[tlb]

Heat->mechanical energy can only be (1-Tc/Th) efficient. But mechanical energy->heat can be 1/(1-Tc/Th) efficient, so you can get close to unity round trip efficiency.

That's why people use heat pumps to heat buildings, because you get more heat out than energy in (the extra heat comes from the ground).

[eximius]

I need further explanation before this makes sense to me. How can M->H have greater than 100% efficiency?

You mentioned getting heat from the ground, but that only happens when the ground heat is greater than T_h, right? At which point it just sounds like geothermal but with extra steps.

[tlb]

A heat pump transfers heat from the cold side to the hot side, making the hot side hotter and the cold side colder. The thing you're heating is at Th and ground is at Tc. By putting 1 J of mechanical work in, you might draw 3 J from the cold side and pump 4 J into the hot side.