Isobaric Heat Capacity Measurements for R1234yf from 303 to 373 K

Article pubs.acs.org/jced

Isobaric Heat Capacity Measurements for R1234yf from 303 to 373 K and Pressures up to 12 MPa Yu Liu, Xiaoming Zhao,* Shaohua Lv, and Hanwei He MOE Key Laboratory of Thermo-Fluid Science and Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China ABSTRACT: The isobaric heat capacity of 2,3,3,3-tetrafluoropropene (R1234yf) was studied in the compressed liquid and supercritical phases. A total of 154 experimental data were acquired for eight isotherms from 303.68 to 373.31 K in the pressure range of 1.5 to 12 MPa. The experimental values of the heat capacity were compared with the literature data. Additionally, the present data were correlated with an empirical equation. The published experimental data sets of thermophysical properties for R1234yf were also summarized in this paper.

1. INTRODUCTION

However, the isobaric heat capacities of R1234yf are still very limited. To the author’s knowledge, only two data sources are available,7,15 Tanaka et al. reported the heat capacities of R1234yf from 310 to 360 K at pressures up to 5 MPa. Gao et al. obtained the heat capacity data at temperatures ranging from 305 to 355 K and pressures from 1.5 to 5 MPa. Isobaric heat capacities of R1234yf at temperatures higher than 360 K and pressures above 5 MPa have not been reported until now. For this reason, the isobaric heat capacities for R1234yf were investigated by means of an adiabatic steady flow calorimeter at temperatures from 303 to 373 K and pressures up to 12 MPa.

2,3,3,3-Tetrafluoropropene (R1234yf) is a new alternative refrigerant. It is considered to be a promising substitute for automotive air-condition systems due to its very low global warming potential of 4 and its high similarity to R134a in thermophysical properties.1 Properties of R1234yf have been extensively investigated over the past few years. Tanaka and Higashi measured the critical parameters, vapor pressures, and surface tensions of R1234yf.2 Kano et al. reported the sound speed of R1234yf as well as its isobaric ideal-gas heat capacities.3 Lago et al. reported the speed of sound from 260 to 360 K at pressures up to 10 MPa.4 Nicola et al. measured the gaseous PVT properties from 243 to 373 K5 and vapor pressures from 224 to 366 K.6 Tanaka et al. measured the isobaric heat capacities and densities of R1234yf in the temperature range from 310 to 360 K at pressures up to 5 MPa.7 Fedele et al. acquired the saturated pressure data in the temperature range between 245 and 343 K.8 Richter et al. studied the PVT behavior from 232 to 400 K at pressures up to 10 MPa as well as the vapor pressures in the temperature range from 250 to 366 K.1 Perkins and Huber reported the thermal conductivity covering a temperature range of 242 to 344 K and pressures from 0.1 to 23 MPa.9 Fedele et al. obtained its densities in the compressed liquid phase from 283 to 353 K and pressures up to 35 MPa,10 Meng et al. measured its viscosity at temperatures from 243 to 363 K and pressures up to 30 MPa by means of a vibrating-wire viscometer.11 Qiu et al reported its liquid densities between 283 and 363 K with pressures up to 100 MPa.12 Zhao et al. measured its viscosities as well as surface tension at temperatures from 293 to 365 K under the saturated condition.13 Yang et al. obtained the vapor pressure of R1234yf over a temperature range from 248 to 361 K.14 Gao et al. measured the compressed liquid heat capacities from 305 to 355 K and 1.5 to 5 MPa.15 Dang et al. reported its viscosity data in the vapor phase and its mixtures in the temperature range from 274 to 338 K.16 The published data sources are summarized in Table 1. © 2017 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Chemicals. HFO-1234yf sample was supplied by Zhejiang Sinoloong refrigerant Co. Ltd. The purity is better than 99.95 wt %. To minimize the influence of the impurity, the sample was purified by freezing the gaseous sample with liquid nitrogen and evacuating the sample with a vacuum pump. 2.2. Experimental Method. The equation of calculating the isobaric heat capacity is given as follows17−19 c p,app =

Q m ·ΔT

(1)

where Q represents the heat flux generated from the heater, m refers to the mass rate of the fluid, ΔT = T2 − T1 is the temperature increase of the sample. Here, T1 and T2 are the inlet and outlet sample’s temperatures inside the calorimeter. In this work, the temperature increment is about 5 K. The heat energy Q consists of the heat obtained by the sample and heat loss released to the surroundings. So that eq 1 becomes c p,app =

Q + QL QL Q = F = cp + m ·ΔT m ·ΔT m ·ΔT

(2)

Received: November 17, 2016 Accepted: February 8, 2017 Published: February 15, 2017 1119

DOI: 10.1021/acs.jced.6b00959 J. Chem. Eng. Data 2017, 62, 1119−1124

Journal of Chemical & Engineering Data

Article

Table 1. Summary of the Data Sets for the Thermophysical Properties of R1234yf authors

thermal physical property

temperature range (K)

Tanaka and Higashi2 Tanaka and Higashi2 Tanaka and Higashi2 Kano et al.3 Lago et al.4 Nicola et al.5 Nicola et al.6 Tanaka et al.7 Tanaka et al.7 Fedele et al.8 Perkins and Huber9 Richter et al.1 Richter et al.1 Fedele et al.10 Meng et al.11 Qiu et al.12 Zhao et al.13 Zhao et al.13 Yang et al.14 Gao et al.15

critical parameters vapor pressure surface tension speed of sound speed of sound PVT property vapor pressure heat capacity density vapor pressure thermal conductivity PVT property vapor pressure compressed liquid density viscosity compressed liquid density liquid viscosity surface tension vapor pressure heat capacity

310−360 273−340 278.15−353.15 260−360 243−373 224−366 310−360 310−360 245.65−343.15 242−344 232−400 250−366 283.15−353.15 243−363 283−363 293−365 293−365 248.17−361.05 305−355

pressure range MPa

2−6 0.084−3.716 0.039−3.218 2−5 2−5 0.1−23

saturation-35 saturation-30 1−100 saturation saturation 0.123−2.955 1.5−5

Figure 1. Relation between cp,app, cp, and 1/m. ■, cp,app; solid line, fitted curve.

Where cp,app represents the observed isobaric heat capacity acquired by the calorimeter, QF is the heat energy exerted on the fluid. QL is the heat loss. cp denotes the true heat capacity of the fluid. From eq 2, it is observed that the influence of heat loss decreases when mass flow rate m increases. In this case, the impact of the heat leak can be obtained by measuring the heat capacity at different mass flow rate then extrapolating m to infinite flow. As shown in eq 2, cp,app can be regarded as cp when 1/m is zero (see Figure 1). We have c p,app = c p (3)

Figure 2. Schematic diagram of the experiment system. TB, thermostatic bath; EC, experimental cell; TS, thermometer; HC, heater; TC, high-accuracy temperature controller; DMM, Keithley 2700 data acquisition system; PC, computer; PS1,PS2, Pressure sensor; MF, Siemens mass flowmeter; VP, vacuum pump; SB, sample bottle; V1−V7, needle valve; PR, pressure reducing valve; PB, back pressure valve; P, constant-flux pump.

Table 2. Standard Uncertainties of the Measurements

We note that the heat capacity data points are always regarded as the values at the average temperature of the inlet sample and the outlet sample. T = (T1 + T2)/2. 2.3. Apparatus. The apparatus mainly includes a flow calorimeter, a mass flow meter, a thermostatic bath, temperature and pressure measuring system, vacuum system, and data acquisition system, as shown in Figure 2. The flow calorimeter is the key part of whole apparatus. The calorimeter is mainly composed of a microheater, two platinum resistance thermometers, and a special designed chamber, whose detailed information was described in our previous work.20

measurable quantity

uncertainty

temperature massflow rate heat flux pressure isobaric heat capacity

10 mK 0.05% 0.01% 15 kPa 0.5%

The fluid was circulated continuously by means of a constant flow rate pump. The liquid flowed out of the sample bottle and entered the thermostatic bath. Before the fluid entered the calorimeter, it passed through a long stainless steel tube that 1120



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Table 3. Experimental Heat Capacities of R1234yfa T (K)

P (MPa)

cp,exp (kJ·kg−1·K−1)

T (K)

P (MPa)


303.58 303.53 303.55 303.72 303.74 303.75 303.81 303.73 303.75 303.80 303.77 303.61 303.61 303.60 303.60 303.61 303.61 303.60 303.72 303.67 303.79 303.79 313.66 313.67 313.69 313.69 313.72 313.66 313.64 313.63 313.79 313.61 313.69 313.66 313.64 313.64 313.65 313.72 313.70 313.70 313.72 313.72 313.70 313.72 323.62 323.65 323.68 323.69 323.71 323.69 323.71 323.71 323.71 323.69 323.63 323.64 323.64 323.64 323.66 323.65 323.66

1.57 2.03 2.53 3.04 3.53 4.02 4.52 5.00 5.52 5.98 6.51 6.98 7.49 8.01 8.49 8.98 9.47 10.01 10.52 10.99 11.45 12.07 1.51 2.01 2.51 3.00 3.51 4.00 4.49 5.00 5.49 6.02 6.50 6.99 7.50 7.98 8.49 8.97 9.50 10.01 10.50 10.98 11.46 12.04 2.02 2.50 3.01 3.51 3.99 4.52 5.02 5.50 5.99 6.49 6.94 7.52 8.00 8.51 8.96 9.54 9.99

1.404 1.378 1.368 1.354 1.352 1.343 1.328 1.323 1.317 1.305 1.303 1.286 1.288 1.281 1.282 1.278 1.278 1.278 1.271 1.267 1.263 1.260 1.456 1.450 1.447 1.439 1.426 1.401 1.387 1.377 1.355 1.353 1.350 1.340 1.330 1.325 1.321 1.318 1.314 1.311 1.306 1.303 1.296 1.293 1.493 1.479 1.468 1.455 1.445 1.425 1.415 1.402 1.395 1.382 1.365 1.359 1.354 1.348 1.345 1.335 1.333

333.72 333.72 333.69 333.72 333.69 333.79 333.79 333.82 333.82 343.68 343.79 343.68 343.74 343.70 343.75 343.81 343.72 343.73 343.71 343.73 343.73 343.77 343.80 343.70 343.75 343.67 343.69 343.68 343.70 353.73 353.73 353.73 353.78 353.71 353.75 353.79 353.81 353.71 353.74 353.77 353.79 353.69 353.73 353.76 353.78 363.75 363.78 363.74 363.69 363.77 363.76 363.78 363.75 363.79 363.78 363.80 363.76 363.73 363.76 363.78 363.83

8.01 8.50 9.01 9.49 9.99 10.52 11.00 11.48 12.03 2.53 3.01 3.51 3.99 4.49 5.02 5.56 6.04 6.51 7.00 7.50 7.98 8.52 9.01 9.47 10.02 10.51 11.06 11.50 12.01 4.51 4.99 5.50 6.04 6.51 6.99 7.49 7.99 8.50 8.99 9.53 10.01 10.52 11.01 11.52 12.01 4.51 4.99 5.48 6.03 6.50 7.02 7.53 7.99 8.51 8.99 9.49 10.01 10.52 11.05 11.50 12.08

1.409 1.400 1.395 1.382 1.374 1.361 1.357 1.351 1.347 1.797 1.724 1.642 1.609 1.565 1.541 1.519 1.485 1.478 1.451 1.442 1.436 1.431 1.425 1.402 1.399 1.384 1.376 1.373 1.367 1.724 1.667 1.629 1.601 1.559 1.543 1.524 1.514 1.484 1.476 1.464 1.455 1.438 1.428 1.426 1.420 1.973 1.836 1.738 1.661 1.635 1.594 1.567 1.542 1.528 1.509 1.500 1.483 1.473 1.467 1.464 1.464

1121



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Table 3. continued

a

T (K)

P (MPa)


T (K)

P (MPa)


323.69 323.68 323.70 323.73 333.67 333.68 333.63 333.66 333.71 333.66 333.68 333.61 333.63 333.68 333.66 333.69

10.53 10.98 11.47 12.01 2.08 2.52 3.00 3.48 4.04 4.50 5.00 5.49 5.98 6.51 7.02 7.50

1.331 1.325 1.318 1.316 1.629 1.613 1.574 1.557 1.538 1.497 1.483 1.451 1.444 1.427 1.418 1.412

373.09 373.19 373.24 373.28 373.30 373.30 373.30 373.32 373.32 373.32 373.34 373.36 373.38 373.39 373.40 373.42

4.51 4.99 5.48 5.98 6.49 7.00 7.52 8.03 8.51 8.99 9.51 9.99 10.53 11.02 11.51 11.98

2.606 2.118 1.910 1.774 1.677 1.623 1.581 1.555 1.534 1.511 1.504 1.499 1.487 1.477 1.472 1.468

Standard uncertainty u is u(T)= 10 mK, u(P) = 15 kPa, and the combined expanded uncertainty Uc,r(cp,exp)= 0.01 (0.95 level of confidence, k = 2).

was placed inside the thermostatic bath to guarantee the sample achieved the temperature of the bath. When the fluid flowed into the calorimeter, it absorbed a target amount of heat energy produced by the heater. Then, the fluid flowed out of the bath and returned to the bottle, and a cycle was completed. The sample’s inlet and outlet temperatures were measured by two platinum resistance thermometers. The pressure was obtained by a pressure sensor. The mass flow rate was measured (about 108−268 mg/s) by a mass flow meter (SIEMENS, MASS 2100, DI1.5). Using the temperature increment, the heat flux, and the mass flow rate, we acquired observed isobaric heat capacities by applying eq 2. 2.4. Assessment of Uncertainties. Applying the propagation law of uncertainty, the relatively expanded uncertainty of heat capacity is expressed in the equation ⎛ δQ ⎞2 ⎛ δT ⎞2 ⎛ δm ⎞2 ⎟ + ⎜ ⎟ 6Uc,c p = k ⎜ ⎟ + ⎜ ⎝ ΔT ⎠ ⎝m⎠ ⎝Q ⎠

Figure 3. Isobaric heat capacities of R1234yf in compressed liquid and supercritical phases; ■, 303.68 K; ○, 313.68 K; △, 323.68 K; ▽, 333.7 K; ◁, 343.73 K; ▷, 353.75 K; ●, 363.77 K; ×, 373.31 K; solid line, calculated from eq 5.

(4)

The detailed information for the uncertainties of variables involved is shown in Table 2. When the coverage factor k = 2, the combined expanded uncertainty of the heat capacity was evaluated to be within 1.0%.

Table 4. Parameters in Equation 5 R1234yf a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 AAD% MAD% No. of points

3. RESULTS AND DISCUSSIONS The isobaric heat capacities of R1234yf were measured in the compressed liquid phase and supercritical phase from 303 to 373 K in the pressure range of 1.5−12 MPa. A total of 154 experimental data were acquired and the experimental results were compiled in Table 3 and illustrated in Figure 3. As observed, the heat capacity value increases with temperature, and an increase in pressure leads to a decrease in heat capacities. Moreover, heat capacities decrease sharply in the low pressure region and nearly remain constant in the high pressure region at each isotherm. An empirical equation was applied to reproduce present results from 303 to 363 K, and the equation was given by Mc p R

=

10.108684 −2.579127 −0.843628 −2.766226 7.610532 −1.556891 0.215961 −0.133541 0.424453 −0.086000 0.56 2.52 138

AAD% = 100 × (∑Ni=1 |(cp,cal − cp,exp)/cp,cal|)/N; MAD% = 100 × MAX(|(cp,cal − cp,exp)/cp,cal|)N

a

a0 + a1ln(1 − Tr) + a 2(ln(1 − Tr))2 + a3Pr + a4Pr 2 + a5Pr 3

where cp refers to the isobaric heat capacity (kJ·kg−1·K−1), Tc represents the critical temperature (367.85 K) and Pc refers to

1 + a6 ln(1 − Tr) + a 7Pr + a8Pr 2 + a 9Pr 3

(5) 1122



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Figure 4. Comparison between present experimental data with results from Tanaka et al, Gao et al., and equation of state by Richter et al. ■, present work 303.68 K; ○, present work 313.68 K; △, present work 323.68 K; ▽, present work 333.70 K; ◁, present work 343.73 K; ▷, present work 353.75 K; ●, present work 363.77 K; ×, present work 373.31 K; □, Gao et al. 313.68 K; ▲, Gao et al. 323.68 K; ▼, Gao et al. 333.70 K; ⧫, Gao et al. 343.73 K; ◊, Gao et al. 353.75 K; ★, Tanaka et al. 313.68 K; ☆, Tanaka et al. 323.68 K; ⊙, Tanaka et al. 333.70 K; +, Tanaka et al. 343.73 K; -, Tanaka et al. 353.75 K; solid line, equation of state by Richter et al.

Figure 6. Deviation between present experimental values and data obtained by Gao et al. ■, 313.686 K; ○, 323.675 K; △, 333.70 K; ▽, 343.73 K; ◁, 353.75 K.

Figure 7. Deviations between experimental results and calculations by Richter et al. equation. ■, 303.68 K; ○, 313.68 K; △, 323.68 K; ▽, 333.7 K; ◁, 343.73 K; ▷, 353.75 K; ●, 363.77 K; ×, 373.31 K;.

experimental measurements are very close to Gao et al. data except at 355 K which is close to critical temperature. Figure 7 illustrates the deviations between present data and calculations from Richter’s equation. It can be found that those calculated data are approximately consistent with our experimental data in compressed liquid phase. The maximum deviation is 6.87% and occurs in the supercritical region. The comparison results confirm the accuracy of Richter’s equation in calculating isobaric heat capacity. Because Tanaka et al.7 and Gao et al.15 have derived heat capacities of R1234yf in the saturated liquid phase in a wide range of temperature and heat capacities in this paper that were far from saturation; saturated liquid heat capacities were not acquired in this paper.

Figure 5. Deviation between present experimental data and data reported by Tanaka et al. ■, 310 K; ○, 320 K; △, 330 K; ▽, 340 K; ◁, 350 K; ▷, 360 K.

the critical pressure (3.3822 MPa).1 R (8.314 J·mol−1·K−1) is general gas constant and M is molar mass (114.04 g·mol−1), Pr = P/Pc, Tr = T/Tc. a0−a9 are the coefficients of eq 5 and their values are shown in Table 4. The relative average deviation and the relative maximum deviation from eq 5 with present results are 0.56% and 2.52%, respectively. The experimental results were compared with Tanaka et al. results, Gao et al. data, and calculated values by Richter et al. The detailed comparisons were shown in Figures 4−7. As shown in Figure 5, the measurements agree well with the data obtained by Tanaka et al., and the mean and maximum deviations of our experimental data are 1.66% and 3.06%, respectively. Figure 6 presents a comparison of experimental results in this study and data acquired by Gao et al. The

4. CONCLUSIONS The measurements of heat capacities for R1234yf were conducted using an adiabatic steady flow calorimeter in both compressed liquid and supercritical phases in a wider temperature and pressure range than data reported by other 1123



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Conditions by Surface Light Scattering. J. Chem. Eng. Data 2014, 59, 1366−1371. (14) Yang, Z.; Kou, L.; Mao, W.; Lu, J.; Zhang, W.; Lu, J. Experimental Study of Saturated Pressure Measurements for 2,3,3,3Tetrafluoropropene (HFO-1234yf) and 2-Chloro-1,1,1,2-Tetrafluoropropane (HCFC-244bb). J. Chem. Eng. Data 2014, 59, 157−160. (15) Gao, N.; Jiang, Y.; Wu, J.; He, Y.; Chen, G. Measurements of the isobaric heat capacity of R1234yf in liquid phase at temperatures from 305K to 355K and pressures up to 5 MPa. Fluid Phase Equilib. 2014, 376, 64−68. (16) Dang, Y.; Kim, H. S.; Dang, C.; Hihara, E. Measurement of vapor viscosity of R1234yf and its binary mixtures with R32, R125. Int. J. Refrig. 2015, 58, 131−136. (17) Wu, Y.; Yu, Q.; Zhong, H.; Lin, R. A new flow calorimeter for the determination of the isobaric heat capacity of vapors. Thermochim. Acta 1995, 254, 93−101. (18) Ernst, G.; Maurer, G.; Wiederuh, E. Flow calorimeter for the accurate determination of the isobaric heat capacity at high pressures; results for carbon dioxide. J. Chem. Thermodyn. 1989, 21, 53−65. (19) Kagawa, N.; Matsuguchi, A.; Yamaya, K.; Watanabe, K. Behavior of isobaric heat capacity of R32 in the gas phase. Int. J. Refrig. 2013, 36, 2216−2222. (20) Lv, S.; Zhao, X.; Liu, Y. Measurements for isobaric specific heat capacity of ethyl fluoride (HFC-161) in liquid and vapor phase. Fluid Phase Equilib. 2016, 427, 429−437.

authors. In this study, experimental isobaric heat capacity values for R1234yf at temperatures above 360 K and pressures higher than 5 MPa were first reported. A total of 154 experimental data were acquired from 303 to 373 K at pressures up to 12 MPa. On the basis of the compressed liquid heat capacity data, an empirical equation was correlated to represent the present results.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86-29-82665445. Fax: +86-29-82668789. ORCID

Xiaoming Zhao: 0000-0003-2938-8080 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS We acknowledge the support of the National Natural Science Foundation of China (Grant 51276143). REFERENCES

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Isobaric Heat Capacity Measurements for R1234yf from 303 to 373 K

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