MEASUREMENTS OF ISOBARIC HEAT CAPACITY OF LIQUID PENTAFLUOROETHANE (R125)

Transcription

1 MEASUREMENTS OF ISOBARIC HEAT CAPACITY OF LIQUID PENTAFLUOROETHANE (R15) Xiang ZHAO, Shigehiro MATSUEDA, and Haruki SATO Faculty of Science and Technology Keio University , Hiyoshi, Kohoku-ku Yokohama 3-85, Japan ABSTRACT The isobaric specific heat capacity, c p, of liquid pentafluoroethane (R15) was measured with flow calorimeter. Twenty-four c p values were obtained in the range of temperatures K and pressures MPa. The expanded uncertainties are estimated to be 8.4 mk in temperature, 10 kpa in pressure, and kj kg -1 K -1 (about 0.6 %) in c p, with the level of confidence corresponding to 95 %. Based upon the measured c p data, a correlation of c p was developed as a function of temperature and pressure. The c p measurements were compared with the values derived from several existing thermodynamic equations of state. The c p measurements are best represented by the internationally recommended equation (Piao and Noguchi 1998) with relative deviations between % and %. 1. INTRODUCTION Reliable measurements of isobaric specific heat capacity, c p, are important in the applications of refrigerating and air-conditioning systems such as heat transfer calculations of heat exchangers. On the other hand, measurement of c p is an important experimental thermodynamic property study for establishing reliable thermodynamic equations of state or evaluating reliability of existing equations of state. The c p is related to an equation of state p( ρ, T ) by c p ρ o = c p R 0 T p T dρ + ρ T ρ p T p ρ ρ T, (1) o c p where is the ideal-gas heat capacity. Accurate values of the heat capacity are useful for establishing the reliable higher-order temperature derivatives of an equation of state. The c p values of liquid R15, which is used as one of the components of the binary or ternary refrigerant mixtures to replace R or R50, were measured in the compressed liquid phase. In addition, the correlation of c p was developed on the basis of the measurements. The c p measurements obtained in this work were compared with the values derived from several existing thermodynamic equations of state. The purity of R15 used was 99.9 mass% analyzed by the manufacturer. IIF - IIR Commission B1 Paderborn, Germany 001/ 5 1

2 . EXPERIMENTAL.1 Principle and apparatus The c p measurements were conducted using flow calorimeter. The apparatus was reconstructed in 1997 because of the overage usage more than 10 years. By using former apparatus, c p values of R114 (Ashizawa et al. 1987; Sato et al. 1987; Saitoh et al. 1989), R134a (Saitoh et al. 1990; Nakagawa et al. 1991b;), R13 (Nakagawa et al. 1990, 1991a, 1991b), R14b, R15a (Nakagawa et al. 1993), R3 (Yomo et al. 1994) were measured. The principle of the reconstructed apparatus is exactly the same as that of former one. The overall assembly is shown in Figure 1. Detailed descriptions regarding the experimental procedure and the flow calorimeter used were reported in previous reports (Ashizawa et al. 1987; Sato et al. 1987; Saitoh et al. 1989). In the apparatus, liquid sample flows in a closed circulation system, and heat flux is supplied by a microheater to the liquid sample when it flows through the highly adiabatic calorimeter (e). In the flow calorimeter, c p can be determined by three different kinds of measurement, heat flux, Q & ; temperature increment, T, which is the difference between the temperatures of the liquid sample before and after heating by the microheater ; and the mass flow rate, m&. With these measured parameters, cp can be defined as follows: Q& c p =. () m & T The heat loss, Q &, has to be examined carefully throughout the measurements. With the heat flux, Q &, and the possible heat loss, Q &, equation () may be rewritten as Q& Q& c p,exp = +, (3) m& T m& T where c p,exp is an apparent isobaric specific heat capacity obtained from the measurements without correction of Q &. If Q & is not negligible, c p, exp depends on m & and T. When heat loss is small enough, however, the same c p values will be measured at different m& and T conditions. The temperature and the temperature increment were measured with two 100 platinum resistance thermometers calibrated by a standard platinum resistance thermometer in accordance with ITS-90. The mass-flow rate was determined from several different periods of sampling time and the mass increment of sampling vessel (b3). The sampling vessel was placed on a digital mass balance (i) so as to measure the mass-flow rate directly and continuously. The flow stability was confirmed in real time by observing the temperature increment of the liquid sample under a constant energy supply, which was always monitored on a computer display. The pressure was measured using a quartz digital pressure gauge (d).. Reliability of the apparatus We have already reported on the measurements for 1,1,1-trifluoroethane (R143a) with the reconstructed apparatus at a domestic academic meeting (Yamamura et al. 1999). For testing the reproducibility and the heat loss of the apparatus, the test was conducted at a state of 310 K and.5 MPa with various m& and T values. As shown in Figure, c p values were reproduced within about kj kg -1 K -1 (about 0. %) at the different conditions of m& and T. If Q & is not negligible, the c p,exp depends on m& and T as shown by equation (3). It was confirmed from Figure that the measured c p,exp did not depend on neither m& nor T and the effect of the heat loss on the measurements is well within the predicted uncertainty. IIF - IIR Commission B1 Paderborn, Germany 001/ 5

3 to vacuum m5 to air j3 to vacuum m4 to air m3 j l m j1 m1 to vacuum a b1 c1 k c3 f to vacuum to air e b3 i c b f1 g to vacuum h to vacuum to air d a, Pump; b1-b3, Accumulator; c1-c3, Digital differential pressure indicators; d, Quartz digital pressure gauge; e, Calorimeter; f1-f, Thermostated baths; g, Needle valve; h, 3-way solenoid valve; i, Digital mass balance; j1-j3, N vessels; k, N bomb; l, Supplying bottle for liquid sample; m1-m5, Pressure gauges., Liquid sample;, N gas;, Heat-transfer fluid. Figure 1. Experimental assembly cp / kj kg -1 K R143a m& / s g -1 Figure. Reproducibility in c p measurements when we measured c p for liquid R143a at 310 K,.5 MPa (Yamamura et al. 1999) as a function of inverse mass flow rate and temperature increment; T = 5 K, T = 3 K, T = 1 K, IIF - IIR Commission B1 Paderborn, Germany 001/ 5 3 1

4 3. RESULTS 3.1 Measurements The c p values at twenty-four state points were obtained for R15, ranging from 85 K to 35 K in temperature and from 1.5 MPa to 3.0 MPa in pressure. The measured c p values of R15 are plotted on a c p - pressure diagram in Figure 3. We follow the ISO guidelines (International Organization for Standardization, 1993) for expressing the experimental uncertainty. The extended uncertainty, U, of the measured values can be represented by the following equation: U = k (u i ) (4) where k and u are the coverage factor and the standard uncertainty, respectively. The subscript, i, is the component of the uncertainty. When k is, then the level of confidence corresponds to 95%. The standard uncertainty corresponds to the standard deviation,, given by 1 n σ = ( x j xm ) (5) n 1 j= 1 where n denotes the number of data points. x j and x m represent the data value and the average of the data, respectively. The coverage factor, k, used equals. The standard uncertainties, u i, and the combined uncertainties, u c = ( (u i ) ) 1/, are shown in Table 1. The experimental uncertainties in temperature, pressure, and c p measurements are estimated to be not greater than 8.4 mk, 10 kpa, and kj kg -1 K -1 (about 0.6 %) K cp / kj kg -1 K K 315 K 310 K 305 K 300 K 95 K 90 K 85 K R p / MPa Figure 3. Measured c p of pentafluoroethane (R15) IIF - IIR Commission B1 Paderborn, Germany 001/ 5 4

5 Table 1. Standard Uncertainty, u i, for Temperature, Pressure, and c p Standard Uncertainty for Temperature u 1 platinum resistance thermometer 3.3 mk u thermometry bridge 0.7 mk u 3 temperature stability 1.0 mk u c combined uncertainty 4. mk Standard Uncertainty for Pressure u 1 dead weight pressure gauge (DH Instruments Inc., Model 50) 0.15 kpa u pressure gauge (d) calibrated with a dead weight pressure gauge 0.08 kpa u 3 pressure stability 5.0 kpa u c combined uncertainty 5.0 kpa Standard Uncertainty for c p u 1 heat flux, Q & J s -1 u mass flow rate, m& kg s -1 u 3 temperature increment, T K u c combined uncertainty kj kg -1 K Discussion The measured values of c p were correlated with the following function of temperature and pressure: c p / R = ( a + bp r cp r ) (6) a = a 1 + a /(1 - T r ) a 3 /(1 - T r ) + a 4 /(1 - T r ) 3 b = b 1 + b /(1 - T r ) b 3 /(1 - T r ) 1.5 c = c 1 + c /(1 - T r ) 1.5 p r = p / p c, T r = T / T c, R = R 0 / M. The critical pressure, p c, is MPa as reported by Yoshida et al. (1996). The critical temperature, T c, is kpa which has been reported by Kuwabara et al. (1995). The universal gas constant, R 0, is J mol -1 K -1, and molar mass, M, is 10.0 g mol -1. The determined coefficients of the correlation are listed in Table. For representing three dimensional state surface of c p in liquid phase, nine parameters were needed. Equation (6) is effective for the temperature range between 85 K to 35 K, and for the pressure range between 1.5 MPa to 3.0 MPa. This correlation reproduces the measured c p data within 0.33 % as the maximum deviation and 0.16 % as the standard deviation. The relative deviation of the measured data from equation (6) is shown in Figure 4. Table. Coefficients of Equation (6) a i e e-4 b i e e-1 0 c i e- 0 0 IIF - IIR Commission B1 Paderborn, Germany 001/ 5 5

6 100 (cp exp- cp cal) / cp cal MPa.5 MPa.0 MPa 1.5 MPa T / K Figure 4. Relative deviations of the measured c p values from equation (6) The c p measurements were compared with the values derived from existing thermodynamic equations of state (EOS); the internationally recommended EOS formulated by Piao and Noguchi (1998); the EOS by Sunaga et al. (1998); and the EOS by Outcalt and McLinden (1995). Figure 5 shows the deviations of the c p measurements from three different EOSs. As shown in Figure 5, the EOS formulated by Piao and Noguchi reproduces the measured c p data within % and with 0.0 % as the standard deviation. The EOS by Sunaga et al. reproduces it within % and with 0.39 % as the standard deviation. The EOS by Outcalt and McLinden reproduces it within % and with 0.37 % as the standard deviation. As a result, the c p measurements are best represented by the internationally recommended EOS (Piao and Noguchi 1998). Other heat capacity data for R15 were available. Wilson et al. reported the c p measurements at temperatures from 16 K to 333 K along two isobars, 0.1 MPa and 3.45 MPa, with the experimental uncertainty of % (Wilson et al. 199). Lüddecke and Magee reported isochoric heat capacity, c v, measurements from the triple-point temperature to 345 K at pressures to 35 MPa with the experimental uncertainty of 0.7 % (Lüddecke and Magee 1996). To make comparisons with this work, we used the internationally recommended EOS formulated by Piao and Noguchi to convert the c v values to c p. Figure 6 shows the deviations of these experimental c p data and the converted c p values from the EOS by Piao and Noguchi. As shown in Figure 6, this work almost completely agrees with the converted c p values from the c v measurements of Lüddecke and Magee. The values of Wilson et al. are within.5 %. 4. CONCLUSION Twenty-four c p values of R15 were measured in the liquid phase at temperatures from 85 K to 35 K and pressures from 1.5 MPa to 3.0 MPa with the extended uncertainty of 0.6 %. The values of c p were correlated with a function of temperature and pressure. Measured c p data were compared with the values derived from available equations of state. IIF - IIR Commission B1 Paderborn, Germany 001/ 5 6

7 (cp exp- cp cal) / cp cal T / K Figure 5. Relative deviations of the c p measurements from three different EOSs; deviation from Piao and Noguchi EOS (1998) ; deviation from Sunaga et al. EOS (1998) ; deviation from Outcalt and McLinden EOS (1995) (cp exp - cp cal) / cp cal T / K Figure 6. Comparison of experimental heat capacity data from the EOS by Piao and Noguchi(1998) this work +; Wilson et al.(199) c v data (Lüddecke and Magee 1996) IIF - IIR Commission B1 Paderborn, Germany 001/ 5 7

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