# Q & A: free heating?

Q:
Would it be possible (at least in theory) to heat a small building using a heat pump, but using no energy to run the pump? It seems unlikely, but why not? I am familiar with the laws of thermodynamics. I know we are not supposed to be able to get work from a non-spontaneous process, like a heat pump. Say you used a Stirling engine to start the process. You could easily get five or ten times more thermal energy out than the energy used. Then you could use some of that energy to run the pump leaving the rest to heat the building. What am I missing here? This is a question about physics theory, not about engineering.
- Robert (age 66)
Manchester, England
A:

That's an important question. It is indeed completely impossible as a matter of fundamental physics to keep heating that house without some sort of external source of free energy, or (in the most general sense) of sub-equilibrium entropy.

Say that you have a nice heat pump that dumps 5J of heat into the house for 1J of energy input. You ask: why not draw the next 1J of input energy from a modest tax on that 5J? The problem is that that's 5J of high-entropy, low free-energy energy, not 5 J of low-entropy, high free-energy mechanical or electrical energy. So when you draw that 1J tax out, you send it to some heat engine to get the type of free energy that you need to drive your pump. The output is much less than 1J. In fact, it's less than 1/5 J. So even when you run it back into your pump, you end up with less heat pumped into the house than if you hadn't bothered with that whole scheme.

Mike W.

(published on 12/12/2014)

## Follow-Up #1: thermodynamic efficiencies

Q:
Thanks Mike. I've now put a bit more effort into this myself. I was pretty sure it was impossible, but the high theoretical maximum "Coefficient of Performance" of a heat pump had got me thinking. In fact, someone else had asked me about it. The efficiency of a heat engine is helped by a large temperature difference between the heat source and the heat "sink". Carnot's formula enabled me to work out the theoretical maximum efficiency, depending on temperatures. For a heat pump, a high Coefficient of Performance has the opposite requirements. It's best to have the interior and exterior temperatures as close as possible.There is a simple formula for maximum theoretical values for that too.When you "do the math", it's pretty obvious why you can't get "free heat".
- Robert (age 66)
Manchester, England
A:

exactly

Mike W.

(published on 12/22/2014)

## Follow-Up #2: heat pumps for houses

Q:
"Would it be possible (at least in theory) to heat a small building using a heat pump...?" Heat from what source and above what temperature? If the source is geothermal say at 50 F and house is at 40 F, then yes, all you have to do is dig a hole down to 50 F stratum and let the natural convection take over, i.e., cool air sink, heat up, and bubble up. But now let's ask the question in terms of mechanical energy: you can harvest enough torque from a low pressure dam to pump small amount of water to a higher pressure. Isn't this equivalent of achieving what Robert had envisioned? What is misgiving here?
- Mehran (age 65)
Arlington Heights, IL
A:

Yes, if the deep ground is at 55°F (typical in our latitude) in principle you can heat the house to 55°F without expending free energy. In practice, almost everyone wants to keep their house a bit warmer than that. In your analogy, that would mean pumping heat slightly "uphill". Also, practical systems do usually use actively powered pumps to maintain enough circulation even when used for cooling, in which case the heat flow is "downhill". Absolute efficiencies of around 5 are common for standard heat pump house heaters.  My downstairs systems (air exchange) work about that well in mildly cold weather, and geothermal ones should work about that well even in very cold weather.

Mike W.

posted without vetting until Lee returns

(published on 01/21/2016)