Reversible Heat Engine

A heat engine receives 500 BTU of heat per cycle from a reservoir at 540^oF and rejects heat to a sink at 40^oF in a hypothetical amounts of (a) 375 BTU per cycle (b) 250 BTU per cycle and (c) 150 BTU per cycle. Which of these respective cases represent a reversible cycle, an irreversible cycle and an impossible cycle?

Maximum efficiency of a heat engine = efficiency of Carnot engine

Efficiency of Carnot engine η _max = 1 - T₂/T₁

T₁ = temperature of source = 540^oF = 540 + 460 = 1000^oR

T₂ = temperature of sink = 40^oF = 40 + 460 = 500^oR

η_max = 1 - 500/1000 = 0.5

η_a = 1 - Q₂/Q₁ = 1 - 375/500 = 0.25

η_b = 1 - 250/500 = 0.5

η_c = 1 - 150/500 = 0.7

From the above calculations we can see that the case 'c' is an impossible one (since the efficiency of a heat engine can not be more than that of Carnot cycle efficiency).

Summary:

Case: a - irreversible cycle

Case: b - reversible cycle

Case: c - impossible cycle