Consider the following system with three thermal reservoirs consisting of: P = p
ID: 1862179 • Letter: C
Question
Consider the following system with three thermal reservoirs consisting of: P = power
cycle, RF = refrigerator, and HP = heat pump.
(a) Calculate the rate of heat transfer (kW) for the power cycle and refrigerator and the
rate of work input (kW) for the heat pump.
(b) Determine the thermal efficiency (%) of the power cycle and the coefficient of
performance of the refrigerator and heat pump for the given system.
(c) Find the maximum possible values of thermal efficiency (%) of the power cycle and
the coefficient of performance of the refrigerator and heat pump for the given system.
(d) Is (are) any of the device(s) impossible?
Answers: (a) 6.6 kW, 2 kW, 1.5 kW;
Explanation / Answer
a. W in + 3.2 = 4.7 ;
Win for pump = 1.5 kW;
Also in the ref section Q in R + 0.9 = 2.9 ;
Heat transfer for refrigerator Q in R = 2.0 kW;
Heat transfer for pump Qin p = 0.9 + Win +1.0 +3.2 ;
Qin P = 0.9 + 1.5 +1 +3.2= 6.6kW;
b . Efficiency of pump = Wnet /Qin = 1 + 1.5 +0.9 /6.6 = 51.5 %
COP ref = QinR / Wnet = 2/0.9 =2.22
COP p= 4.7 / Wnet = 4.7 / 1.5 =3.13
C.efficiency of power cycle = 1- T2/Th ;
T2 = 255.22 K , T h = 477.4 K , Tm = 366.3 K;
power cycle = 1- 255.22/477.4 = 0.4653 = 46.53 %;
COP ref = Tm/Th-Tm = 366.3/(477.4-366.3) = 3.29;
COP p = Tm/(Tm-T2) = 366.3/( 366.3- 255.22) = 3.297
d. Yes the Power cycle is impossible as its actual efficincey is more than the ideal value