Heat pump COP theoretical maximum

[Thermolelctric]

I must admit that there was logical mistake in my COP=5 cycle. The heat pump will not pump any more when the cold reservoir is heated(above the ambient) back from hot reservoir. Thanks everybody for explaining patiently.

So there is no other limitation to the COP than COP≤Th/(Th−Tc).
The COP can be very high if temperature dT is very small.

The practical heat pumps COP is so much below the theoretical maximum only because the various constructional problems.

The other interesting question is: theoretically, can we run the heat engine outside the building and use the work from the heat engine to run the heat pump to heat the building from the outside air and get the same amount or more heat, than burning the fuel inside the building with 100% efficiency?

 

[Andrew Mason]

The other interesting question is: theoretically, can we run the heat engine outside the building and use the work from the heat engine to run the heat pump to heat the building from the outside air and get the same amount or more heat, than burning the fuel inside the building with 100% efficiency?

That is exactly how most heat pumps run. The input work is provided by electricity generated by heat engines operating in an outside power plant. As I explained in my earlier post #57, in that case you need a COP of about 3.5 just to break even (ie. to get the same amount of heat than you would from burning the fuel with 100% efficiency). If the COP>3.5 you get more heat than burning the fuel inside at 100% efficiency. And a COP > 3.5 is easily possible. If the temperatures are Th/Tc = 293K/273K, the maximum Carnot COP would be 293/20 ≈ 15

AM

 

[Dale]

The other interesting question is: theoretically, can we run the heat engine outside the building and use the work from the heat engine to run the heat pump to heat the building from the outside air and get the same amount or more heat, than burning the fuel inside the building with 100% efficiency?

I answered this already in post 50.

 

[Thermolelctric]

I answered this already in post 50.

This was supposed to be the case when the heat engine is inside the house, you answered in post 50.

The usual case is the is that heat engine is outside the building (in power plant). I have feeling that when the heat engine in the power plant uses same temperature as outside for cooling then no way we can get more heat with the air to air heat pump to heat the building, than was used at the power plant.

I was out gathering some free energy (firewood) :)

 

[Dale]

This was supposed to be the case when the heat engine is inside the house, you answered in post 50.

The usual case is the is that heat engine is outside the building (in power plant). I have feeling that when the heat engine in the power plant uses same temperature as outside for cooling then no way we can get more heat with the air to air heat pump to heat the building, than was used at the power plant.

I was out gathering some free energy (firewood) :)

I was assuming that the heat engine and the heat pump were both using the outside air as the cold reservoir in both cases. The difference is that the heat engine uses a hot reservoir heated by the fuel and the heat pump uses the inside of the building as the hot reservoir. The equation I provided applies.

 

[Thermolelctric]

Thanks!

 

[Dale]

You are welcome!

 

[TopiRinkinen]

An engineering way to proceed is to try it in practice ;)

Years ago, I deviced LTSPICE models of Peltier thermoelements. Can be found from LTspice yahoo groups: Files > tut > Thermal > tec_fridge.zip.

The TEC allows you to set realistic parameters, and also creating ideal (lossless) models.

Then you should generate a LTSpice model where you have the hot container (capacitor) and a cold container (another capacitor) and a heat pump (TEC) and the electrical power source (e.g. current source).

If you can build a heat pump model (using supplied TEC model, and resistors (R>0) and other passive realistic components) which seems to break laws of thermodynamics, I'll buy you a beer.

BR, -Topi