Question

A Carnot engine has a power output of 160 kW. The engine operates between two reservoirs at 20°C and 470°C.

(a) How much energy enters the engine by heat per hour?

(b) How much energy is exhausted by heat per hour?

Answer 1

Output power = 160 kW = 160000 W = 160000 J/s

This implies that the useful work done, W = 160000 J/s

Source temperature, T1 = 4700C = 470 + 273 = 743 K

Sink temperature, T2 = 200C = 20 + 273 = 293 K

efficiency of the Carnot engine, η = ( T1 -T2)/T1 = (743 – 293 )/743 = 0.61

(a)

Efficiency = work /heat enters the engine = W/Q1

Q1 = W/η = 160000/0.61 = 262295 J/s = 9.44 x 108 J/hour

heat enters the engine, Q1 = 9.44 x 108 J/hour

(b)

heat exhausted, Q2 = Q1 – W = 262295 – 160000 = 102295 J/s = 3.6 x 108 J/hour

heat exhausted, Q2 = 3.6 x 108 J/hour