Question

A Carnot engine is operated between two heat reservoirs at temperatures of 520 K and 300 K.

a) If the engine receives 6.45 kJ of heat energy from the reservoir at 520 K in each cycle, how many joules per cycle does it reject to the reservoir at 300 K?

b) How much mechanical work is performed by the engine during each cycle?

c) What is the thermal efficiency of the engine?

Answer 1

(a)
Q_hot/T_hot + Q_cold/T_cold = 0
Hence
- Q_cold = Q_hot/T_hot * T_cold
- Q_cold = 6.45 kJ * 300K/520K
Q_cold = - 3.72kJ
P.S :- negative sign means that the heat is transferred from the engine.

(b)
Using Conservation of energy, work done on engine and heat transferred to engine = zero:

W + Q_hot + Q_cold = 0
- W = Q_hot + Q_cold
- W = 6.45kJ - 3.72kJ
- W = 2.73 kJ
Mechanical work performed by the engine during each cycle, =  2.73 kJ

(c)
efficiency = -W/Q_hot = 2.73/6.45 * 100%
efficiency = 0.423 * 100%
Thermal efficiency of the engine = 42.3%