Question

A heat pump working on a reversed carnot cycle takes in energy from a reservoir maintained at 5°C and delivers it to another reservoir where temperature is 77°C. The heat pump derives power for its operation from a reversible engine operating within the higher and lower temperatures of 1077°C and 77°C. For 100 kJ/kg of energy supplied to reservoir at 77°C, estimate the energy taken from the reservoir at 1077°C.

Answer 1

Given : T₃ = 5 + 273 = 278 K ; 

T₂ = T₄ = 77 + 273 = 350 K ; 

T₁ = 273 + 1077 = 1350 K ;

Energy taken from the revervoir at 1077°C, Q₁ :

For reversible engine

For reversiblea heat pump, C.O.P. = \(\cfrac{Q_4}{Q_4-Q_3}\) = \(\cfrac{T_4}{T_4-T_3}\)

Since work for running the pump is being supplied by the engine