Question

A heat pump working on the Carnot cycle takes in heat from a reservoir at 5°C and delivers heat to a reservoir at 60°C. The heat pump is driven by a reversible heat engine which takes in heat from a reservoir at 840°C and rejects heat to a reservoir at 60°C. The reversible heat engine also drives a machine that absorbs 30 kW. If the heat pump extracts 17 kJ/s from the 5°C reservoir, determine

(a) The rate of heat supply from the 840°C source

(b) The rate of heat rejection to the 60°C sink.

Answer 1

COP of H.P.

∴ Work output of the Heat engine 

W_H.E. = 30 + 3.36 

= 33.36 kW 

η of the H.E. = 1 - \(\frac{333}{1113}\)

= 0.7

(a) ∴ \(\frac W{Q_1}\) = 0.7

∴ Q₁ = \(\frac W{0.7}\) = 47.61 kW

(b) Rate of heat rejection to the 333 K

(i) From H.E. = Q₁ – W 

= 47.61 – 33.36

= 14.25 kW

(ii) For H.P. = 17 + 3.36 

= 20.36 kW

∴ Total = 34.61 kW