Reversible Heat Engine

A heat engine receives 500 BTU of heat per cycle from a reservoir at 540oF and rejects heat to a sink at 40oF 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?

Calculations:

Maximum efficiency of a heat engine = efficiency of Carnot engine

Efficiency of Carnot engine h max = 1 - T2/T1

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

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

h max = 1 - 500/1000 = 0.5

(a) Heat rejected to the sink = 375 BTU

h a = 1 - Q2/Q1 = 1 - 375/500 = 0.25

(b) Heat rejected to the sink = 250 BTU

h b = 1 - 250/500 = 0.5

(c) Heat rejected to the sink = 150 BTU

h 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