Isobaric Heat Capacity of Liquid 1,1,1,3,3-Pentafluoropropane

Article pubs.acs.org/jced

Isobaric Heat Capacity of Liquid 1,1,1,3,3-Pentafluoropropane (R245fa) by Flow Calorimeter from 278 K to 343 K Hiroshi Tanaka,† Naoki Fujiwara,† and Haruki Sato*,‡ †

Graduate School of Science and Technology, and ‡Department of System Design Engineering, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan ABSTRACT: Isobaric heat capacity of liquid 1,1,1,3,3-pentafluoropropane (R245fa) was measured. Since our group constructed a flow-calorimeter in 1985, specific isobaric heat capacity of liquid refrigerants have been measured for R32, R123, R125, R134a, R142b, and R152a. In 2014, the authors modified the apparatus of flow calorimetry with an improvement for achieving a stable mass-flow-rate by introducing plastic accumulators and two parallel needle valves. The apparatus is able to measure isobaric heat capacity with unmeasurable level small heat loss and good repeatability mostly within 0.4 % (80 % of the data) and the largest 1.5 % from the maximum scatter. The measurements were obtained at 15 points of state parameters, along two pressures of 500 kPa and 800 kPa in a temperature range from 278 K to 343 K. The expanded uncertainty (coverage factor of k = 2) for the heat capacity value is predicted for each datum as being between 0.36 and 1.12 %. The purity of the sample liquid R245fa is analyzed as being better than 99.99 in mass fraction by the manufacture.

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INTRODUCTION Accurate thermophysical information on technically important fluids is requested in development of energy devices for efficient energy-utilization. Our group developed an apparatus of a flow-calorimeter in 1985 to measure the heat capacity at constant pressure, cp, of liquid refrigerants of R32, R123, R125, R134a, R142b, and R152a.1−5 Improvement of the apparatus has been continuously conducted. In 2008, Suzuki, a member of our group, reconstructed the apparatus with a new massflow-rate measurement system. The reliability of the measurements was improved and a simpler operation of the measurement was achieved. Then, the cp of ethanol6 and methanol7 was measured. The present authors modified the apparatus for improving the stability of the mass-flow-rate by replacing a high pressure accumulator of metallic bellows with a plastic accumulator which does not have any spring effect and by installing a set of two parallel needle-valves for precisely and surely controlling a mass-flow-rate. The cp of liquid 1,1,1,3,3-pentafluoropropane, R245fa, being measured with the modified apparatus is reported in this paper. R245fa may be used as a working fluid in a 100 °C grade heat pump or organic Rankine power cycle for effective utilization of geothermal or waste heat energy resources. The cp of liquid R245fa is obtained at 15 points of state parameters along two pressures of 500 kPa and 800 kPa in a temperature range from 278 K to 343 K.

Table 1. List of Components in Sample Liquid of R245fa mass fraction 99.99 % 1.0 ppm 0.2 ppm 4.0 ppm

is the guarantee of the worst case in the sample liquids provided by the manufacturer. We filled the sample liquid several times into our apparatus and tested the repeatability of measured values. We expect the effect of impurities is small enough not to be detected in measured cp values. Experimental Procedure. Figure 1 shows a schematic of the principle of flow calorimetry. A sample liquid flows in a calorimeter at a constant temperature, pressure, and mass-flow-rate.

Figure 1. Principle of flow calorimetry.

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EXPERIMENTAL SECTION Sample Liquid. Sample liquid was supplied from Asahi Glass Co., Ltd. with the purity being higher than 99.99 % in mass fraction. Table 1 shows the results of component analysis of the sample R245fa. The amount of impurities listed in Table 1 © XXXX American Chemical Society

component 1,1,1,3,3-pentafluoropropane (R245fa) nonvolatile component HCl H2O

Special Issue: Memorial Issue in Honor of Anthony R. H. Goodwin Received: July 14, 2015 Accepted: November 2, 2015

A

DOI: 10.1021/acs.jced.5b00597 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Figure 4. Constant-temperature bath including a calorimeter. A, adiabatic material; B, calorimeter; C, standard platinum resistance thermometer; D1 and D2, sheathed platinum resistance thermometers.

Figure 2. Sample liquid flow circuit. A, accumulator 1; B, accumulator 2; C, accumulator 3; D, pump; E, calorimeter; F, needle valve; G, solenoid three-way-valve.

Figure 3. Overall view of apparatus. A, pump; B, accumulator 1; C, constant-temperature bath; D, calorimeter; E1 and E2, crystal oscillation pressure gauges; F, constant temperature circulator; G, a set of two parallel needle valves; H1 and H2, digital pressure gauges; I, solenoid three-way-valve; J, timer; K1, K2, K3, electronic balances; L, accumulator 2; M, accumulator 3; N, differential pressure gauge; O, constant temperature bath; P, sample-liquid bomb; Q1, Q2, Q3, nitrogen-gas buffers; R, nitrogen cylinder; S1 and S2, bourdon pressure gauges; T, mantle heater; U, temperature controller; V1 to V34, valves; W, digital multimeter; X, personal computer; Y, digital-multimeter; Z, standard resistor; AA, DC power supply; AB, switch.

Figure 5. Calorimeter: a, radiation shield; b, microheater; D1 and D2, sheathed platinum resistance thermometers.

from the microheater. A temperature increment (ΔT) between before (T0) and after (Th) heating is measured with the sheathed thermometer. Figure 2a shows a closed sample-liquid flow circuit. The sample-liquid circulates in a closed loop including a calorimeter. Figure 2b shows a sample-liquid flow while mass-flow-rate is being measured. The flow channel is changed for 60 s by a

A sheathed platinum resistance thermometer and a microheater are installed in a calorimeter. A sample liquid receives heat B



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Table 2. Calibration of Inlet and Outlet Thermometers

inlet temperature (D1) outlet temperature (D2) heating medium temperaturea

average temp

standard deviation

K

mK

316.427 316.424 316.426

1.3 0.6 1.5

a

Heating medium temperature was measured with a standard platinum resistance thermometer.

Figure 8. Comparison of the results with an existing equation of state at 500 kPa: ○, cp measurement with expanded uncertainties; ―, Lemmon and Span.8

Figure 6. Calibration of three thermometers: ○, inlet temperature D1; □, outlet temperature D2; △, heating medium temperature measured with a standard platinum resistance thermometer.

Table 3. Specific Heat Values for Six Different Inverse of Mass-Flow-Rates ṁ −1 at 308 K and 500 kPa ṁ −1 s·g

−1

3.9294 4.4176 4.6313 4.8972 5.3438 6.0201

T K 307.930 307.866 307.875 307.893 307.891 307.886

cp −1

kJ·kg ·K 1.363 1.352 1.359 1.356 1.355 1.363

U(cp) −1

Figure 9. Comparison of the results with an existing equation of state at 800 kPa: ○, cp measurement with expanded uncertainties; ―, Lemmon and Span.8

% 1.067 0.663 0.460 0.727 0.402 0.812

Table 4. Specific Heat Capacity of R245fa Measured at 500 kPa T K 277.894 277.904 282.868 282.870 287.923 287.923 287.896 292.906 297.894 297.894 302.891 302.897 307.875 307.875 307.875 313.892 312.890 317.902 317.902 322.947 322.938 322.947

Figure 7. Measurements for six different inverse mass-flow-rates ṁ −1 at 308 K and 500 kPa. ○, cp measument with expanded uncertainties; ···, average value of six data.

solenoid three-way-valve, while a mass-flow-rate is measured. The mass-flow-rate is determined from a weight change of accumulator 3. The temporary cp is obtained from the following equation. Q̇ cp = (1) ΔT ·ṁ C

cp −1

kJ·kg ·K 1.269 1.278 1.281 1.283 1.294 1.282 1.294 1.309 1.325 1.322 1.331 1.336 1.359 1.358 1.351 1.350 1.356 1.357 1.367 1.379 1.385 1.377

U(cp) −1

% 0.381 0.411 0.387 0.367 0.898 0.360 0.388 0.362 0.374 0.364 0.441 0.395 0.460 0.370 0.370 0.407 0.409 0.382 0.410 0.792 0.364 0.362



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Table 5. Specific Heat Capacity of R245fa Measured at 800 kPa T

cp

K

kJ·kg−1·K−1

%

327.961 327.969 332.974 332.969 337.978 342.989 342.957

1.396 1.387 1.413 1.401 1.422 1.436 1.434

0.461 0.686 0.464 0.442 0.486 0.412 0.393

Table 8. Uncertainty Factors of Temperature Measurement uncertainty factor

U(cp)

combined standard uncertainty of sheathed platinum resistance thermometer temperature detector bridge standard deviation of measurement temperature combined standard uncertainty expanded uncertainty (k = 2)

T

kPa

K

415.8 504.1 808.1

307.921 307.875 307.880

cp

U(cp)

−1

−1

kJ·kg ·K

%

1.348 1.351 1.354

note

3.3 0.27 below 2.0

from experiment

below 2.7 below 5.5

thermal equilibrium state in the constant temperature bath. After that, the sample liquid flows into the calorimeter, the temperature at inlet is measured by a platinum resistance thermometer D1 in Figure 5. The liquid sample flows in a calorimeter and then the temperature at outlet is measured with a thermometer D2. We confirmed that the temperature of heating medium of water and the temperatures of the sample liquid at entrance and exit agree each other within a combined standard uncertainty of 3.3 mK in the case of no heating by a microheater. Table 2 and Figure 6 show the results. For calculating cp, temperatures measured before and after heating with the thermometer of D2 were used.

Table 6. cp of Liquid R245fa at 308 K and Different Pressures at (400, 500, and 800) kPa p

uncertainty/mK

0.39 0.37 0.44

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RESULTS AND DISCUSSION Reliability of Apparatus. To evaluate reliability of apparatus, heat loss in the calorimeter was examined. If measurements of heat capacity are affected by heat loss, it is expressed in the following equation. Q̇ + Q̇ loss Q̇ loss cp ,exp = = cp + (2) ΔT ·ṁ ΔT ·ṁ In this experiment, isobaric heat capacity is measured with temperature increment (ΔT) of about 3 K. Q̇ loss is assumed as a constant value and the second term of eq 2 would be a function of the reciprocal of mass-flow-rate. The heat capacity values at different mass-flow-rates were measured at a temperature of 308 K and a pressure of 500 kPa. Table 3 and Figure 7 show the results. The measurements at different flow-rates agree with each other within the expanded uncertainty. So we judged that our apparatus can measure isobaric heat capacity with negligibly small heat loss in this mass-flow-rate range and isobaric heat capacity with the expanded uncertainty value can be determined with eq 1. Furthermore, repeatability was confirmed by these six measurements. Measurement of Heat Capacity for R245fa. The cp of liquid R245fa at 15 points of state parameters were measured at pressures of 500 kPa and 800 kPa in a temperature range from 278 K to 343 K. Figures 8 and 9 show the results of the measurements. Tables 4 and 5 provide the numerical results. On the basis of the measurements at the same temperature, the reproducibility was confirmed within respective uncertainties but the greater deviation about 1.5 % than the predicted uncertainty is also observed. Figures 8 and 9 show a comparison of the results with an existing equation of state by Lemmon and Span.8 The currently existing equation of state for R245fa is a short fundamental equation of state developed by Lemmon and Span.8 The equation well agrees with our data almost within the claimed uncertainty in a liquid-phase region. An uncertainty of specific heat values derived from the equation of state is expressed as being 5 % in the literature.8 In addition, cp of R245fa at pressures of about (400, 500, and 800) kPa were measured at a temperature of 308 K in order to

Figure 10. Pressure dependence in cp of liquid R245fa at 308 K: ○, cp measurement with expanded uncertainties; ···, average values of these three data.

Table 7. Uncertainty Factors of Sheathed Platinum Resistance Thermometer uncertainty factor standard platinum resistance thermometer sheathed platinum resistance thermometer correlating equation temperature detector bridge combined standard uncertainty expanded uncertainty (k = 2) a

uncertainty/mK

note

0.2

from calibration result of NRLMa from experiment from specifications

1.0 0.2 3.0 0.27 1.0 3.3 6.6

from experimental data from specifications from experiment

National Research Laboratory of Metrology.

Where Q̇ is a heat rate in J·s−1, ΔT is (Th − T0) in K, and ṁ is a mass-flow-rate in kg·s−1. Experimental Apparatus. Figure 3 shows an overall view of the apparatus, which consists of sample liquid circuit, a pressure-control system with three accumulators, a calorimeter, and a temperature-measurement system. Figures 4 and 5 show a constant temperature bath including a calorimeter and the calorimeter itself, respectively. A sample liquid of R245fa and a heating medium of water become a D



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Table 9. Uncertainty Components of cp Values Listed in Table 3 T

p

cp

U(p)

U(T)

uc(ΔT)/ΔT

u(Q)/Q

u(m)/m

U(cp)/cp

K

kPa

kJ·kg−1·K−1

kPa

mK

%

%

%

%

307.930 307.866 307.875 307.893 307.891 307.886

520.4 519.5 514.4 518.2 522.2 517.9

1.363 1.352 1.359 1.356 1.355 1.363

6.6 6.6 6.6 6.6 6.6 6.6

5.0 5.0 5.0 4.9 4.9 4.7

0.33 0.34 0.34 0.33 0.33 0.32

0.02 0.05 0.01 0.01 0.01 0.26

1.01 0.56 0.31 0.65 0.23 0.70

1.07 0.66 0.46 0.73 0.40 0.81

uc(ΔT)/ΔT

u(Q)/Q

u(m)/m

U(cp)/cp


p

K

kPa

277.894 277.904 282.868 282.870 287.923 287.923 287.896 292.906 297.894 297.894 302.891 302.897 307.875 307.875 307.875 313.892 312.890 317.902 317.902 322.947 322.938 322.947

518.3 519.0 509.6 511.0 512.5 512.5 513.9 518.1 514.6 514.6 517.2 518.0 514.4 514.4 514.4 520.4 514.5 522.6 522.2 517.7 518.4 517.7

cp −1

kJ·kg ·K

−1

1.269 1.278 1.281 1.288 1.294 1.282 1.294 1.336 1.325 1.322 1.331 1.336 1.358 1.351 1.371 1.350 1.356 1.357 1.367 1.379 1.385 1.377

U(p)

U(T)

kPa

mK

%

%

%

%

6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6 6.6

4.8 4.9 4.8 4.7 4.9 4.7 5.0 5.0 4.8 4.7 4.9 4.9 4.7 4.7 5.0 5.1 5.1 4.8 4.8 4.8 4.7 4.7

0.32 0.32 0.32 0.32 0.32 0.31 0.33 0.33 0.32 0.31 0.33 0.33 0.32 0.32 0.34 0.34 0.34 0.32 0.33 0.31 0.31 0.31

0.01 0.01 0.01 0.01 0.01 0.00 0.01 0.01 0.01 0.00 0.01 0.01 0.00 0.00 0.01 0.01 0.01 0.01 0.01 0.01 0.00 0.00

0.21 1.07 0.21 0.26 0.84 0.19 0.20 0.21 0.20 0.19 0.29 0.22 0.19 0.19 0.31 0.22 0.23 0.21 0.25 0.73 0.19 0.19

0.38 1.12 0.39 0.41 0.90 0.36 0.39 0.39 0.37 0.36 0.44 0.40 0.37 0.37 0.46 0.41 0.41 0.38 0.41 0.79 0.36 0.36


p

cp

U(p)

U(T)

uc(ΔT)/ΔT

u(Q)/Q

u(m)/m

U(cp)/cp

K

kPa

kJ·kg−1·K−1

kPa

mK

%

%

%

%

332.974 332.969 327.961 327.969 337.978 342.989 342.957

815.0 816.5 806.4 808.9 810.3 813.6 817.2

1.413 1.401 1.396 1.387 1.422 1.436 1.434

6.6 6.6 6.6 6.6 6.6 6.6 6.6

5.3 5.3 5.1 5.1 5.3 4.9 4.8

0.36 0.36 0.34 0.34 0.35 0.33 0.32

0.01 0.01 0.01 0.01 0.01 0.01 0.01

0.29 0.26 0.31 0.60 0.33 0.25 0.23

0.46 0.44 0.46 0.69 0.49 0.41 0.39

U(cp)/cp


p

cp

U(p)

U(T)

uc(ΔT)/ΔT

u(Q)/Q

u(m)/m

K

kPa

kJ·kg−1·K−1

kPa

mK

%

%

%

%

307.921 307.875 307.880

415.8 504.1 808.1

1.348 1.351 1.354

6.6 6.6 6.6

5.0 4.7 5.1

0.33 0.32 0.34

0.01 0.00 0.01

0.21 0.19 0.27

0.39 0.37 0.44

of “Guide to the Expression of Uncertainty in Measurement” by ISO. Tables 7 and 8 show the details of uncertainty estimation for temperature measurements. Because heat capacity is determined from eq 1, the uncertainty of heat capacity is expressed by components of ΔT, Q̇ , and ṁ . The uncertainty is principally

confirm the pressure dependency of cp. Table 6 and Figure 10 show the results. Pressure dependence being greater than the uncertainties was not observed. Uncertainty. All the uncertainty components of our measurements are examined based on the evaluation method E



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calculated from the following equation under the coverage factor of k = 2. uc(cp) =

⎛ u(Q̇ ) ⎞2 ⎛ u(ṁ ) ⎞2 ⎛ u(ΔT ) ⎞2 ⎟ +⎜ ⎟ ·c ⎜ ⎟ +⎜ ⎝ ṁ ⎠ ⎝ ΔT ⎠ p ⎝ Q̇ ⎠

(3)

Tables 9 to 12 show the uncertainty components for each measurement given in Table 3 to 6, respectively.

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CONCLUSIONS Isobaric heat capacity of liquid R245fa was measured and the data were obtained at 15 points of state parameters along pressures of 500 kPa and 800 kPa in a temperature range from 278 K to 343 K. Although the expanded uncertainty (coverage factor of k = 2) for the isobaric heat capacity is predicted to be between 0.36 % and 1.12 %, the maximum scatter of 1.5 % was observed.

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AUTHOR INFORMATION

Corresponding Author

*Tel. +81-45-566-1729, E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Isobaric Heat Capacity of Liquid 1,1,1,3,3-Pentafluoropropane

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