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//(6.8) Components of a heat pump for supplying heated air to a dwelling are shown in the schematic below. At steady state, Refrigerant 22 enters the compressor at -5C, 3.5 bar and is compressed adiabatically to 75C, 14 bar. From the compressor, the refrigerant passes through the condenser, where it condenses to liquid at 28C, 14 bar. The refrigerant then expands through a throttling valve to 3.5 bar. The states of the refrigerant are shown on the accompanying T–s diagram. Return air from the dwelling enters the condenser at 20C, 1 bar with a volumetric flow rate of 0.42 m3/s and exits at 50C with a negligible change in pressure. Using the ideal gas model for the air and neglecting kinetic and potential energy effects, (a) determine the rates of entropy production, in kW/K, for control volumes enclosing the condenser, compressor, and expansion valve, respectively. (b) Discuss the sources of irreversibility in the components considered in part (a).
//solution
//variable initialization
P1 = 3.5 //pressure of refrigerant entering the compressor in bars
T1 = 268 //temperature of refrigerant entering the compressor in kelvin
P2 = 14 //pressure of refrigerant entering the condenser in bars
T2 = 348 //temperature of refrigerant entering the condenser in kelvin
P3 = 14 //pressure of refrigerant exiting the condenser in bars
T3 = 301 //temperature of refrigerant exiting the condenser in kelvin
P4 = 3.5 //pressure of refrigerant after passing through expansion valve in bars
P5 = 1 //pressure of indoor return air entering the condenser in bars
T5 = 293 //temperature of indoor return air entering the condenser in kelvin
AV5 = .42 //volumetric flow rate of indoor return air entering the condenser in m^3/s
P6 = 1 //pressure of return air exiting the condenser in bar
T6 = 323 //temperature of return air exiting the condenser in kelvin
//part(a)
//from table A-9
s1 = .9572 //in kj/kg.k
//interpolating in table A-9
s2 = .98225 //in kj/kg.k
h2 = 294.17 //in kj/kg
//from table A-7
s3 = .2936 //in kj/kg.k
h3 = 79.05 //in kj/kg
h4 = h3 //since expansion through valve is throttling process
//from table A-8
hf4 = 33.09 //in kj/kg
hg4 = 246 //in kj/kg
sf4 = .1328 //in kj/kg.k
sg4 = .9431 //in kj/kg.k
x4 = (h4-hf4)/(hg4-hf4) //quality at state 4
s4 = sf4 + x4*(sg4-sf4) //specific entropy at state 4
/////condenser!!
v5 = ((8314/28.97)*T5)/(P5*10^5) //specific volume at state 5
mairdot = AV5/v5
cp = 1.005 //in kj/kg.k
h6 = cp*T6
h5 = cp*T5
mrefdot = mairdot*(h6-h5)/(h2-h3)
deltaS65 = cp*log(T6/T5)-(8.314/28.97)*log(P6/P5) //change in specific entropy
sigmacond = (mrefdot*(s3-s2)) + (mairdot*(deltaS65))
/////compressor!!
sigmacomp = mrefdot*(s2-s1)
////valve!!
sigmavalve = mrefdot *(s4-s3)
printf('\nthe rates of entropy production, in kW/K, for control volume enclosing the condenser is \n\t R1 = %e ',sigmacond)
printf('\nthe rates of entropy production, in kW/K, for control volume enclosing the compressor is \n\t R2 = %e ',sigmacomp)
printf('\nthe rates of entropy production, in kW/K, for control volume enclosing the expansion valve is \n\t R3 = %e ',sigmavalve)
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