Isochoric Heat Capacity and T–ρ Dependence of Cooling Agents along the Phase Equilibrium Line Alkhasov A. B., Dvoryanchikov V. I., Rabadanov G. A. and Ramazanova D. P. Institute of Geothermal Problems, Dagestan Scientific Center, Russian Academy of Sciences, pr. Shamilya 39a, Makhachkala, 367003 RussiaE-mail: vasiliy_dv01@mail.ru Abstract: The entropy data were used to calculate the isochoric heat capacity along the phase equilibrium line. The rules governing the thermodynamic properties of cooling agents and possible alternative mixture variants were analyzed. Keywords: isochoric heat capacity; cooling agents. Because of their toxicity, corrosion activity, and inflammability, ammonia, ethers, and sulfurous anhy dride do not suit consumers who use cold for domestic and industrial purposes. Transition cooling agents appeared; these are binary, ternary, and even quarter nary mixtures of the known Freons that do not destroy ozone. New cooling agents with the required proper ties were synthesized. They are largely based on R125, R32, R134a, R143a, etc. cooling agents. In certain cases, propane, butane, isobutane, and ethers [1] are added to them. One of the advantages of thermal pump units is their universality with respect to the power level, from fractions to dozens thousands kilowatt units. The use of thermal pumps offers much promise in combined systems together with other technologies for use of renewable energy sources (solar, wind, bioenergetic, etc.), because it allows the parameters of conjugated systems to be optimized and the highest economic performance to be attained. These advantages of ther mal pumps explain their extensive use in developed countries and the world at large. In Russia, the introduction of thermal pump units encounters difficulties. Mainly, high power (100– 1000 kW) machines are installed. Currently, 20 MW aggregates are developed. The main problem of the introduction of high power thermal pump units is the absence of the required efficiency if the circuitry is not worked out fairly well and the source parameters are selected poorly [2]. Studies of the thermophysical properties of cooling agents that allow the effective ness of heat engines to be increased are therefore of considerable interest. The search for new mixtures is based on binary compositions whose components have substantially different normal boiling temperatures and ternary mixtures with intermediate component boiling temperatures. The appearance of new working substances required studies of their thermophysical properties, largely by numerical methods. There are very few experimental studies, especially for mixtures ([3,4,7-9] etc.). The data on liquid–vapor phase equilibria over the whole concentration range, liquid and vapor den sities, p–V–T dependences, heat capacities of mix tures, and the transfer properties of gaseous mixtures and solutions are of importance. The purpose of this work was to analyze the rules governing the thermodynamic properties of cooling agents and possible alternative cooling agent mixture (two and three component) variants. These rules are of importance for the selection of heat transfer agents, the construction of phase diagrams, calculations of cycle parameters, and the optimization of cooling machine (thermal pump) operation.

CV, kJ/(kg K)
8
6
4
2
0
300	320	340	360	380
				T, K

Fig. 1. Calculated heat capacities of Freon R134a along the phase equilibrium line. Fig. 2. Phase equilibrium curves [5] for Freons (1) R134a

Fig. 3. Phase equilibrium curves [5] for Freons (1)R402A and (2) R404A. The literature entropy data were used to calculate the isochoric heat capacities C''v and C'v along the phase equilibrium line by equation:S₂ – S₁ = C_V ln ( T₂ / T₁ ).

The isochoric heat capacities C'v and C''v of Freon R134a along the phase equilibrium line were calculated over the temperature, density, and pressure ranges 290–374.18 K, 26.9–1229.2 kg/m³, and 0.064–4.06 MPa from the entropy data [5], respectively (Fig. 1). The R134a Freon coexistence curves are shown in Fig. 2. The T–ρ values close to the critical point of Freon R134а were determined graphically [6]. A similar procedure was used to determine the isochoric heat capacities of the R227ea, R401A, R404A, R402A, etc. Freons. The curves of the coexistence of the R402A and R404A Freons are shown in Fig. 3. The T–ρ values close to the critical points of the R402A and R404A Freons were also determined graphically. Attempts to describe the phase equilibrium curve by polynomials of degrees n = 5 and 6 for Freon R402a gave very approximate results [7] (Fig. 4). Satisfactory results were obtained graphically. The critical parameters determined this way are listed in Table 1. It was found empirically that the γ(T) = (ρ' + ρ'')/2 function was a linear function of the temperature of saturation. The extrapolation of this experimental dependence to T = T_c c yields the corresponding ρ_c value (Fig. 3). Note that the critical densities obtained this way are as a rule exaggerated. This explains deviations from the “rectilinear diameter” rule (linearity of the γ(T) function) as we approach the critical point. This method only allows approximate ρ_c values to be obtained [8].

Fig. 4. Phase equilibrium curves [5] for Freon R402A: (1) experimental and (2) calculated (n = 5)

Fig. 5. Chromatogram of the R404A (Forane FX 70) cooling agent. Studies of the thermophysical properties of cooling agents and possible alternative mixture variants are of importance for the selection of heat transfer agents, the construction of diagrams and calculations of cycle parameters, and the optimization of heat engine or thermal pump operation. The data on the isochoric heat capacity of Freons can be used for optimizing the operation of thermal pumpsthat use coolants as heat transfer agents in a secondary circuit for heat removal with the use of geothermal sources. We studied samples of the R404A cooling agent (trade name Forane FX70) produced in Spain under license from Arkema (France) for the subsequent experimental determination of the C_V heat capacity on an adiabatic calorimeter and a Khrom5 chromatograph with a flame ionization detector and a 3.7 m column packed with chromatron N-AW. The results obtained are shown in Fig. 5. The composition of the samples was 52.410 wt % R143a, 43.700 wt % R125, and 4.322 wt % R134a. This closely corresponds to the GOST R certificate R404A (R125 (CF₃–CHF₂)/R134a (CF₃–CH₂F)/R143a(CF₃–CH₃) = 44/4/52). The appearance of new working substances required studies of their thermophysical properties and the creation of a bank of data on the properties of cooling agents. A large number of binary, ternary, and quaternary cooling agent compositions was suggested. These compositions find wide applications in the creation of new aggregates used in industry and everyday life. Table 1. Critical parameters of cooling agents that do not destroy ozone

Cooling agent	–Tb, °С [1]	Тc , К	ρc , kg/m^3
R 134а	26.2	374.18 [5]	508.00 [5]
R 401А	33.1	381.25	510.60
R 402А	49.2	349.00*	500.00*
R 404А	46.5	345.20*	485.00*
R 407А	45.5	351.00*	500.00*

Note: The values obtained graphically are labeled by asterisks. INTRODUCTION Analysis of the thermodynamic properties of refrigerants and possible alternative mixtures is an impor₃ tant practical problem. The safe freons of the new generation of methane, ethane, and propane series are, along with their mixtures (Table 2), considered the most promising substituents of conventional chlorine containing freons [10].The aim of this work is to perform an analysis of the thermodynamic properties of refrigerants of a propane series. EXPERIMENTAL Based on data on the entropy of HFC 227ea freon [11], we calculated the C''_V and C'_V values of isochoric heat capacities on the line of phase equilibrium over the temperature range of 245.15 to 375.04 K and densities of 5.17 to 589.99 kg/m³ according to the isochore in the Т–S coordinate system:

Table. 2. Ozonesafe refrigerants of a propane series

Refrigerants	Formula	^Tboili^,^°^C	^Tcritical^, K	^Pcritical^,^MPa	ρcritical, kg/m^3
R218 R227ea R227ca R236ea R236fa R245ca R290 R1270 Ethyl methyl ether Trimethylamine	CF3–CF2–CF3 CF3–CHF–CHF3 CF3–CF2–CHF3 CF3–CHF–CHF2 CF3–CH2–CF3 CF3–CF2–CF2 C3H8 C3H6 C3H8O C3H9N	–36.1 –17.3 –16.0 6.5 –0.7 25.0 –41.6 –47.73 7.45 3.0	345.05 375.04 – 412.4 – – 369.85 365.05 437.8 432.79	2.677 2.930 – 3.412 – – 4.248 4.640 4.430 4.087	628.0 589.99 – – – – 227 ± 2 230.0 272.0 232.7

Table. 3. Thermodynamic properties of HFC 227ea Freon
T, K	ρ' . 10	–3	kg/m^3	ρ'' . 10	–3	,kg/m^3	C'V , kJ/(kg K)	C"V , kJ/(kg K)
245.15	1.5842			0.0051675			1.210	0.2669
250.15	1.5677			0.0064448			1.219	0.2893
255.15	1.5508			0.0079646			1.228	0.3093
256.728	1.5454			0.0084998			1.236	0.3229
260.15	1.5336			0.00975954			1.241	0.3308
265.15	1.5158			0.0118630			1.249	0.3431
270.15	1.4977			0.0143120			1.261	0.3398
273.15	1.4866			0.0159650			1.271	0.3695
275.15	1.4791			0.0171480			1.278	0.3743
280.15	1.4601			0.0204110			1.288	0.3843
285.15	1.4405			0.0241510			1.303	0.3969
290.15	1.4204			0.0284210			1.318	0.4091
295.15	1.3997			0.0332800			1.336	0.4203
300.15	1.3785			0.0387970			1.355	0.4317
305.15	1.3566			0.0450500			1.376	0.4419
310.15	1.3349			0.0521060			1.399	0.4510
315.15	1.3102			0.0601560			1.426	0.4596
320.15	1.2857			0.0692520			1.455	0.4670
325.15	1.2600			0.0795870			1.488	0.4737
330.15	1.2329			0.0913680			1.528	0.4784
335.15	1.2043			0.1048600			1.572	0.4810
340.15	1.1737			0.1204400			1.626	0.4815
345.15	1.1405			0.1385900			1.692	0.4770
350.15	1.1041			0.1600600			1.774	0.4663
355.15	1.0632			0.1860000			1.883	0.4458
360.15	1.0155			0.2184000			2.035	0.4049
365.15	0.9566			0.2613000			2.269	–
370.15	0.8739			0.3258600			2.714	–
371.15	0.8512			0.3258600			3.231	–
372.15	0.8243			0.3663200			3.555	0.4276
373.15	0.7905			0.3945300			4.058	0.8279
374.15	0.7417			0.4360300			5.039	1.7346
375.04	0.58999			0.5899900			14.215	6.6801

Table. 4. Thermodynamic and thermal properties of propane (ρ, kg/m^3)
T, К	P, MPa	ρ' [14]	ρ'' [14]	ρ' [13]	ρ'' [13]	СV , J/(g K)
						[14]	[13]
270.15	4.427	539.9				1.627
270.67	–	–		531		–	1.645
275.15	7.953	539.6				1.616
280.15	11.458	539.3				1.617
285.15	14.939	539.0				1.647
290.15	18.398	538.7				1.666
295.15	21.836	538.4				1.691
300.15	25.251	538.1				1.692
305.15	28.640	537.8				1.686
310.15	6.561	490.3				1.691
315.15	9.049	490.1				1.706
320.15	11.532	489.8				1.727
325.15	14.008	489.6	454.8			1.732
330.15	16.475	489.3	454.6			1.738
330.59	–	–	–	436		–	1.828
335.15	18.934	489.1	454.3			1.744
340.15	21.386	488.9	454.1			1.751
345.15	23.827	488.6	453.9			1.731
350.15	26.253	488.4	453.7			1.758
355.15	28.668	488.2	453.5			1.756
366.66	–	–	–	306		–	2.192
369.86	–	–	–	229		–	3.323
Tcritical = 369.95	Ркр ^= 4.200	^ρcritic ^= 227 ^± ^2
369.88	–	–			224	–	4.052
368.28	–	–			159	–	2.903
375.15	5.095	301.1				2.236
380.15	5.744	301.0				2.110
385.15	6.404	300.9				2.032
390.15	7.072	300.8				1.952
395.15	7.746	300.7				1.924
400.15	8.425	300.6				1.824
405.15	9.109	300.5				1.788
410.15	9.795	300.4				1.814
420.15	11.176	300.2				1.810
425.15	11.869	300.1				1.854

Fig. 6. Calculated values of heat capacity of HFC 227ea freon

on the line of phase equilibrium. Fig.7. Line of phase equilibrium of HFC 227ea freon[6]. Fig. 8. Line of phase equilibrium of R290 (propane) in the given coordinates: (1) the results from [13]; (2–6), the results from [14].

The calculated values of C''_V and C'_V isochoric heat capacities on the line of phase equilibrium (Table. 3) are given in Fig. 6. The line of phase equilibrium of HFC 227ea freon is given inFig.7. The critical parameters of system are Т_c = 375.04 К, and ρ_c = 589.99 kg/m³. Interest in studying the thermal and volume properties of propane remains strong [12–16]. Various ways of measuring are used that yield satisfactory results when compared. Of special interest are mixtures of propane with isobutene, propylene (as a heat carrier in heat pumps), and other refrigerants: R402A, R402B, R403A, and R403B (as a refrigerant in refrigerating equipment). Natural refrigerants can substitute for R404A, R134A, and R407C, while others can reduce the refrigerant load, thus saving electricity.Existing experimental data on thermodynamic and transfer properties of mixture refrigerants are limited and often contradictory [10]. Measurements of isochoric heat capacity С_V for propane were performed by Anisimov et al. at the Gubkin Russian State University of Oil and Gas. The purity of the propane was 99.98%. The measurements of heat capacity were performed on six isochors: 0.159, 0.224, 0.229, 0.306, 0.436, and 0.531 g/cm³ in the temperature range of 80 to 374 K. The maximum relative error of the obtained heat capacity values were 0.48% far away from the transit point of the coexist ence curve and 1.5% nearer to it. At density ρ = 0.159 g/cm³, the maximum relative error of heat capacity values rose to 0.68%; near the transit point, to 2% [13]. In [14], the error of determining the heat capacity was ±3.2% on the line of phase equilibrium and ±4.8% in the critical range. The measurements of heat capacity were performed in the temperature range of 270 to 425 K. In Fig. 8, we see a comparison of the results on the dependence of density vs. temperature of propane, in the coordinates given in [13]. The results from comparing the measurements on isochoric heat capacity are given in Table 4. CONCLUSIONS Studies of the heat and physical properties of refrigerants and possible alternative mixture variants are important in selecting a heat carrier, plotting diagrams and calculating the parameters of a cycle, and optimizing the functioning of refrigerators and heat pumps. Data on the isochoric heat capacity of freons can be used for to optimize heat pumps that employ refrigerants as heat carriers in the secondary heat line when using geothermal sources [6]. REFERENCES 1. Tsvetkov O. B. and Laptev Yu. A., Khim. Komp. Modelir., Butler. Soobshch., Att., No 10, 54 (2002). 2. Ermakov A. M., Extended Abstract of Candidate’s Dissertation in Technical Science (Kazan, 2007). 3. Magee J. W. Int. Thermophys. 21, 151 (2000). 4. Baginskii A. V., Stankus S. V. and Kosheleva A. S, Teplofiz. Aeromekh. 11, 647 (2004). 5. Sahverdiyev A. N. and Quliyev H. M. Alternativ Soyuducu Agentler Veqarisiqlar (Baki, 2002).6. Dvoryanchikov V. I., Thermal Field of the Earth and Methods of Its Study, Collected vol. (2008), p. 79. [in Russian]. 7. Demidovich B.P. , Maron I. A. and Shuvalova E. Z. , Numerical Methods of Analysis (Fizmatgiz, Moscow, 1963) [in Russian]. 8. Spielrein E.E. and Kesslman P.M., Fundamental Principles of the Theory of Thermophysical Properties of Substances (Moscow, 1977) [in Russian]. 9. Dvoryanchikov V. I. and Rabadanov G. A., Zh. Fiz. Khim. 84, 1009 (2010) [Russ. J. Phys. Chem. A 84, 010)]. 10. Stankus S. V., Baginskii A. V., Verba O. I., et al., in Proceedings of the 12th Russian Conference on Thermophysical Properties of Substances (2008) p. 41.11. Chen Z. S., Hu P., and Cheng W. L., in Proceedings of the 15th Symposium on Thermophysical Properties(Boulder, CO, 2003), p. 398.12. Amirkhanov Kh. I., Levina L. N., and Zakar’yaev Z. R., in Thermophysical Properties of Substances and Materials (Izdvo Standartov, Moscow, 1982), p. 24 [in Russian].13. Anisimov M. A. , Beketov V. G. , Voronov V. P. , et al., in Thermophysical Properties of Substances and Materials (Izdvo Standartov, Moscow, 1982), p. 48 [in Russian].14. Kitajima N., N. Kagawa, S. Tsuruno, J. W. Magee, and K. Watanabe, in Proceedings of the 15th Symposium on Thermophysical Properties (Boulder, CO, 2003), p. 567.15. Lim J. S., Ho Q. N., Park J. Y., and Lee B. G., in Proceedings of the 15th Symposium on Thermophysical Properties (Boulder, CO, 2003), p. 3597. 16. Higashi Y., in Proceedings of the 15th Symposium on Thermophysical Properties (Boulder, CO, 2003), p. 467.

ФИО	Дворянчиков Василий Иванович
Название статьи	Isochoric Heat Capacity and T-ρ Dependence of Cooling Agents along the Phase Equilibrium Line
Рубрика	Технические науки. Химическая термодинамика.
Телефон (с кодом)	89634115657
E- mail	vasiliy_dv01@mail.ru
Адрес (домашний)	г.Махачкала, ул. Карабудагова, 7.
Индекс	367000

Алхасов Алибек Басирович – доктор тех. наук, Институт проблем геотермии, Дагестанский научный центр, Российская академия наук.

Дворянчиков Василий Иванович – доктор тех. наук, Институт проблем геотермии, Дагестанский научный центр, Российская академия наук. E-mail: vasiliy_dv01@mail.ru

Рабаданов Гаджи Аппасович – кандидат хим. наук, Институт проблем геотермии, Дагестанский научный центр, Российская академия наук.

Рамазанова Динара Пашаевна – аспирант, Институт проблем геотермии, Дагестанский научный центр, Российская академия наук.

Alkhasov A. B. - Doctor of Technical Sciences, Institute sor Geotheemal Problems of the Dagestan Scientific Centre of Russian Academy of Sciences.

Dvoryanchicov V. I. – Doctor of Technical Sciences, Institute sor Geotheemal Problems of the Dagestan Scientific Centre of Russian Academy of Sciences.

Rabadanov G. A. – Candidate of Chemical Sciences, Institute sor Geotheemal Problems of the Dagestan Scientific Centre of Russian Academy of Sciences.

Ramazanova D. P. - postgraduate, Institute sor Geotheemal Problems of the Dagestan Scientific Centre of Russian Academy of Sciences.

Institute sor Geotheemal Problems of the Dagestan Scientific Centre of Russian Academy of Sciences. Makhachkala, pr. Shamilya, 39a, 367030. Russian.