Question

A heat engine operates between a high-temperature reservoir at 610 K and a low-temperature reservoir at 320 K. In one cycle, the engine absorbs 6800 J of heat from the high-temperature reservoir and does 2200 J of work.

A) What is the net change in entropy as a result of this cycle?

Answer 1

For the case of a heat engine, the isolated system consists of the engine, the reservoir from which it extracts heat, and the outside device upon which it does work. The engine itself returns periodically to the same state, so its entropy is clearly unchanged after each cycle. The entropy change per cycle of the heat reservoir, which is at absolute temperature T₁ (constant during the cycle) is given by:

The other body is a second heat reservoir at temperature T₂. The entropy of the second reservoir increases by dumping some of the heat extracted from the first reservoir into it. The heat per cycle extracted from the first reservoir is q₁, and the heat per cycle we reject into the second reservoir is q₂. Tthe work done on the external device is W per cycle. The first law of thermodynamics tells us that:    q₁ = W + q₂

The total entropy change per cycle is due to the heat extracted from the first reservoir and the heat dumped into the second, and has to be positive (or zero) according to the second law of thermodynamics. So

Then,