At steady state a reversible heat pump cycle discharges ene

At steady state, a reversible heat pump cycle discharges ene at the rate Q_H to a hot reservoir at temperature T_H. wl receiving energy at the rate Q_c from a cold reservoir temperature T_c. If T_H = 21degreec and T_c = 7degreeC. determine the coefficient Performance. If Q_H = 10.5 kW. Q_c = 8.75 kW, and T_c = 0degreeC, determine T_H, in degreeC. if the coefficient of performance is 10 and T_c = 27degreeC, determine T_C, in degreeC.

Solution

a) for heat pump, COP = T_H/(T_H-T_C) where temp. are in Kelvin   (Also K = 273 + ^oC)

hence COP = 294/(294-280) = 21

b) COP = Q_H/(Q_H-Q_C) = 10.5/(10.5-8.75) = 6

-----> 6 = T_H/(T_H-T_C)

-----> 6 = T_H/(T_H-273)

solving for T_H, we get T_H = 327.6 K = 54.6^o C

c) COP = T_H/(T_H-T_C)

------> 10 = 300/(300-T_C)

solving for T_C, we get T_C = 270 K = -3^oC