presented here was the equation for propane (Lemmon et al.68); other equations have been outlined by Span et al.69 and Lemmon and Jacobsen.70 Most of the 30 fluids are fully characterized over the entire fluid surface by measurements, quite often with multiple publications for a single property over similar ranges of temperature and pressure. Lemmon and Span71 and Span et al.69 reviewed the development and history of these equations. Quite often state-of-the-art measurements are not available over all liquid and vapor states (including states in the critical region or at high temperatures and pressures) for pure fluids. Unlike high accuracy equations, which generally use 15 to 50 fluid-specific terms to describe densities to the order of (0.01 to 0.1) %, and where the terms in the equations are not fixed beforehand, equations with semifixed functional forms can be used to characterize the properties of fluids with limited data. (A fixed functional form means that the number of terms and the temperature and density exponents are the same in an equation for a particular fluid, and only the coefficients are fitted; a semifixed form is similar, except that the temperature exponents are additionally fitted.) Previous work (Lemmon and Span1) was based on the work presented by Span and Wagner,72 which used two 12-term fundamental equations with fixed functional formsone for nonpolar or slightly polar substances, and one for polar fluids. Their equations extrapolate properly at low temperatures (as demonstrated by the curvature of the isobaric and isochoric heat capacities, and the speed of sound), and at high temperatures (as demonstrated by the ideal curves). In addition, the number of terms in the equations (12 each) was kept to a minimum, thus decreasing the correlation among terms and the possibility of overfitting. These forms were used here for the R-115 and R-13I1 equations. The equations of Span and Wagner72 were used in a first attempt to fit the experimental data for R-227ea and R-365mfc. However, because of the amount of data available for these fluids, and possibly because of their polarity, the fixed functional forms were not fully able to characterize the measured values. Further fitting revealed that the functional form used in the propane equation of state68 had enough flexibility to fit these new fluids, and this form was subsequently used as the initial starting point, although the number of terms was reduced slightly for R-365mfc because of a lack of sufficiently accurate data in the critical region.

Tc = 374.9 K ± 0.1 K ρc = 3.495 mol ·dm−3 ± 0.1 mol · dm−3

pc = 2.925 MPa ± 0.01 MPa

When the equation for R-365mfc was developed, the critical point had not been measured and was thus fitted simultaneously with the other coefficients and exponents of the equation of state. This was possibly due to the very accurate single-phase criticalregion measurements of McLinden.41 The resulting values are Tc = 460.0 K ± 0.2 K

ρc = 3.2 mol· dm−3 ± 0.2 mol· dm−3 pc = 3.266 MPa ± 0.1 MPa

In 2010, Soo et al.73 published results for the critical temperature and pressure for R-365mfc; these values are 459.91 K and 3.20 MPa. The results of Soo et al. agree with our values within the combined uncertainty and give good confidence in the singlephase density data reported by McLinden.41 The selected triple-point temperatures are 146.35 K for R-227ea as reported by Beyerlein et al.,5 and 239 K for R-365mfc (McLinden41). The molar masses are 170.02886 g·mol−1 for R-227ea and 148.07452 g·mol−1 for R-365mfc, which were calculated from the atomic weights of the elements given by Wieser and Berglund.74 2.2. Equation of State. The equations of state presented in this article are explicit in the Helmholtz energy. The independent variables in this functional form are density and temperature, a ( ρ , T ) = a 0 (ρ , T ) + a r (ρ , T )

(1) 0

where a is the Helmholtz energy, a (ρ,T) is the ideal-gas contribution to the Helmholtz energy, and ar(ρ,T) 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 = ρ2 ⎜ ⎟ ⎝ ∂ρ ⎠T

(2)

In practical applications, the functional form is the dimensionless Helmholtz energy α as a function of dimensionless density and temperature. The form of this equation is

2. FUNCTIONAL FORM OF THE EQUATION OF STATE 2.1. Critical and Triple Points. The values of temperature and density at the critical point are two of the most important parameters required in the development of equations of state, especially in equations such as those of this work. However, measurements of the critical point are scarce for many fluids and

a(ρ , T ) = α(δ , τ ) = α 0(δ , τ ) + α r(δ , τ ) RT

(3)

where δ = ρ/ρc, τ = Tc/T, and the subscript c refers to the values at the critical point. 3746



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2.3. Properties of the Ideal Gas. The ideal-gas Helmholtz energy given in a dimensionless form can be written as α0 =

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

1 R

∫τ

0 τ cp

0

τ

∫τ

τ

0

dτ

cp0 τ

2

Table 1. Parameters in the Ideal-Gas Isobaric Heat-Capacity Equations for R-227ea and R-365mfc

dτ

c0 v1 u1 v2 u2 a1 a2

(4)

where cp0 is the ideal-gas isobaric heat capacity, δ0 = ρ0/ρc, and τ0 = Tc/T0. The values of T0 and p0 are arbitrary constants, and ρ0 is the ideal-gas density at T0 and p0, ρ0 = p0/(T0R). The values for h00 and s00 are chosen based on common convention in a particular industry or according to the recommendations of the International Union for Pure and Applied Chemistry (IUPAC). For the refrigerants reported here, the enthalpy and entropy of the saturated-liquid state at 0 °C are, respectively, set to 200 kJ·kg−1 and 1 kJ·kg−1·K−1. For hydrocarbons, the enthalpy and entropy are often set to zero for the liquid at the normal boiling point. Other industries use a similar convention setting the enthalpy and entropy to zero at −40 °C. The calculation of thermodynamic properties from the idealgas Helmholtz energy requires an equation for the ideal-gas isobaric heat capacity, cp0. These values can be obtained from heat-capacity or speed-of-sound measurements extrapolated to zero pressure, or from calculations with statistical methods based on spectroscopically determined frequencies of internal vibrations. For the fluids presented here, little information is available on the heat capacity, especially at temperatures outside the range (250 to 350) K. However, values calculated from statistical techniques are available from Marsh et al.75 for temperatures from (50 to 5000) K. For both fluids, the same functional form was used to describe the ideal-gas isobaric heat capacity, namely, cp0 R

2

= c0 +

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

∑ νk⎝ k=1

α r (δ , τ ) =

k

k

+

5 r

α (δ , τ ) =

∑ Nkδ d τ t k

k

exp( −δ lk)

(7)

∑ Nkδ k=1

11 dk tk

τ +

∑ Nkδ d τ t k

k

exp( −δ lk)

k=6

m

+

∑ k = 12

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

(8)

where m is 18 for R-227ea and 15 for R-365mfc. The coefficients and exponents of the residual part of the equation of state are given in Table 2. 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 are given in various publications, such as Lemmon et al.,68 Span and Wagner,72 Span,77 or Wagner and Pruss,79 and will not be repeated here. These publications also give the derivatives of the Helmholtz energy equation of state required to calculate thermodynamic properties. Ancillary equations for saturation properties are given in Appendix B. 2.5. Fitting Procedures. In the development of equations of state, various data types are useful in evaluating other types of data. Since one equation is used to represent multiple properties, the accuracy of one property can influence the behavior of another. In particular, the availability of speedof-sound and heat-capacity data in addition to density and vapor pressure is essential in equation of state development. Without them, equations can inadvertently give negative heat capacities at low temperatures or show unrealistic curvature. Although the amount of data for a fluid may be limited, even a few values in the liquid phase can often be sufficient to tie down the equation of state. A well behaved equation is validated by plotting various properties over the surface of state, and by comparing the slopes of constant property lines (e.g., isotherms, isobars, etc.) to expected behavior. Good extrapolation behavior of the functional form at low and high temperatures, pressures, and densities gives confidence in the equation of state in the absence of highly accurate experimental data.

(5)

2 k=1

∑ Nkδ d τ t

where each summation typically contains 4 to 20 terms, and where the index k points to each individual term (see Span,77 Span et al.69). Although the values of dk, tk, and lk are arbitrary, the tk should be greater than zero, and dk and lk are integers greater than zero. Equations of state can also contain Gaussian-bell-shaped terms as described by Span and Wagner.78 These terms aid in the correlation of fluid properties in the critical region. The functional form used for the two refrigerants is

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

∑ vk ln[1 − exp(−ukτ /Tc)]

R-365mfc 4.0 17.47 569.0 K 16.29 2232 K −16.3423704513 10.2889710846

A common functional form used for the residual Helmholtzenergy equation of state is

where the molar gas constant, R, is 8.3144621 J·mol−1·K−1 (Mohr et al.76). The Plank-Einstein function in this equation containing the coefficients uk was used so that the temperature dependence of the ideal-gas isobaric heat capacity would be similar to that derived from statistical methods. However, the uk are empirical coefficients and should not be confused with the vibrational frequencies. The ideal-gas Helmholtz energy equation, derived from eqs 4 and 5, is

+

R-227ea 4.0 11.43 403.0 K 12.83 1428 K −15.8291124137 11.0879509962

(6)

where a1 and a2 were calculated to correspond to the reference state defined above. The coefficients are given in Table 1. 2.4. Properties of the Real Fluid. The residual behavior of the real fluid is described with empirical models that are only loosely tied to theoretical methods such as the second and thirdvirial coefficients. The models are consistent with current knowledge on fluid-phase thermodynamic behavior, except in the asymptotic critical region; however, the coefficients of the equations depend mostly on the experimental data representing the thermodynamic properties of the considered fluid. 3747



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Table 2. Parameters of the Equations of State for R-227ea and R-365mfc k

Nk

tk

dk

2.024341 −2.605930 0.4957216 −0.8240820 0.06543703 −1.024610 0.6247065 0.2997521 −0.3539170 −1.232043 −0.8824483 0.1349661 −0.2662928 0.1764733 0.01536163 −0.004667185 −11.70854 0.9114512

0.34 0.77 0.36 0.9 1.0 2.82 2.1 0.9 1.13 3.8 2.75 1.5 2.5 2.5 5.4 4.0 1.0 3.5

1 1 2 2 4 1 3 6 6 2 3 1 2 1 1 4 2 1

2.20027 −2.86240 0.384559 −0.621227 0.0665967 −1.19383 0.635935 0.461728 −0.533472 −1.07101 0.139290 −0.385506 0.885653 0.226303 −0.166116

0.24 0.67 0.5 1.25 1.0 3.35 2.5 0.96 1.07 5.6 6.9 3.0 3.6 5.0 1.25

1 1 2 2 4 1 3 6 6 2 3 1 1 1 2

lk

ηk

βk

γk

εk

0.83 2.19 2.44 3.65 8.88 8.23 2.01

1.72 5.20 2.31 1.02 5.63 50.9 1.56

0.414 1.051 1.226 1.700 0.904 1.420 0.926

1.13 0.71 1.20 1.70 0.546 0.896 0.747

0.97 0.94 2.15 2.66

1.07 1.08 10.9 22.6

1.48 1.49 1.01 1.16

1.02 0.62 0.53 0.48

R-227ea 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 1 1 1 2 2

R-365mfc 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

1 1 1 1 2 2

3. EXPERIMENTAL DATA AND COMPARISONS TO THE EQUATIONS OF STATE The units adopted for this work were kelvins for temperature, megapascals 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) (Preston-Thomas80). 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 (whereby the stated 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

Fitting the coefficients of the equation of state is a process of correlating selected experimental data with a model that is generally empirical in nature. In this work, the equations of state use a fixed functional form that exhibits proper behavior in the ideal-gas and low-density regions, and extrapolates to temperatures and pressures higher than those defined by experiment. In all cases, experimental data are considered paramount, and the proof of validity for any equation of state is evidenced in its ability to represent the thermodynamic properties of the fluid generally within the uncertainty of the experimental values. Nonlinear fitting techniques were used to fit the coefficients of the equation. The selected data used in fitting were a subset of the available database, and were determined to be representative of the most accurate values measured. The nonlinear algorithm adjusted the coefficients of the equation of state to reduce the overall sum of squares of the deviations of calculated properties from the input data. Each data point was individually weighted according to type, region, and uncertainty. Additionally, the values of the first and second derivatives of pressure with respect to density at the critical point were forced to be near zero at the selected critical point. The final set of coefficients for each equation represents not only the fitted data, but also the consistent data available for each fluid. Additional information is given in Lemmon et al.68

⎛ Xexp − Xcalc ⎞ ⎟⎟ %ΔX = 100⎜⎜ Xexp ⎝ ⎠

(9)

and the average absolute deviation is defined as

AAD = 3748

1 n

n

∑ |%ΔXi| i=1

(10) DOI: 10.1021/acs.jced.5b00684 J. Chem. Eng. Data 2015, 60, 3745−3758


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Table 3. Summary and Comparisons of Experimental Data for R-227ea ref

no. points

R-227ea: Vapor Pressure 28 Beyerlein et al.5 Coquelet et al.7 10 Di Nicola9 27 Feng et al.18 61 Gruzdev et al.21 32 Hou and Duan23 5 Hu et al.26 145 Kim et al.31 6 Koo et al.36 2 Lee et al.37 3 Lim et al.38 2 Park et al.45 3 Salvi-Narkhede et al.49 21 Scalabrin et al.50 15 Seong et al.53 6 Shi et al.55 84 Tuerk et al.59 43 Valtz et al.61 9 Valtz et al.60 6 Wang and Duan62 72 Yun et al.65 6 R-227ea: PVT Defibaugh and Moldover8 1014 Di Nicola9 58 Fedele et al.17 300 Gruzdev et al.21 104 Hu et al.25 97 Ihmels et al.30 257 Klomfar et al.33 83 Patek et al.46 81 Scalabrin et al.50 10655 Shi et al.54 141 Tack and Bier56 50 Tang et al.58 52 R-227ea: Saturated-Liquid Density Beyerlein et al.5 7 Fedele et al.17 6 Gruzdev et al.21 13 Hu and Chen24 14 Salvi-Narkhede et al.49 8 Scalabrin et al.50 9 R-227ea: Saturated-Vapor Density Hu and Chen24 4 Salvi-Narkhede et al.49 5 R-227ea: Second Virial Coefficients Duan et al.11 20 Hu et al.25 8 Patek et al.46 2 Salvi-Narkhede et al.49 1 R-227ea: Third Virial Coefficients Duan et al.11 12 R-227ea: Ideal-Gas Isobaric Heat Capacity Benedetto et al.4 8 Wirbser et al.63 7 Zhang et al.66 10 R-227ea: Isobaric Heat Capacity Baginskii and Stankus3 52 Hykrda et al.29 62

temp. range

pressure range

density range

T/K

p/MPa

ρ/(mol·dm−3)

277 278 235 234 273 263 233 278 298 303 283 283 238 296 273 243 203 293 276 253 288

to to to to to to to to to to to to to to to to to to to to to

376 353 365 371 373 323 375 328 313 323 293 323 373 374 323 375 375 353 367 373 363

0.24 to 2.94 0.234 to 1.86 0.035 to 2.4 0.033 to 2.72 0.192 to 2.82 0.132 to 0.912 0.032 to 2.94 0.234 to 1.04 0.456 to 0.693 0.526 to 0.917 0.28 to 0.391 0.276 to 0.922 0.041 to 2.83 0.421 to 2.85 0.194 to 0.92 0.054 to 2.94 0.005 to 2.93 0.389 to 1.85 0.217 to 2.5 0.087 to 2.83 0.335 to 2.29

243 293 283 294 318 278 205 393 253 283 333 243

to to to to to to to to to to to to

368 355 333 383 380 473 316 423 403 377 398 363

0.6 to 6.5 0.215 to 0.679 0.985 to 34.6 0.407 to 3.19 0.122 to 2.83 0.916 to 30 0.652 to 52.5 0.221 to 50.8 0.093 to 22.4 0.098 to 2.45 0.331 to 52.8 0.54 to 11.5

296 283 294 327 258 253

to to to to to to

358 333 365 375 372 363

375 303 to 424

AAD/% 3.66 0.125 0.053 0.149 0.341 0.272 0.156 0.403 0.15 0.229 0.312 0.733 0.461 0.189 0.293 0.151 0.399 0.123 0.08 0.059 0.264

5.78 to 9.48 0.094 to 0.259 7.18 to 9.29 0.324 to 8.23 0.047 to 1.68 1.68 to 9.34 8.19 to 10.6 0.069 to 8.13 0.059 to 9.55 0.038 to 1.35 0.111 to 8.1 6.28 to 9.54

0.025 0.118 0.034 0.823 0.119 0.23 0.029 0.258 1.35 0.09 0.165 0.21

5.96 7.15 5.64 3.54 5.36 5.79

2.04 0.01 0.124 0.412 2.7 0.122

to to to to to to

8.12 8.52 8.23 7.35 8.95 9.15

2.8 to 3.46 0.253 to 5.02

4.62 13.3

283 to 377 318 to 380 393 to 423 357

2.76 3.67 6.3 2.4

323 to 377

7.27

270 to 370 253 to 423 273 to 333

0.415 0.32 0.701

294 to 344 223 to 283

3749

1.01 to 2.94 1.1 to 20

6.51 0.251



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Table 3. continued ref R-227ea: Isobaric Heat Capacity Hwang et al.27 Wirbser et al.63 R-227ea: Speed of Sound Benedetto et al.4 Fröba et al.19 Gruzdev et al.21 Meier and Kabelac43 Pires et al.47 Zhang et al.66 R-227ea: Joule Thomson Coef. Wirbser et al.63

no. points

temp. range

pressure range

density range

T/K

p/MPa

ρ/(mol·dm−3)

3 160

308 to 323 253 to 423

78 33 180 160 263 72

270 293 273 280 248 273

66

to to to to to to

370 374 393 420 333 333

303 to 423

where n is the number of data points. The AADs between experimental data and the equation of state are given in the tables summarizing the data. Discussions of maximum errors or of systematic offsets use the absolute values of the deviations. In the figures, data points shown at the upper or lower vertical limits of the graph indicate that the point is off scale. 3.1. R-227ea: 1,1,1,2,3,3,3-Heptafluoropropane. Two other groups have published equations of state for R-227ea that cover the liquid, vapor, and supercritical regions. Scalabrin et al.50 published an extended corresponding states equation in 2002 with a neural-network technique to fit the coefficients of the equation. Wang et al.81 published a modified Benedict−Webb− Rubin (mBWR) type equation in 2007. The work presented here is the first publication of a Helmholtz energy equation covering all fluid states, although Benedetto et al.4 developed a Helmholtzenergy equation for only the vapor phase in 2001. Experimental measurements for R-227ea and their deviations from the equation of state are given in Table 3 and shown in Figures 1 to 7. Comparisons of calculated vapor pressures

0.03 to 15 0.012 to 0.5 0.005 to 4.07 0.604 to 90.2 0.39 to 65 0.026 to 0.316 0.6 to 15

AAD/% 1.67 1.2 0.015 42.6 0.265 0.04 0.805 0.052 4.93

As shown in Figures 2 to 4, there are several consistent data sets for the density of liquid R-227ea at temperatures below

Figure 2. Comparisons of single-phase densities as a function of pressure calculated with the equation of state to experimental data for R-227ea.

Figure 3. Comparisons of single-phase densities as a function of temperature calculated with the equation of state to experimental data for R-227ea.

Figure 1. Comparisons of vapor pressures calculated with the equation of state to experimental data for R-227ea.

360 K, with differences less than 0.1 %. These include the data of Defibaugh and Moldover8 (AAD = 0.022 %), Fedele et al.17 (0.034 %), Klomfar et al.33 (0.029 %), and Scalabrin et al.50 (0.067 %). Unlike many other refrigerants, there is a substantial amount of data in the vapor region of R-227ea. Except for the data of Scalabrin et al., the equation of state represents vapor-phase densities within about 0.2 % for the data of Di Nicola,9 Hu et al.,25 Shi et al.,54 and Tack and Bier.56 The data of

with experimental data show that most of the measurements are represented within 0.2 % from (250 to 360) K; see Figure 1. Nine of the 21 data sets show average deviations of less than 0.1 % for temperatures above 290 K, even near the critical point. Below this temperature, the scatter in the data increases, and the equation follows the data of Di Nicola9 and Wang and Duan.62 3750



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Figure 4. Comparisons of single-phase densities as a function of density calculated with the equation of state to experimental data for R-227ea.

development of the equation, only the data of Gruzdev et al.21 and Pires et al.47 were available in the liquid phase, and these data differed by more than 1 %, as shown in Figure 6. In order

Scalabrin et al. show deviations of up to 2 % in density at the highest temperatures, and are in disagreement with other overlapping data. Saturated-liquid densities compare favorably as well as shown in Figure 5, with most of the deviations within 0.2 %. The equation

Figure 6. Comparisons of speeds of sound calculated with the equation of state to experimental data for R-227ea. Figure 5. Comparisons of saturated-liquid densities calculated with the equation of state to experimental data for R-227ea.

to resolve this discrepancy, Meier and Kabelac43 took measurements of the speed of sound with a high-accuracy instrument designed for this specific task. These data have uncertainties of about 0.03 %. The final equation represents these data to within 0.01 % on average, with a maximum deviation of 0.048 %. With these new data, the speeds of sound of Gruzdev et al. are now about 0.25 % larger than values calculated from the equation, and the speeds of sound of Pires et al. are 0.75 % smaller than values calculated from the equation. There are three data sets for the isobaric heat capacity (shown in Figure 7) covering the range (220 to 425) K. These data show a scatter of about 1 %, with the equation passing through the middle of the data of Hykrda et al.29 and Wirbser et al.63 There are also three data sets for the ideal-gas isobaric heat capacity. The data of Wirbser et al.63 tend to show positive deviations from the equation, whereas the data of Benedetto et al.4 and Zhang et al.66 show negative deviations.

shows exceptional agreement (0.01 %) with the saturated-liquid densities published by Fedele et al.,17 even though we were not aware of these data until after the equation was finished. In the supercritical region above 360 K, the scatter in all of the data sets starts to rise due to the proximity of the critical point. Differences for the data of Ihmels et al.30 are on average about 0.2 % except for the isobar at 5 MPa. The data of Ihmels et al. extend up to 470 K, which is 50 K higher than any other data. Comparisons with other data show deviations of 0.1 % for Defibaugh and Moldover8 and 0.25 % for Patek et al.46 The limited data near the critical point show increased deviations, with differences exceeding 1 % in density (but less than 1 % in pressure). In the vapor phase, speed-of-sound measurements of Benedetto et al.4 show deviations of 0.01 %, and those of Zhang et al.66 show deviations of 0.05 %. During the initial 3751



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Figure 7. Comparisons of isobaric heat capacities calculated with the equation of state to experimental data for R-227ea.

Figure 8. Comparisons of vapor pressures calculated with the equation of state to experimental data for R-365mfc.

The equation of state for R-227ea is valid from the triple point temperature (146.35 K) to 475 K, with pressures up to 60 MPa. The uncertainties in densities are 0.05 % in the liquid region up to 360 K, 0.3 % in the vapor phase, and 0.5 % in the supercritical region. For vapor pressures, the uncertainties are 0.1 % above 270 K and 0.4 % between 240 K and 270 K (with the higher value at the lower temperature). The uncertainty in heat capacities is 1 % (with increasing uncertainties in the critical region and at high temperatures). For sound speeds, the uncertainties are 0.05 % in the vapor phase up to pressures of 0.5 MPa and 0.03 % in the liquid phase between 280 K and 420 K. 3.2. R-365mfc: 1,1,1,3,3-Pentafluorobutane. Experimental measurements for R-365mfc and their deviations from the equation of state are given in Table 4 and are shown in Figures 8 to 13. Marrucho et al.40 and Bobbo et al.6 both measured vapor pressures of R-365mfc. The data generally agree within 0.05 % except one data point by Marrucho et al. The equation deviates from these data sets by 0.1 % at most, except 2 data points, as shown in Figure 8. These data span the range from (283 to 358) K, and additional measurements are needed between this upper temperature and the critical point.

Three data sets are available for single-phase liquid densities of R-365mfc; the deviations between these data and the equations are shown in Figures 9 to 11. These data sets include measurements of McLinden,41 Marrucho et al.,40 and Bobbo et al.6 The latter two sets also contain saturated liquid-phase data, along with values given in the publication from Fröba et al.20 The data of McLinden41 were presented only in an unpublished report to the project sponsor and are presented here in the Supporting Information to publically document them. Densities were measured along 17 isochores from (354 to 1296) kg·m−3, with temperatures from (280 to 490) K and pressures up to 33 MPa. They were measured with the dual-sinker densimeter described by McLinden and Frederick.82 The experimental sample had a mole-fraction purity greater than 0.9999, as confirmed by GC analysis. The sample was degassed by repeated cycles of freezing in liquid nitrogen, evacuating the vapor space, and thawing, but otherwise it was used as received. The R365mfc decomposed in the densimeter at temperatures above 440 K, forming hydrofluoric acid (HF), which etched the sinkers and changed their mass. The standard uncertainty in temperature was 0.010 K, and the uncertainty in pressure was 5 kPa. Because

Table 4. Summary and Comparisons of Experimental Data for R-365mfc ref

temp range

pressure range

density range

T/K

p/MPa

ρ/(mol·dm−3)

8 17 24 12

283 to 343 313 to 388 333 to 448 303 to 358

0.03 to 0.266 0.102 to 0.836 0.195 to 2.64 0.069 to 0.403

200 95 56 313

283 to 343 237 to 353 289 to 413 280 to 490

0.12 to 25.1 0.957 to 40.1 0.039 to 9.85 0.449 to 34.1

8 19 8

283 to 343 273 to 363 289 to 413

4

315 to 345

29 229 29

298 to 459 250 to 420 315 to 345

no. points

R-365mfc: Vapor Pressure Bobbo et al.6 El Ahmar et al.15 Madani et al.39 Marrucho et al.40 R-365mfc: PVT Bobbo et al.6 Klomfar et al.35 Marrucho et al.40 McLinden41 R-365mfc: Saturated-Liquid Density Bobbo et al.6 Fröba et al.20 Marrucho et al.40 R-365mfc: Ideal-Gas Isobaric Heat Capacity Scott52 R-365mfc: Speed of Sound Fröba et al.20 Meier and Kabelac43 Scott52

3752

AAD/% 0.049 0.158 0.39 0.087

7.76 to 9.01 7.93 to 9.34 6.36 to 8.74 3.92 to 8.75

0.078 0.037 0.124 0.05

7.75 to 8.7 7.45 to 8.83 6.36 to 8.6

0.137 0.046 0.11 0.695

1.1 to 100 0.02 to 0.186

36.4 0.008 0.027 DOI: 10.1021/acs.jced.5b00684 J. Chem. Eng. Data 2015, 60, 3745−3758


Article

above 320 K. In some instances, the disagreement between the different experimental data sets reaches 0.4 %, such as between 340 K and 360 K, but in other cases, such as at 370 K to 400 K, all three data sets match within 0.15 %. Only the data of McLinden41 extend above 400 K, except for seven points from Marrucho et al. at 413 K. These seven points show good consistency with those of McLinden. The equation of state tends to follow the measurements of McLinden, with maximum errors of 0.06 % for the majority of the data between 280 K and 340 K, 0.1 % for 340 K to 455 K, and a maximum of 0.28 % for the rest of the data (which extend up to 490 K and to nearly the critical point). Differences between the equation of state and the saturatedliquid density data (see Figure 12) are a maximum of 0.07 % for the Figure 9. Comparisons of single-phase densities as a function of pressure calculated with the equation of state to experimental data for R-365mfc.

Figure 12. Comparisons of saturated-liquid densities calculated with the equation of state to experimental data for R-365mfc.

data of Fröba et al.20 and 0.2 % for the data of Marrucho et al.,40 and range between 0.01 % and 0.5 % for the data of Bobbo et al.6 Scott52 measured speed of sound in the vapor phase for R-365mfc and derived values for the ideal-gas isobaric heat capacity from these data. The maximum deviation between the equation of state and the speed-of-sound values is 0.1 %, with an average deviation of 0.027 % (see Figure 13). Deviations from

Figure 10. Comparisons of single-phase densities as a function of temperature calculated with the equation of state to experimental data for R-365mfc.

Figure 11. Comparisons of single-phase densities as a function of density calculated with the equation of state to experimental data for R-365mfc. Figure 13. Comparisons of speeds of sound calculated with the equation of state to experimental data for R-365mfc.

of the damage to the sinkers, a definitive uncertainty in density could not be determined, but it was estimated to be 0.10 % at temperatures below 440 K and 0.25 % at higher temperatures. Below 320 K, densities calculated from the equation of state and the data of Bobbo et al.6 agree within 0.04 %. The densities measured by Marrucho et al.40 are 0.2 % lower than those of the other two data sets at these temperatures, except at 313 K where the difference drops to 0.05 %. The agreement is not as close

the ideal-gas isobaric heat-capacity values derived from the speed-of-sound data are up to 1.4 %. These speed-of-sound measurements were presented in the same unpublished report to sponsor as were the data of McLinden;41 they are also presented here in Tables 5 and 6. Vapor-phase speeds of sound were measured in a spherical acoustic resonator at temperatures from 3753



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equation of state and their data are generally less than 0.025 %. Because speed-of-sound data contain substantial information on various derivatives of the equation of state, these data were extremely important during fitting, and helped ensure that other properties that have not been measured, such as isochoric heat capacity, will be better represented. The equation of state for R-365mfc is valid from 239 K to 500 K, with pressures up to 35 MPa. The uncertainties in densities of the equation of state range from 0.1 % in the liquid to 1 % near the critical point, and the uncertainty in the speeds of sound is 0.05 %. The uncertainty in heat capacities is 2 %, and the uncertainty in vapor pressures is 0.25 % at temperatures between 280 K and 360 K. In the critical region, the uncertainties are higher for all properties.

Table 5. Experimental Values of the Speed of Sound of R-365mfc of Scott.52 T/K

p/MPa

w/(m·s−1)

T/K

p/MPa

w/(m·s−1)

315 315 315 315 315 315 325 325 325 325 325 325 325

0.0633 0.0497 0.0414 0.0345 0.0276 0.0204 0.0934 0.0748 0.0621 0.0482 0.0345 0.0275 0.0207

133.54 134.28 134.71 135.08 135.44 135.80 134.54 135.43 136.05 136.74 137.38 137.71 138.03

335 335 335 335 335 335 345 345 345 345 345 345 345 345 345 345

0.1310 0.0909 0.0695 0.0554 0.0414 0.0312 0.1862 0.1584 0.1277 0.1103 0.0909 0.0690 0.0414 0.0344 0.0275 0.0206

135.15 137.05 138.02 138.64 139.24 139.68 135.46 136.70 138.01 138.73 139.53 140.41 141.49 141.77 142.04 142.31

4. CONCLUSIONS Helmholtz energy equations of state have been developed for the fluids R-227ea and R-365mfc. These fluids are available in the REFPROP program (Lemmon et al.67), which can be used to calculate thermodynamic and transport properties of a wide variety of fluids. As an aid to computer implementation, values of properties calculated from the equations of state are given in Table 7. The number of digits displayed does not indicate the uncertainty in the values, but are given only for validation of computer code. Two additional equations for R-115 and R-13I1 are given in the appendix to document unpublished work.

Table 6. Experimental Values of the Ideal-Gas Isobaric Heat Capacity of R-365mfc of Scott.52 T/K

cp0/(J·mol−1·K−1)

315 325 335 345

18.21 18.532 18.762 18.795

■

APPENDIX A

Thermodynamic Properties of Chloropentafluoroethane (R-115) and Trifluoroiodomethane (R-13I1)

(315 to 345) K, with pressures ranging from 0.020 MPa to approximately 70 % of the vapor pressure. The same experimental sample used by McLinden was used for the speed-of-sound measurements. The standard uncertainties were 0.015 K in temperature, (7 to 17) Pa in pressure, and 0.025 % in the speed of sound. Fröba et al.20 also measured the speed of sound in the vapor phase, but only for saturation states. Differences range between 0.3 % and 3.5 %. This highest deviation is 0.85 K away from the critical point, where the equation of state is unable to reproduce the steep decrease of the speed of sound in the vicinity of the critical point. In the liquid phase, both Fröba et al. and Meier and Kabelac43 measured speed-of-sound values. The data of Meier and Kabelac are high-accuracy measurements taken with a dualpath-length time-of-flight apparatus. The deviations between the

The data situation for R-115 is quite different from that of R-227ea and R-365mfc. Measurements have not been made since the work of Kleiber32 in 1994; however, the experimental database for this fluid includes measurements of liquid isochoric and isobaric heat capacities and speeds of sound, thus making it a good candidate for developing an equation of state. However, the accuracies in the data are not comparable to those of R-227ea and R-365mfc, and only a simple functional form was required to fit the available data. The molar mass of R-115 is 154.466416 g·mol−1, and the triple-point temperature, taken from Aston et al.,2 is 173.75 K. The critical point and reducing parameters of the equation of state are Tc = 353.1 K ± 0.015 K

Table 7. Calculated Values of Properties from the Equations of State to Verify Computer Code Fluid

R-227ea

R-365mfc

R-115

R-13I1

temp

density

pressure

isochoric heat capacity

isobaric heat capacity

speed of sound

T

ρ

p

cv

cp

w

K

mol·dm−3

MPa

J·mol−1·K−1

J·mol−1·K−1

m·s−1

300.0 300.0 375.0 300.0 300.0 461.0 300.0 300.0 354.0 300.0 300.0 397.0

0.0 9.0 3.5 0.0 8.5 3.2 0.0 10.0 4.0 0.0 10.9 4.4

0.0 31.71911 2.931467 0.0 2.293261 3.324581 0.0 57.40521 3.190363 0.0 16.52331 3.991241

127.9514 140.7151 194.8406 137.9013 153.5866 224.7732 102.2181 111.0519 137.4032 58.90476 66.39803 90.32758

136.2659 184.6787 83893.36 146.2158 203.6507 10987.87 110.5326 146.0220 5990.358 67.21922 101.9090 11675.81

124.9935 646.6591 59.90978 133.6443 735.3004 68.71050 132.1423 728.9583 70.43849 120.5370 529.4695 74.67026

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Table A-1. Parameters of the Equations of State for R-115 and R-13I1 R-115

R-13I1

k

Nk

tk

dk

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

1.20873 −3.54460 0.745302 0.114128 0.000436572 0.988385 1.13878 −0.0215633 −0.630230 0.0167901 −0.149412 −0.0271153

0.25 1.25 1.5 0.25 0.875 2.375 2.0 2.125 3.5 6.5 4.75 12.5

1 1 1 3 7 1 2 5 1 1 4 2

lk

Nk

tk

dk

lk

1 1 1 2 2 2 3

1.12191 −3.08087 1.11307 −0.184885 0.110971 0.000325 0.333357 −0.0288288 −0.371554 −0.0997985 −0.0333205 0.0207882

0.25 1.125 1.5 1.375 0.25 0.875 0.625 1.75 3.625 3.625 14.5 12.0

1 1 1 2 3 7 2 5 1 4 3 4

1 1 2 2 3 3

states from 317 K to 443 K). The data of Mears et al.42 deviate on average by 1.8 %; however, these data are located only in the critical region. Agreement between the Mears et al. data and the others are similar in the overlapping regions. Six publications on the vapor pressure are available for R-115; these are the data of Aston et al.,2 Hongo et al.,22 Kleiber,32 Mears et al.,42 Romanov,48 and Yada et al.64 The data of Kleiber, Romanov, and Yada et al. are represented within 0.3 % on average, and the others within 1 %. Average deviations are 0.5 % for the isochoric heat-capacity data of Hwang,28 0.16 % for the ideal-gas and liquid-phase isobaric heat capacities of Ernst and Busser,16 0.9 % for the saturation heat-capacity data of Aston et al.,2 and about 0.6 % for both the liquid-phase speed-of-sound data of Takagi and Teranishi57 and of Meyer.44 The equation of state for R-115 has uncertainties of 0.5 % in density and vapor pressure, and 1 % in sound speed and heat capacity. The equation is valid from the triple-point temperature to 550 K, with pressures up to 60 MPa. For R-13I1, nearly all of the data sources come from one lab as mentioned above. The equation represents the data from these publications within (on average) 0.3 % in vapor-phase density, 0.3 % in saturated liquid-phase density (except two points near the critical point), 0.04 % in vapor pressure, 0.08 % in vaporphase speed of sound, and 0.24 % in ideal-gas isobaric heat capacity. The equation of state deviates from the recent data of Klomfar et al.34 on average to within 0.04 %. These data extend to high pressures (40 MPa) and demonstrate that the equation extrapolated far beyond the data available (at saturated states only) at the time of its development. The Klomfar et al. data also extend down to nearly 200 K, far below the lower limit of the Duan et al. data (300 K). The systematic deviations between the equation of state and the new Klomfar et al. data to low temperatures are mostly negligible. The equation of state for R-13I1 has uncertainties of 0.1 % in density in the liquid phase, 0.3 % in density in the vapor phase, and 0.1 % in vapor pressures and vapor-phase speeds of sounds. Uncertainties in other properties in the liquid phase except density are unknown. The equation is valid from the triple-point temperature to 420 K, with pressures up to 50 MPa.

ρc = 3.98 mol· dm−3 ± 0.15 mol· dm−3

pc = 3.129 MPa ± 0.03 MPa R = 8.3144621 J·mol−1·K−1

The critical temperature and density were taken from Mears et al.,42 and the critical pressure was calculated from the equation of state. For R-13I1, all experimental measurements come from Duan et al.,10,12−14 except a new data set from Klomfar et al.34 that was measured after the equation of state was finished. Data are available for the critical point, single phase densities (vapor only), saturated-vapor and liquid densities, vapor pressures, speed of sound (vapor only), acoustic virials, and ideal-gas isobaric heat capacities. The molar mass of R-13I1 is 195.9104 g·mol−1 and the triple-point temperature is unknown. The lower temperature limit of the equation was set at 120 K. The critical point and reducing parameters of the equation of state are Tc = 396.44 K ± 0.01 K

ρc = 4.4306 mol ·dm−3 ± 0.016 mol · dm−3 pc = 3.953 MPa ± 0.005 MPa

These values were taken from Duan et al.10 The ideal-gas isobaric heat capacity equation for both fluids is given by cp0 R

m

=4+

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

∑ vk⎝ k=1

(A-1)

where m = 2, v1 = 7.142, u1 = 289 K, v2 = 10.61, and u2 = 1301 K for R-115, and m = 1, v1 = 6.2641, and u1 = 694 K for R-13I1. The functional form of the equation of state for R-115 is the same as the polar form presented in Span and Wagner;72 that for R-13I1 uses the nonpolar form presented in their work. This form can be generalized as n

α r (δ , τ ) =

12

∑ Nkδ d τ t k

k=1

k

+

∑ k=n+1

Nkδ dkτ tk exp( −δ lk)

■

(A-2)

where n = 5 for R-115 and n = 6 for R-13I1, and with the coefficients and exponents given in Table A-1. The equation for R-115 represents the density data on average to within 0.5 % for the data of Romanov48 (data are liquid phase and cover 212 K to 550 K) and Yada et al.64 (which cover liquid

APPENDIX B

Ancillary Equations

The boundaries between liquid and vapor are defined by saturation states, and ancillary equations can be used to give good 3755



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density can be represented by the equation

estimates. These ancillary equations are not required when a full equation of state is available, since application of the Maxwell criteria to the equation of state yields the saturation states. This criteria for a pure fluid requires finding states in the liquid and vapor that have the same temperature, pressure, and Gibbs energy. The ancillary equations can be used to give good estimates for the pressure and densities required in the iterative procedure to find the saturation states. The vapor pressure can be represented with the ancillary equation ⎛p ⎞ T ln⎜⎜ σ ⎟⎟ = c T ⎝ pc ⎠

⎛ ρ″ ⎞ ln⎜⎜ ⎟⎟ = ⎝ ρc ⎠

■

n i

ai

R-227ea 1 −7.7961 2 2.1366 3 −2.6023 4 −5.7444 5 2.3982 6 7 R-365mfc 1 −8.0955 2 2.0414 3 −13.333 4 25.514 5 −19.967 R-115 1 −7.7016 2 4.3462 3 −4.0020 4 −6.5510 5 3.9278 6 R-13I1 1 −6.8642 2 1.7877 3 −1.0619 4 −2.1677 5 6 7

Bi −0.29926 2.8025 −1.9602 2.0784 0.21701

1.0 1.5 2.2 4.8 6.2

bi

Ci

ci

0.15 0.3 0.44 0.6 2.75

−109.367 332.88 −485.87 417.10 −174.52 −52.695 −114.41

0.64 0.77 0.96 1.2 1.45 5.35 12.0

−1.4964 −6.5917 −21.364 −70.331

■

*E-mail: [email protected]. Tel: +1-303-497-7939.

1.0 1.5 3.4 4.3 5.0

1.7667 −1.6156 8.1107 −10.439 5.0346

0.31 0.6 0.9 1.2 1.5

1.0 1.5 1.9 5.2 6.0

18.245 −57.373 78.511 −50.979 14.361

0.556 0.75 0.95 1.2 1.5

−10.179 49.312 −150.13 219.87 −129.65 −54.218

0.53 0.9 1.2 1.5 1.75 6.0

1.0 1.5 1.9 3.8

18.776 −78.705 149.49 −130.69 43.856

0.58 0.8 1.0 1.2 1.4

−47.722 108.57 −169.00 171.54 −82.244 −40.758 −83.584

0.65 0.8 1.1 1.4 1.75 5.8 13.0

Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are grateful for the help from Mostafa Salehi, now deceased, in searching and retrieving much of the data that were used in this work to fit the equations of state. We thank Mark McLinden and Jennifer Scott for permission to report their data in this work. The NIST TRC Source database was used extensively for data collection.

0.271 0.88 2.85 6.7

■

i

i=1

REFERENCES

(1) Lemmon, E. W.; Span, R. Short Fundamental Equations of State for 20 Industrial Fluids. J. Chem. Eng. Data 2006, 51, 785−850. (2) Aston, J. G.; Wills, P. E.; Zolki, T. P. The Heat Capacities from 10.9 K, Heats of Transition, Fusion and Vaporization, Vapor Pressures and Entropy of Pentafluorochloroethane, the Barrier Hindering Internal Rotation. J. Am. Chem. Soc. 1955, 77, 3939−3941. (3) Baginskii, A. V.; Stankus, S. V. Thermodynamic and Transport Properties of Liquid HFC-227ea. Int. J. Thermophys. 2003, 24, 953−961. (4) Benedetto, G.; Gavioso, R. M.; Spagnolo, R.; Grigiante, M.; Scalabrin, G. Vapor-Phase Helmholtz Equation for HFC-227ea from Speed-of-Sound Measurements. Int. J. Thermophys. 2001, 22, 1073− 1088. (5) Beyerlein, A. L.; DesMarteau, D. D.; Hwang, S. H.; Smith, N. D.; Joyner, P. A. Physical Properties of Fluorinated Propane and Butane Derivatives as Alternative Refrigerants. ASHRAE Trans. 1993, 99, 368− 379. (6) Bobbo, S.; Scattolini, M.; Fedele, L.; Camporese, R. Compressed Liquid Densities and Saturated Liquid Densities of HFC-365mfc. Fluid Phase Equilib. 2004, 222−223, 291−296. (7) Coquelet, C.; Nguyen Hong, D.; Chareton, A.; Baba-Ahmed, A.; Richon, D. Vapour-Liquid Equilibrium Data for the Difluoromethane + 1,1,1,2,3,3,3-Heptafluoropane System at Temperatures from 283.20 to 343.38 K and Pressures up to 4.5 MPa. Int. J. Refrig. 2003, 26, 559−565. (8) Defibaugh, D. R.; Moldover, M. R. Compressed and Saturated Liquid Densities for 18 Halogenated Organic Compounds. J. Chem. Eng. Data 1997, 42, 160−168. (9) Di Nicola, G. P-V-T Behavior of 1,1,1,2,3,3,3-Heptafluoropropane (R227ea). J. Chem. Eng. Data 2003, 48, 1332−1336. (10) Duan, Y.-Y.; Shi, L.; Zhu, M.-S.; Han, L.-Z. Critical Parameters and Saturated Density of Trifluoroiodomethane (CF3I). J. Chem. Eng. Data 1999, 44, 501−504.

n

∑ Bi θ b

AUTHOR INFORMATION

Corresponding Author

of n for all four fluids are simply equal to the number of terms given in this table. The values for the critical points of the ancillary equations presented in this appendix are given in the main document and in Appendix A. The saturated-liquid density can be represented by the ancillary equation ρ′ =1+ ρc

ASSOCIATED CONTENT

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.5b00684. The unpublished p−ρ−T data for R-365mfc of McLinden41 (PDF)

Table B-1. Coefficients and Exponents of the Ancillary Equations for Vapor Pressure and Saturated Densities Ai

(B-13)

i=1

S Supporting Information *

(B-11)

where θ = (1 − T/Tc), pσ is the vapor pressure, and the coefficients and exponents are given in Table B-1. The values

i

i

where ρ″ is the saturated-vapor density. The ancillary equations were developed by fitting calculated saturation values obtained through the use of the Maxwell criteria applied to the equation of state. Values calculated from these ancillary equations and the equation of state agree to within ± 0.1 %.

∑ Ai θ a i=1

n

∑ Ciθ c

(B-12)

where ρ′ is the saturated-liquid density and again the coefficients and exponents are given in Table B-1. The saturated-vapor 3756



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