# Do all reversible engines become heat pumps?

1. Feb 23, 2013

### joycounts

I have a cycle (and the gas is ideal) that starts at Pressure=4Po Volume=Vo and and Temperature=Th. First step it's cooled at constant volume to Tc and Po; Second step, it is reheated at constant pressure to Th and 4Vo, and lastly it is compressed at constant temperature to Vo and 4Po. For those who are drawing the picture to see this, it is going counterclockwise (suggesting a heat pump).

Clockwise it makes a reasonable engine as it pulls heat from the hot reservoir and dumps into the cold to make work. But reversed it doesn't make much sense to me. The first leg has no work and dumps heat into the cold reservoir, the second leg the system does work and draws heat from the hot reservoir, and the third leg work is done on the system and heat is released into the hot reservoir. It does not pull heat out of the cold and if my math is right (I can show my work if needed) I got that that 15/2 PoVo is absorbed from the hot reservoir and 4 ln(4) PoVo is put back in, creating and overall loss of heat from the hot and a gain to the cold.

This appears to me to just be an engine that takes work instead of becoming a heat pump. Am I just missing something obvious?

2. Feb 23, 2013

### Simon Bridge

That's a pretty standard cycle - you should be able to reverse and so drive heat the other way.

You've noticed that you have to add work to reverse it - where does that energy go?

3. Feb 23, 2013

### Andrew Mason

I agree that it is not going to make any sense as a heat pump. It is not a reversible cycle (ΔS>>0). The machine can be made to go in the reverse direction, of course, but that does not mean that it will achieve the same temperatures and pressures that are achieved when it operates as a heat engine.

AM