Maximizing Efficiency: Exploring the Possibility of Self-Running Heat Pumps

[some bloke]

TL;DR Summary

now I want to make it completely clear that I am not talking of the dread PM here! I want to know whether a heat pump can use some of it's heat to generate the electricity needed to run itself!

So heat pumps are an interesting thing which I've recently discovered, and it has led to curiosity about how they work and what you can do with them. I hope to make my own property at some point, so a heat pump will doubtless come up then as I would like it to be an eco-home.

Ground source heat pumps work by taking cold liquid or gas, running it underground in pipes to gain a few degrees from the ambient ground temperature, then compressing it to amplify the temperature, using a heat exchanger to claim the thermal energy for your hot water or heating, and then they decompress the now cool liquid and recycle it to gather more heat from underground. They're an excellent example of using simple physics to create elegant solutions.

They claim that for each unit of electricity used, the pump produces 3-4 units of heat, giving it a 300-400% efficiency (of energy you pay for, obviously, not the total energy in).

This implies to me that if you could use, say, a thermoelectric system which is 50% effecient, you could harness that 1 unit of electricity from the 3-4 units of heat and run the pump, and keep 1-2 units of thermal energy for heating the house up. The whole system would run for as long as the liquid can be warmed up to take heat from the ambient surroundings, and the bearings don't give out.

I am assuming that the issue is that methods for getting electricity from heat are not efficient enough to make them viable - is this correct?

 

[erobz]

I think if you get rid of the idea of it "feeding itself", the question becomes could you extract enough power to run the pump/compressor if you had a turbine across the same thermal reservoirs $T_H$ and $T_C$.

You would have to show that the pump system (accounting) for its efficiency consumes well under theoretical limit of useful work that can be extracted from the turbine across $T_H$ and $T_C$.

I would say the answer to that depends on $T_H$ and $T_C$. Theoretically it seems ok (not violating the Second Law as far as I can tell) but economically, probably not.

EDIT:
Just to be clear: I'm telling you how you "could" run the pump system without external input of electricity, not how you could run it without external input of power.

 

[jbriggs444]

If you could use, say, a thermoelectric system which is 50% effecient, you could harness that 1 unit of electricity from the 3-4 units of heat and run the pump

The amount of electricity you can get from heat depends on the [absolute] temperature ratio between the heated reservoir and the environment.

If the heat pump is 300 to 400 percent efficient that demands a temperature ratio close to 1:1. (e.g. 4:3 or 5:4). That in turn means that a heat engine using the temperature difference can be no more than 33% or 25% efficient. Real world losses mean that you cannot even do that well.

TANSTAAFL

If you could tack an ideal heat engine onto an ideal heat pump and thereby increase the net efficiency of your heat pumping efforts, you would have the makings for a PMM. So this discussion is definitely treading on thin ice.

 

[russ_watters]

Summary: now I want to make it completely clear that I am not talking of the dread PM here! I want to know whether a heat pump can use some of it's heat to generate the electricity needed to run itself!

That statement is a contradiction that indicates you are misunderstanding what a PMM is...because that's exactly what you are describing.

A PMM is simply a device that violates one or more laws of thermo. Yours would violate, at least, the 2nd one.

 

[russ_watters]

If the heat pump is 300 to 400 percent efficient that demands a temperature ratio close to 1:1. (e.g. 4:3 or 5:4). That in turn means that a heat engine using the temperature difference can be no more than 33% or 25% efficient.

In other words, the efficiency equations are inverses of each other.

 

[vela]

Summary: now I want to make it completely clear that I am not talking of the dread PM here! I want to know whether a heat pump can use some of it's heat to generate the electricity needed to run itself!

I am assuming that the issue is that methods for getting electricity from heat are not efficient enough to make them viable - is this correct?

Exactly. There's a theoretical maximum to how much heat a heat engine can turn into useful work. There's always some heat left over that must be discarded.

The engine-pump system you described, if it worked as you envision, would violate the second law of thermodynamics because the system would move heat from a cold reservoir to a hot reservoir without requiring any energy input. In other words, it would look like heat spontaneously moved from a cold object to a hot object.

 

[hutchphd]

This in no way means that there are sometimes not simple solutions. Co-generation (electric power plants that use peoples homes as the "cold resevoir" make very good sense in certain climates) in fact is nearly a free lunch by circumstance. But you always have a one-way flow from which to extract.
One cannot pump the water back up the hill and have energy left over.

 

[russ_watters]

I think we've adequately covered the issue here. Thread locked.