Question

HE2W2 Operating in series are two reversible heat pumps. Heat transfer gives energy to the first cycle from a cold reservoir at 105 K and rejects energy by heat transfer to a reservoir at an intermediate temperature T greater than 105 K The second cycle receives energy by heat transfer from the reservoir at T" and rejects energy by heat transfer to a higher-temperature reservoir at 1200 K. If the heat pump cycles have the same co-efficient of performance, calculate: lt The coefficient of performance γ for each heat engine: Check

Operating in series are two reversible heat pumps. Heat transfer gives energy to the first cycle from a cold reservoir at 105 K and rejects energy by heat transfer to a reservoir at an intermediate temperature T greater than 105 K. The second cycle receives energy by heat transfer from the reservoir at T and rejects energy by heat transfer to a higher-temperature reservoir at 1200 K. If the heat pump cycles have the same co-efficient of performance, calculate: Low temperature, Mid temperature, High Temperature reservoir connected with heat pumps TM= K The coefficient of performance γ for each heat engine: γ1= γ2=

Answer 1

The Cop of First heat pump cycle is Cop_1 = T/T - 105 The COP of second heat pump cycle is COP_2 = 1200/12000 - T Given that C O P of both cycle remains same COP_1 = COP_2 T/T - 105 = 1200/1200 - T 1200 - T/1200 = T - 105/T T/1200 = m 105/T T^2 = 1200 times 105 T^2 = 126000 T = 354.9 k The value of COP of the heat pump cycle is COP_2 = COP_1 = T/T - 105 = 354,9/354.9 - 105 CoP_2 = m C oP_1 = 1.42