(a) Explanation The following figure shows the vapor-compression heat pump cycle. Figure-(1) In Figure-(1), the process 1 to 2 is actual compression, the process 1 to 2s is isentropic compression, process 2 to 3 is heat rejection in condenser, process 3 to 4 is expansion in throttle valve and process 4 to 1 is heat absorption in evaporator. Calculate the mass flow rate of refrigerant. m ˙ = Q ˙ out h 2 − h 3 (I) Here, mass flow rate of refrigerant is m ˙ , heat transfer rate is Q ˙ out , enthalpy at state 2 is h 2 and enthalpy at state 3 is h 3 . Write the expression for temperature at state 3. T 3 = Δ T cond + 21 ° C (II) Here, temperature at state 3 is T 3 and the temperature difference at condenser is Δ T cond . Write the expression for temperature at state 1. T 1 = 0 ° C − Δ T evap (III) Here, temperature at state 1 is T 1 and temperature difference at evaporator is Δ T evap . Conclusion: Substitute 10 ° C for Δ T cond in Equation (II). T 3 = 10 ° C + 21 ° C = 31 ° C Substitute 10 ° C for Δ T evap in Equation (III). T 1 = 0 ° C − 10 ° C = − 10 ° C Refer to Table A-7 “Properties of saturated refrigerant R-22-temperature table” to obtain pressure ( p 31 ) as 11.313 bar , pressure ( p 32 ) as 12.556 bar , temperature ( T 31 ) as 28 ° C and temperature ( T 32 ) as 32 ° C corresponding temperature 31 ° C . Write the expression for interpolation to obtain the pressure at state 3. p 3 = p 31 + ( T 3 − T 31 T 32 − T 31 ) ( p 32 − p 31 ) (IV) Here, pressure at state 3 is p 3 . Substitute 11.313 bar for p 31 , 12.556 bar for p 32 , 31 ° C for T 3 , 28 ° C for T 31 and 32 ° C for T 32 in Equation (IV). p 3 = 11.313 bar + [ ( 31 ° C − 28 ° C 32 ° C − 28 ° C ) ( 12.556 bar − 11.313 bar ) ] = 11.313 barr + 0.93225 bar = 12.245 bar ≈ 12 bar The pressure at state 3 is equal to the pressure ( p 2 ) at state 2 because it is constant pressure process. Refer to Table A-7 “Properties of saturated refrigerant R-22-temperature table” to obtain enthalpy of vapor ( h 1 ) as 246.15 kJ/kg and entropy of vapor ( s 1 ) as 0.9424 kJ/kg ⋅ K corresponding to temperature − 10 ° C . The process 1 to 2s is isentropic process. The entropy at state 1 is equal to entropy ( s 2 s ) at state 2s. Refer to Table A-12 “Properties of superheated refrigerant R-22-vapor” to obtain entropy ( s 2 s 1 ) as 0 (b) To determine The power input to the compressor. (c) To determine The coefficient of performance of heat pump. The coefficient of performance of Carnot heat pump.

Fundamentals of Engineering Thermodynamics, Binder Ready Version

8th Edition

ISBN: 9781118820445

Author: Michael J. Moran, Howard N. Shapiro, Daisie D. Boettner, Margaret B. Bailey

Publisher: WILEY

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Chapter 10.7, Problem 38P

(a)

To determine

The mass flow rate of the refrigerant.

(b)

To determine

The power input to the compressor.

(c)

To determine

The coefficient of performance of heat pump.

The coefficient of performance of Carnot heat pump.

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Chapter 10.7, Problem 37P

Chapter 10.7, Problem 39P

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Fundamentals of Engineering Thermodynamics, Binder Ready Version

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