Article pubs.acs.org/jced
Isochoric p−ρ−T Measurements for trans-1,3,3,3-Tetrafluoropropene [R-1234ze(E)] and Trifluoroiodomethane (R13I1) at Temperatures from (205 to 353) K under Pressures up to 40 MPa Jaroslav Klomfar, Monika Součková, and Jaroslav Pátek* Institute of Thermomechanics, v.v.i., Academy of Sciences of the Czech Republic, Dolejškova 5, CZ 182 00 Prague 8, Czech Republic ABSTRACT: Experimental liquid phase data on the pressure−density−temperature relation are reported for two refrigerants with considerably low global warming potential (GWP) and zero ozone depletion potential (ODP). The data for trans1,3,3,3-tetrafluoropropene [R-1234ze(E)] and trifluoroiodomethane (CF3I) were obtained with a constant volume apparatus at temperatures from (205 to 353) K and from (208 to 353) K, respectively, and at pressures from (1 to 40) MPa. The data for R-1234ze(E) substantially extend the temperature−pressure region covered with experimental p−ρ−T data, and for trifluoroiodomethane they are the first p−ρ−T data available in the open literature. The combined uncertainty at the 0.95 confidence level of the reported density data takes its maximum value at the lower end of the temperature interval; 1.4 kg·m−3 for R-1234ze(E) and 2.4 kg·m−3 for CF3I, which is about 10−3ρ for both substances. The root-mean-square deviation of the reported data from the Helmholtz free energy equation of state fitted to them is for R-1234ze(E) 0.46 kg·m−3 (4 × 10−4 ρ) and 0.32 kg·m−3 (1.6 × 10−4 ρ) for trifluoroiodomethane.
■
Table 1. Sources of the Experimental p−ρ−T Data
INTRODUCTION Alternative refrigerants with suitable environmental properties are presently the subject of considerable research interest. Candidate substances are required to have suitable thermodynamic properties, to be nonflammable, nontoxic, and to have low ozone depletion potential (ODP) and global warming potential (GWP). Three groups of fluorinated greenhouse gases, the so-called “F-Gases”, hydrofluorocarbons (HFCs), perfluorocarbons (PFCs), and sulfur hexafluoride (SF6) were included among greenhouse gases covered by the Kyoto Protocol. The EU controls emissions of F-gases through two legislative acts, the F-Gas Regulation and the MAC Directive. The European Directive on mobile airconditioning systems (MACs) prohibits the use of F-Gases with a Global Warming Potential (GWP) higher than 150 in new types and all new vehicles starting from the year 2011 and 2017, respectively. trans-1,3,3,3-Tetrafluoropropene (R-1234ze(E) or HFO1234ze(E) in the ASHRAE nomenclature) is a fluorinated derivative of propene. Besides HFO-1234yf, HFO-1234ze(E) is being considered as alternative low GWP replacement for HFC134a in household refrigerators and automotive and building air conditioning systems. Owing to the carbon−carbon double bond, HFO-1234ze(E) has the atmospheric lifetime of only 18 days and a greenhouse warming potential (GWP) of 6 relative to CO2 on a 100-year time horizon (Grebenkov et al.1). It has found some initial use in Europe as a replacement for HFC-134a in PU One Component Foams. In comparison with conventional HFC refrigerants, available experimental property data for R-1234ze(E) are still limited. Only a few liquid-phase density measurements for R-1234ze(E) have been reported in the open literature. Table 1 gives an overview of the literature1−4 for experimental p−ρ−T data for © 2012 American Chemical Society
author(s)
year
temp. range T/K
press. range p/MPa
trans-1,3,3,3-Tetrafluoropropene (R-1234ze(E)) Grebenkov et al.1 2009 292 to 370 0.64 to 9.5 Tanaka et al.2 2010 310 to 380 1.0 to 5.0 McLinden et al.3 2010 240 to 400 1.0 to 15 Matsuguchi et al.4 2010 270 to 425 2.7 to 16 this work 2012 205 to 353 1.0 to 40 Trifluoroiodomethane (CF3I) this work 2012 208 to 353 1.0 to 40
no. of data 20 26 79 37 101 90
liquid R-1234ze(E) together with the corresponding temperature and pressure region and the number of data points. Grebenkov et al.1 reported measurements at temperatures from (292 to 370) K and from (0.64 to 9.5) MPa in pressure. Tanaka et al.2 published experimental density values for R-1234ze(E) in temperature range from (310 to 380) K, and up to 5.0 MPa. McLinden et al.3 presented results of the R-1234ze(E) density measurements in temperature range from (240 to 400) K and up to 15 MPa. Based on them they developed a Helmholtz energy equation of state with the stated upper pressure limit of applicability of 20 MPa and with the uncertainty in density of 0.1 % for the liquid phase from (240 to 320) K up to 10 MPa. The uncertainty increases outside of this region. Akasaka5 presented an equation of state explicit in the Helmholtz energy for temperatures from (240 to 420) K and for pressures up to 15 MPa with uncertainty of 0.1 % in liquid density. Received: August 13, 2012 Accepted: October 16, 2012 Published: October 25, 2012 3270
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noxious volume. The mass mnox = ρ(Tref,p)Vnox is the mass of the sample contained in the noxious volume, Vnox, at the temperature Tref and the pressure p in the cell at the measurement moment. The function ν(p,T) describes the temperature and pressure expansion of the cell from the state of the piezometer volume calibration. It is given by eq 2
R-1234ze(E) have been also considered as one of possible components for azeotrope-like compositions comprising trifluoroiodomethane (CF3I) intended for uses as a refrigerant. CF3I has a low ozone depleting potential less than 0.008, and its value of GWP is less than 5.6 Trifluoroiodomethane has also been considered as a candidate replacement agent for CBrF3 for use as a fire suppressant and as a potential alternative to SF6 for use as a dielectric material and arc quenching medium. Morlat et al.7 tested a CF3I-loaded superheated droplet detector to search for weakly interacting massive particle (WIMPs) forming the hypothetical dark matter halo of our Galaxy. Recently, Guo et al.8 presented experimental data for pressure− composition−temperature relation for the binary system of CF3I− R-1234ze(E) at vapor−liquid equilibrium in the temperature range of (258.150 to 298.150) K. Duan et al. reported saturated vapor pressure data9 and saturated vapor and liquid densities10 for CF3I and PVT relation for the CF3I gas phase.11 Chang et al.12 published data on the p−T relation for trifluoroiodomethane at vapor−liquid equilibrium. No compressed liquid p−ρ−T data are available for CF3I in the open literature. A preliminary short Helmholtz equation of state for CF3I of Lemmon et al. is implemented in the NIST Standard Reference Database REFPROP,18 version 8.0, 2006. The aim of the present study was to obtain new experimental data for the p−ρ−T relationship of liquid R-1234ze(E) and CF3I and extend thus the pressure and temperature range of the database for the development of their equation of state.
ν = 1 + 3αcell(T − Tcal) + βcell (p − pcal )
(2)
The evaluation of the temperature dilatation coefficient αcell (K−1) of the measuring cell material and of the temperature-dependent coefficient β c e l l (MPa − 1 ) of the cell volume expansion with pressure is described in ref 13. We have verified experimentally that eq 2 provides values of the temperature and pressure expansion function ν(p,T) fairly close to its actual values.13,15 For brevity, the input variables of eq 1 are hereinafter denoted as Xi so that the variables Xi, i = 1 to N = 8, stand in eq 3 for the directly measured quantities Vref, ρref, Tref, Vnox, Vcal, αcell, βcell, and ρ(Tref,p) entering into the working eq 1 and contributing significantly to the uncertainty in the measured density. Assuming that all the values of the input variables are independent, the variance of ρ is ⎛ ∂ρ ⎞2 u ( X ) ∑⎜ i ⎟ ∂Xi ⎠ i=1 ⎝ N
uc(ρ)2 =
■
(3)
and the combined standard uncertainty uc is the square root of the variance.16 Evaluating the combined expanded uncertainty for density at 0.95 confidence level Uc from eq 3 one obtains that it takes its maximum value at the lower end of the temperature interval; Uc = 2uc = 1.4 kg·m−3 for R-1234ze(E) and 2.4 kg·m−3 for CF3I, which is about 10−3 ρ for both substances. As for the pressure measurements, they were recorded by two absolute pressure gauges (Paroscientific Inc., Digiquartz model 43KR and 415K) with a measuring range of (20 and 100) MPa, respectively. The manufacturer-specified standard uncertainty of the pressure measurements is 0.01 % of the full gauge range, that is, less than (0.002 and 0.01) MPa for the range of (20 and 100) MPa, respectively. The measuring cell temperature was measured on the ITS-90 with a precision thermometry bridge ASL F700 and a 25 Ω platinum resistance thermometer Tinsley (type 5187 SA) calibrated with ITS-90 fixed points at National Physical Laboratory, London. The thermometer has a certified uncertainty of ± 1 mK. The total uncertainty in the temperature measurement due to the thermometer and due to inhomogeneity of the bath temperature field is estimated to be close to ± 5 mK. Determination of the Reference Density. The reference density ρref has to be determined independently of the isochoric method. For both investigated fluids, it was obtained by weighting a sample filled into a pycnometer with a volume precisely calibrated under accurately adjusted reference conditions, Tref = 298.15 K, pref = 2 MPa. The procedure is in detail described in ref 15. The volume of the waiting pycnometer was determined by filling it with propane under accurately realized reference conditions. The density ρref,p of propane at reference conditions was calculated from the reference equation for propane by Lemmon et al.17 The reference density ρref,s of the sample is then given by eq 4
EXPERIMENTAL SECTION Apparatus and Experimental Uncertainties. The present measurements of the p−ρ−T relation for liquid R-1234ze(E) and CF3I were performed using an isochoric apparatus constructed in the Laboratory of Thermophysical Properties of Fluids of the Institute of Thermomechanics, Prague, which makes density measurements at temperatures from (183 to 363) K and up to 60 MPa in pressure possible. The apparatus has been already described in detail together with the measuring and data evaluation procedure in our previous paper.13 Some additional details of the apparatus are given in ref 14. Here, we briefly recall a few key points related to the evaluation of the uncertainty in the measured density. The used isochoric method provides values for the density relative to a density ρref of the sample at some selected reference state Tref, pref, which is used to determine volumetrically the mass mtot of the sample filled into the measuring cell13 as mtot = ρrefVref. Here, Vref is the sample volume at the reference conditions determined using a filling volumeter. The volume of the measuring cell is accurately calibrated at selected temperature Tcal and pressure pcal. In the construction of the piezometer for a constant volume apparatus working at subzero temperatures, it is impossible to avoid so-called noxious volume, Vnox, which is a part of the pressure measuring system connected with the sample cell but at a different temperature. The noxious volume Vnox and the mass mnox of the sample contained in it must be allowed for in the sample density evaluation. The noxious volume is thermostated to the reference temperature Tref for this purpose. Thus, for a real constant volume apparatus the density is evaluated from the equation mtot − mnox ρ= (Vcal − Vnox )ν(p , T ) (1) where mtot = ρrefVref is the total mass of the sample filled at the reference conditions in the piezometer system including the
ρref,s = 3271
ms − me ρ mp − me ref,p
(4)
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Table 2. Basic Information on the Samples Used in the Present Study: Their Suppliers, Stated Mass Fraction Purity, Mass Fraction Water Content, and the Nominal Values of the Reference Temperature, Pressure, and Density Tref, pref, and ρrefa, Used in Measurements and Data Evaluation chemical name R-1234ze(E) CF3Ic
CAS no.
b
29118-24-9 2314-97-8
supplier Honeywell Apolloe
mass fraction purity d
0.995 0.99
water content 50·10
−6
Tref/K
pref/MPa
ρref/kg·m−3
298.15 298.15
2.0 2.0
1170.52 2046.84
Combined uncertainties Uc are Uc(ρref) = 0.52 kg·m−3 for R-1234ze(E) and Uc(ρref) = 0.96 kg·m−3 for CF3I (level of confidence = 0.95). btrans1,3,3,3-Tetrafluoropropene. cTrifluoroiodomethane. dHoneywell Fluorine Products, Europe B.V., The Netherlands. eApollo Scientific Ltd., Cheshire, United Kingdom. a
amounts to 25 cm3. The ratio ρref,s/ρref,p is equal to 2.6 for R-1234ze(E) and to 4.1 for CF3I. The reference temperature and reference pressure were adjusted in the reference density measurements with an estimated standard uncertainty u(Tref) = 0.01 K and u(pref) = 5·10−4 MPa. The thermal expansion and compressibility coefficients were calculated from the equation of state fitted to the resultant p−ρ−T data. Thus, the combined standard uncertainties of the reference density of R-1234ze(E) and CF3I measured using the weighting pycnometer are estimated to be ± 0.26 kg·m−3 and ± 0.48 kg·m−3, respectively, which is 2.3·10−4 ρref,s for both substances. Materials. Commercially supplied samples were used in the measurements. Table 2 lists main primary characteristics of the samples studied, including their suppliers, their manufacturer stated minimum mass fraction purities, and the initial water mass fraction in the samples. The samples were used without further purification.
where the masses me, ms, and mp of the empty pycnometer and the pycnometer filled at the reference conditions with the sample and with propane, respectively, were determined using an analytical balance Mettler Toledo AB304-S/FACT with readability of 0.1 mg. The obtained value of ρref,s is equal to 1170.52 kg·m−3 for R-1234ze(E) and to 2046.84 kg·m−3 for CF3I. The obtained density reference values at temperature of 298.15 K and pressure of 0.1 MPa differ from values 1170.69 kg·m−3 and 2046.52 kg·m−3 calculated from equations of state by McLinden et al.3 and Lemmon et al.17 by 0.06 kg·m−3 and 0.17 kg·m−3, respectively. The combined standard uncertainties uc(ρref,s) of the measured reference densities have been evaluated using the law of propagation of uncertainty16 (eq 5) from the standard uncertainties in the directly measured quantities entering into eq 4. ⎛ ∂ρref,s ⎞2 ⎜ u(Xi)⎟ uc(ρref,s ) = ∑ ∂Xi ⎠ i=1 ⎝ N
2
■
(5)
RESULTS AND CONCLUSION The p−ρ−T measurements for R-1234ze(E) were performed at 101 individual pressure/temperature set points along 10 isochors at temperatures from (208 to 353) K and at the set point pressures of (1, 2, 3, and 4) MPa and from (5 to 40) MPa with a 5 MPa step. The p−ρ−T measurements for CF3I were performed at 90 individual pressure/temperature set points along 9 isochors at temperatures from (203 to 353) K and at the same set point pressures. The resultant densities obtained from the evaluation procedure taking into account all necessary corrections13 are presented in Tables 3 and 4. Figure 1 shows deviations of the present experimental densities and of densities by other authors, corresponding to pressures less than 20 MPa, from the values calculated from the equation of state for R-1234ze(E) by McLinden et al.3 The data of Grebenkov et al.1 showing considerable scatter with a relative standard deviation of 1.8·10−2 are not shown in the figure. The pressure of 20 MPa forms the stated upper pressure limit of applicability of the model. The deviations of the present R-1234ze(E) experimental densities with p < 20 MPa from the model by McLinden et al.3 lie within the interval ± 0.0027 of the measured density. In the narrowed pressure and temperature region from (240 to 320) K and pressures up to 10 MPa with stated uncertainty of ± 0.1 %18 the deviations of the present density data from the model3 lie within the interval of ± 0.05 % ot the measured density. The reported new data on the density of R-1234ze(E) substantially extend the temperature−pressure region covered with experimental data. Figure 2 gives the distribution of the present data points and the data points by other authors over the T−p plane, showing thus how the region covered by data was extended. The existing lower temperature limit of the region covered with experimental data at 240 K is shifted to 205 K. The upper pressure limit of the region of about 20 MPa has been increased to 40 MPa.
The variables Xi, i = 1 to N = 8, stand in eq 5 for the directly measured quantities me, ms, mp, ρref,p, Tref,s, pref,s, Tref,p, and pref,p, entering into the working eq 4. The uncertainties u(Tref,s), u(pref,s), and u(Tref,p), u(pref,p) involved in the adjustment of the reference temperature and reference pressure during the filling the weighting pycnometer with the sample and with propane, respectively, are included into eq 5 as they represent additional independent sources of the reference density uncertainty. They originate from the terms αiρi(T − Tref,i)V and βiρi(p − pref,i)V, i∈(s,p), describing temperature and pressure dependence of the masses mi. Here αi and βi denote, respectively, the isochoric thermal expansion and the isothermal compressibility coefficients of the substance indicated by the letter subscript i. V is the volume of the waiting pycnometer. In reference density evaluation, these terms are assumed to be equal to zero in eq 4 due to an assumption that owing to reference conditions adjustment T = Tref and p = pref. After some manipulations eq 5 can be rewritten in the form of eq 6 ⎛ ρ ⎞2 ⎤ ⎤2 ⎡ ⎡ ⎡ u(ρ ) ⎤2 ρref,s ( ) u m ref,s ⎟ ⎥ ref,s ⎢ ⎥ 1− ⎢ ⎥ = 2⎢ +⎜ ⎢⎣ ρs ⎥⎦ ⎢⎣ Vρref,s ⎥⎦ ⎢ ρref,p ⎜⎝ ρref,p ⎟⎠ ⎥ ⎣ ⎦ + [u(Tref )]2 [αs2 + αp2] + [u(pref )]2 [βs2 + βp2] (6)
where u(m), u(Tref), and u(pref) are the common values of u(ms) = u(mp), u(Tref,s) = u(Tref,p) and u(pref,s) = u(pref,p). The values of the quantities necessary for evaluation of the reference density uncertainty are as follows. The standard uncertainty u(m) in the masses ms, me, and mp is 0.002 g. Lemmon et al.17 claim that the uncertainty u(ρp) in the density of propane calculated from their equation of state is 0.0001ρ in the liquid phase below 350 K. The volume V of the weighting pycnometer 3272
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Table 3. Present Experimental Data on Densities ρ for Liquid R-1234ze(E) as a Function of Temperature T and Pressure p with a Combined Expanded Uncertainty at 0.95 Confidence Level in Density Uc(ρ) and Standard Uncertainties u(T) and u(p) in Temperature and Pressure, Respectivelya T/K
p/MPa
ρ/kg·m−3
T/K
p/MPa
ρ/kg·m−3
298.136 291.449 289.406 288.321 286.919 285.495 305.083 341.914 334.340 327.000 319.801 312.582 312.583 320.409 304.383 302.811 301.210 299.621 298.032 353.154 345.093 336.831 328.716 328.714 337.810 347.531 353.150 319.604 317.507 315.611 313.700 312.400 328.712 330.830 333.129 335.429 346.837 353.153 291.423 297.139 303.686 285.341 309.914 316.033 279.496 273.300 271.987 270.861 269.641 268.481 273.308
9.9284 5.2218 3.7799 3.0105 2.0215 1.0185 14.792 40.043 34.952 29.927 24.935 19.938 10.069 14.882 4.9913 4.0268 3.0255 2.0457 1.0625 34.806 29.935 24.924 19.949 9.9868 14.797 19.908 22.854 5.1429 4.0332 3.0389 2.0325 1.3493 2.0425 2.9633 3.9642 4.9684 9.9434 12.717 20.124 24.771 30.067 15.133 34.977 39.863 10.161 5.0692 3.9783 3.0495 2.0215 1.0540 20.110
1204.5 1205.0 1205.2 1205.3 1205.4 1205.5 1203.9 1201.0 1201.6 1202.2 1202.7 1203.3 1164.5 1163.9 1165.1 1165.2 1165.3 1165.5 1165.6 1161.4 1162.0 1162.6 1163.2 1116.5 1115.9 1115.2 1114.8 1117.2 1117.4 1117.5 1117.6 1117.7 1060.1 1060.0 1059.8 1059.7 1058.9 1058.5 1254.7 1254.2 1253.6 1255.2 1253.1 1252.6 1255.7 1256.3 1256.4 1256.5 1256.6 1256.7 1296.9
278.357 284.030 273.289 289.452 294.996 268.181 262.693 256.683 255.478 254.400 253.372 257.482 257.488 261.713 266.956 271.680 252.698 248.185 243.668 238.990 237.405 236.485 235.623 239.151 239.152 243.152 247.543 251.699 235.074 231.769 227.750 223.787 222.918 222.122 221.296 220.443 223.729 227.191 230.735 234.585 220.626 217.294 213.579 209.970 209.368 208.329 207.730 207.192 210.015 205.220
24.809 30.064 20.020 34.965 40.022 15.201 9.9803 4.2502 3.0749 2.0454 1.0612 4.9963 25.124 29.771 35.381 40.411 19.955 15.008 10.013 4.8350 3.0681 2.0458 1.0848 5.0090 25.006 29.768 35.124 39.870 19.402 15.259 10.219 5.2483 4.1300 3.1286 2.0978 1.0154 25.073 29.919 34.674 39.412 20.112 15.438 10.225 5.1143 4.2753 2.8119 1.9305 1.1431 25.106 17.702
1296.4 1295.9 1296.5 1295.0 1294.5 1296.9 1297.4 1298.0 1298.1 1298.2 1298.3 1297.9 1342.2 1341.8 1341.3 1340.9 1342.7 1343.1 1343.6 1344.8 1344.2 1344.3 1344.4 1344.0 1381.9 1381.5 1381.1 1380.7 1382.4 1382.7 1383.2 1383.6 1383.7 1383.8 1383.9 1384.0 1416.5 1416.1 1415.8 1415.4 1416.9 1417.3 1417.7 1418.1 1418.2 1418.3 1418.4 1418.5 1447.6 1448.1
a Standard uncertainties u are u(T) = 0.001 K, u(p) = 0.002 MPa for p < 20 MPa, else u(p) = 0.01 MPa, and combined expanded uncertainty Uc is Uc(ρ) = 1.4 kg·m−3 (level of confidence = 0.95).
forms the stated upper pressure limit of applicability of the model.18 The deviations of the experimental densities from the model lie within the interval ± 0.0009 of the measured density. The present data are the first p−ρ−T data for
Figure 3 shows deviations of the present experimental densities for CF3I corresponding to pressures less than 20 MPa from the density values calculated from the preliminary Helmholtz equation of state for CF3I by Lemmon et al.18 The pressure of 20 MPa 3273
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Table 4. Present Experimental Data on Densities ρ for Liquid CF3I as a Function of Temperature T and Pressure p with a Combined Expanded Uncertainty at 0.95 Confidence Level in Density Uc(ρ) and Standard Uncertainties u(T) and u(p) in Temperature and Pressure, Respectivelya T/K
p/MPa
ρ/kg·m−3
T/K
p/MPa
ρ/kg·m−3
298.142 290.430 288.884 287.337 285.917 284.362 321.682 343.843 337.320 329.492 305.558 313.532 313.581 322.382 297.945 300.011 301.745 303.435 305.168 353.149 340.454 331.308 331.297 353.136 341.639 315.121 313.219 317.179 319.169 321.220 331.301 328.988 333.641 336.004 353.150 298.148 318.542 311.691 304.543 291.686 285.083 272.124 266.414 267.966 269.237
10.026 4.9508 3.9303 2.9055 1.9768 0.9405 25.300 39.291 35.169 30.240 14.805 19.969 9.9328 14.998 0.8614 2.0682 3.0701 4.0616 5.0695 32.431 25.264 20.061 10.058 20.828 15.161 1.9583 0.9825 2.9902 3.9762 5.0052 2.9858 1.9944 3.9723 4.9857 12.322 25.035 40.060 35.046 29.729 20.129 15.134 5.2165 0.7760 1.9928 2.9762
2103.9 2104.9 2105.2 2105.4 2105.6 2105.8 2100.7 2097.7 2098.6 2099.6 2102.8 2101.8 2036.1 2034.9 2038.1 2037.9 2037.6 2037.4 2037.2 2031.0 2032.6 2033.8 1955.3 1952.6 1954.0 1957.3 1957.5 1957.0 1956.8 1956.5 1875.6 1875.8 1875.3 1875.0 1873.0 2183.8 2180.9 2181.8 2182.8 2184.7 2185.7 2187.6 2188.5 2188.2 2188.0
270.534 266.749 278.488 278.499 272.852 267.062 284.171 290.405 296.147 278.477 261.502 254.155 253.207 251.973 255.274 255.320 260.193 265.126 270.931 250.456 245.453 240.522 234.659 233.569 231.744 235.464 235.504 239.910 244.172 248.776 231.249 226.989 222.617 217.732 216.710 215.963 214.916 218.368 218.480 222.404 226.210 229.954 214.873 210.400 207.789
3.9846 1.0529 10.098 24.979 20.116 15.109 29.780 34.997 39.750 25.009 10.373 3.8844 3.0631 1.9755 4.8734 25.028 29.834 34.684 40.330 20.143 15.114 10.116 4.114 2.9901 1.1095 4.9304 24.985 29.944 34.707 39.783 20.002 15.121 10.052 4.3815 3.1755 2.3050 1.0557 5.1164 25.008 29.924 34.684 39.202 20.130 14.322 10.925
2187.8 2188.4 2186.6 2251.5 2252.3 2253.2 2250.6 2249.7 2248.8 2252.2 2254.8 2256.0 2256.2 2256.4 2255.8 2330.8 2330.0 2329.2 2328.3 2331.6 2332.4 2333.3 2334.3 2334.5 2334.8 2334.1 2397.3 2396.6 2395.8 2395.1 2398.1 2398.8 2399.6 2400.5 2400.7 2400.9 2401.1 2400.4 2453.5 2452.8 2452.1 2451.5 2454.2 2455.0 2455.5
a Standard uncertainties u are u(T) = 0.001 K, u(p) = 0.002 MPa for p < 20 MPa, else u(p) = 0.01 MPa, and combined expanded uncertainty Uc is Uc(ρ) = 2.4 kg·m−3 (level of confidence = 0.95).
trifluoroiodomethane available in the open literature. Figure 4 gives the distribution of the present p−ρ−T data points for CF3I in the p−T plane. To test the internal consistency of the obtained density data sets over their whole range of parameters, we correlated the experimental data on the p−ρ−T relation, using the form of eq 7, ⎡ ⎛ ∂ϕr ⎞ ⎤ ⎟⎥ p = ρRT ⎢1 + δ ⎜ ⎝ ∂δ ⎠τ ⎥⎦ ⎢⎣
associated with the fundamental equation of state formulated in the reduced Helmholtz energy ϕ(τ,δ). Here, τ is the inverse reduced temperature Tc/T, δ is the reduced density ρ/ρc, and R (J·kg−1·K−1) is the specific gas constant of the substance. The function ϕr(τ,δ) is the residual part of the Helmholtz energy describing the real behavior of the fluid given by eq 8. n
ϕr = (7)
i=1
3274
m
∑ aiδ liτ ki +
∑ i=n+1
aiδ liτ ki exp(−δ ni)
(8)
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Figure 1. Relative deviations 102·(ρexp/ρcalc − 1) of the experimental liquid density data, ρexp, of different authors for R-1234ze(E) from the values ρcalc calculated from the fundamental equation of state by McLinden et al.3 as a function of temperature T and pressure p. △, Tanaka et al.;2 +, McLinden et al.;3 ○, this work.
Figure 3. Relative deviations 102·(ρexp/ρcal − 1) of the present experimental liquid density data for CF3I, ρexp, from the values ρcal calculated from the short Helmholtz equation by Lemmon et al.18 as a function of temperature T and pressure p. ○, this work.
Figure 4. Distribution of the present experimental data points on the p−ρ−T relation for CF3I over the T−p plane. ○, this work.
Figure 2. Distribution of the experimental data points on the p−ρ−T relation for liquid R−1234ze(E) by different authors over the T−p plane. △, Tanaka et al.;2 +, McLinden et al.;3 ○, this work.
Table 5. Exponents ki, li, and ni and Coefficients ai of the Correlation eq 7 of the Present Experimental p−ρ−T Data for R-1234ze(E)a
From the 12 terms found by Span and Wagner19 for residual Helmholtz energy model for non- and weakly polar fluids the terms statistically significant in the present experimental p−ρ−T data were selected using stepwise regression and included into the model. Tables 5 and 6 give, respectively, the exponents ki li and ni of the selected terms together with corresponding coefficients ai and also the used values of critical temperature, Tc, critical density, ρc, the specific gas constant R, and root-mean-square deviation, rmsd. The number of significant figures given in Tables 5 and 6 is necessary and sufficient to reproduce the experimental densities with the reported rmsd values. Figures 5 and 6 show relative deviations of the experimental densities for R-1234ze(E) and CF3I from the values calculated from eq 7, respectively. The root-meansquare deviation of the experimental densities from the densities calculated from eq 7 amounts to 0.46 kg·m−3 (0.0004ρref) for R-1234ze(E) and 0.32 kg·m−3 (0.00016ρref) for CF3I. The rootmean-square deviation is a measure of the spread of the density
i
ki
li
1 2 3 4 5 6 7 8
0.250 1.250 0.250 0.875 2.375 2.125 6.500 12.500
1 1 3 7 1 5 1 2
ni
ai
1 1 2 3
1.20848·100 −1.47078·100 4.65229·10−2 2.30158·10−4 9.94032·100 8.66750·10−2 −1.46420·100 1.65058·100
a Tc = 382.52 K, ρc = 489.24 kg·m−3, R = 72.9071 J·kg−1·K−1, rmsd = 0.46 kg·m−3.
data with respect to eq 7. This is the reason why it can be nearly an order of magnitude less than the estimate of the uncertainty in the density, which is dominated by contributions of the 3275
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uncertainties in the coefficients αcell and βcell common for all the data points.
Table 6. Exponents ki, li, and ni and Coefficients ai of the Correlation eq 7 of the Present Experimental p−ρ−T Data for CF3Ia i
ki
li
1 2 3 4 5 6 7
0.250 1.250 0.250 0.875 1.750 3.625 3.625
1 1 3 7 5 1 4
ni
ai
1 2 2
1.02511·100 −2.30839·100 8.28066·10−2 3.37401·10−4 −3.40503·10−2 −4.52702·10−1 −1.81705·10−1
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AUTHOR INFORMATION
Corresponding Author
*Phone: +420 266053153. Fax: +420 286584695. E-mail: patek@ it.cas.cz. Funding
The work described in this paper has been performed under Grant No. GA101/09/0010 awarded by the Grant Agency of the Czech Republic and under Research Plan No. AV0Z20760514 of the Academy of Sciences of the Czech Republic.
Tc = 396.44 K, ρc = 868.00 kg·m−3, R = 42.4402 J·kg−1·K−1, rmsd = 0.32 kg·m−3. a
Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Grebenkov, A. J.; Hulse, R.; Pham, H.; Singh, R. Physical Properties and Equation of State for Trans-1,3,3,3-tetrafluoropropene. Proceedings of the 3rd IIR Conference on Thermophysical Properties and Transfer Processes of Refrigeration, Boulder, CO, 2009. (2) Tanaka, K.; Takahashi, G.; Higashi, Y. Measurements of the Vapor Pressures and pρT Properties for trans-1,3,3,3-Tetrafluoropropene (HFO-1234ze(E)). J. Chem. Eng. Data 2010, 55, 2169−2172. (3) McLinden, M. O.; Thol, M.; Lemmon, E. W. Thermodynamic Properties of trans-1,3,3,3-tetrafluoropropene [R1234ze(E)]: Measurements of Density and Vapor Pressure and a Comprehensive Equation of State. International Refrigeration and Air Conditioning Conference at Purdue, West Lafayette, IN, July 12−15, 2010. (4) Matsuguchi, A.; Kagawa, N.; Koyama, S. Study on Isochoric Specific Heat Capacity of Liquid OF-1234ze(E). International Symposium on Next-generation Air Conditioning and Refrigeration Technology, Tokyo, Japan, February 17−19, 2010. (5) Akasaka, R. New fundamental equations of state with a common functional form for 2,3,3,3-tetrafluoropropene (R-1234yf) and trans1,3,3,3-tetrafluoropropene (R-1234ze(E)). Int. J. Thermophys. 2011, 32, 1125−1147. (6) Solomon, S.; Burkholder, J. B.; Ravishankara, A. R.; Garcia, R. R. Ozone depletion and global warming potentials of CF3I. J. Geophys. Res. 1994, 99, 20929−20935. (7) Morlat, T.; Giuliani, F.; Girard, T. A.; Ramos, A. R.; Felizardo, M.; Marques, J. G. Response study of a CF3I superheated droplet detector for dark matter applications. Nucl. Instr. Meth. Phys. Res. A 2007, 580, 274−277. (8) Guo, K. H.; Gong, M.; Dong, X.; Wua, J. (Vapour + liquid) equilibrium data for the binary system of trifluoroiodomethane (R13I1) + trans-1,3,3,3-tetrafluoropropene (R1234ze(E)) at various temperatures from (258.150 to 298.150). J. Chem. Thermodyn. 2012, 47, 397−401. (9) Duan, Y. Y.; Zhu, M. S.; Han, L. Z. Experimental vapor pressure data and a vapor pressure equation for trifluoroiodomethane (CF3I). Fluid Phase Equilib. 1996, 121, 227−234. (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. (11) Duan, Y. Y.; Shi, L.; Sun, L. Q.; Zhu, M. S.; Han, L. Z. Thermodynamic Properties of Trifluoroiodomethane (CF3I). Int. J. Thermophys. 2000, 21, 393−404. (12) Chang, Z.; Duan, Y. Y.; Shi, L.; Zhu, M.; Han, L. Vapor Pressure of Pentafluoroethane and Trifluoroiodomethane. J. Therm. Sci. 2001, 10, 193−197. (13) Klomfar, J.; Součková, M.; Pátek, J. Experimental p−ρ−T data for 1-butyl-3-methylimidazolium tetrafluoroborate at temperatures from (240 to 353) K and pressure up to 60 MPa. J. Chem. Eng. Data 2011, 56, 426−436. (14) Klomfar, J.; Součková, M.; Pátek, J. P−ρ−T measurements on 1alkyl-3-methylimidazolium-based ionic liquids with tetrafluoroborate
Figure 5. Relative deviations 102·(ρexp/ρcalc − 1) of the present experimental liquid density data, ρexp, for R-1234ze(E) from the values ρcalc calculated from the eq 7 as a function of temperature T and pressure p.
Figure 6. Relative deviations 102·(ρexp/ρcalc − 1) of the present experimental liquid density data, ρexp, for CF3I from the values ρcalc calculated from the eq 7 as a function of temperature T and pressure p. 3276
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and trifluoromethanesulfonate anion. J. Chem. Eng. Data 2012, 57, 708−720. (15) Klomfar, J.; Součková, M.; Pátek, J. Experimental study of p−ρ− T relation of compressed liquid phase for octafluoropropane and two near azeotropic ternary HFC/HC Mixtures. J. Chem. Eng. Data 2012, 57, 1627−1634. (16) Taylor, B. N.; Kuyatt, C. E. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results; NIST Technical Note 1297; National Institute of Standards and Technology: Gaithersburg, MD, 1994. (17) Lemmon, E. W.; McLinden, M. O.; Wagner, W. Thermodynamic Properties of Propane. III. A Reference Equation of State for Temperatures from the Melting Line to 650 K and Pressures up to 1000 MPa. J. Chem. Eng. Data 2009, 54, 3141−3180. (18) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties−REFPROP, Version 8.0; National Institute of Standards and Technology, Standard Reference Data Program: Gaithersburg, MD, 2007. (19) Span, R.; Wagner, W. Equations of state for technical applications. III. Results for Polar Fluids. Int. J. Thermophys. 2003, 25, 111−162.
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