Heat Pump Stirling Generator?

[Devin-M]

I was reading about heat pumps and it made me wonder… would the following process be physically possible…?

I attach the hot side of the heat pump to the hot side of the stirling engine. 400% COP (coefficient of performance) means 1 kilowatt hour of electricity consumed by the heat pump delivers 4 kilowatt hours of heat to the stirling engine (heat mostly transferred from the environment to the stirling engine, rather than the electricity itself being directly converted to heat).

…the stirling engine operates at 32% efficiency… for every 4 kilowatt hours of heat supplied, 1.28 kilowatt hours of mechanical energy is generated. the mechanical output of the stirling engine is attached to a generator…

the generator operates at 95% efficiency… for every 1.28 kilowatt hours of mechanical energy supplied, 1.21 kilowatt hours of electrical power is produced. the electrical power is used to charge a battery…

… the battery charges at 95% efficiency… for every 1.21 kilowatt hours supplied, 1.15 kilowatt hours of energy is stored. 1.15 kilowatt hours of stored electricity has been produced from 1 kilowatt hour of electricity input. the extra energy obtained came from the heat energy of the surroundings which have now decreased in temperature as a result of the process.

 

[sophiecentaur]

I was reading about heat pumps and it made me wonder… would the following process be physically possible…?

There is no such thing as a free lunch. What you are suggesting is an 'over unity device' which you feel should deliver more than you put in. PF doesn't discuss this concept or perpetual motion machines because the idea is fundamentally flawed.
The easiest way to destroy your idea is to tell you that the efficiency of a heat engine of any sort depends upon the temperature difference between the hot source and cold sink of heat. Your statement of the efficiency of the Stirling assumes a temperature difference that a refrigeration unit (driven by the sterling engine) couldn't produce. Your efficiency figures have no foundation so the results of your sums are not feasible.
I think this thread will have a short life, once the mods see it. My post may not even make it on board!

 

[berkeman]

There is no such thing as a free lunch. What you are suggesting is an 'over unity device'

I'm not sure that's correct (but I'm no expert in thermo). The OP says this at the end of his post:

the extra energy obtained came from the heat energy of the surroundings which have now decreased in temperature as a result of the process.

 

[Bystander]

heat energy of the surroundings which have now decreased in temperature as a result of the process.

"Possible?" Yes. Why?

 

[jrmichler]

The COP of a heat pump increases as the temperature difference decreases. The efficiency of a Stirling (or any heat) engine decreases as the temperature difference decreases. The temperature difference of a heat pump at 400% COP, when applied to a Stirling engine, will result in engine efficiency closer to 2% than to 32%.

Some good sources on Stirling engine efficiency:
Search Stirling engine efficiency
Stirling Engine Design and Feasibility for Automotive Use, edited by M.J. Collie, Noyes Data Corporation, 1979
Air Engines - The History, Science, and Reality of the Perfect Engine, by Finklestein and Organ, ASME, 2001
Stirling Engines, by G. Walker, Clarendon Press, 1980

A search using search terms heat pump efficiency will bring up good information on how the efficiency (COP) varies with temperature difference.

 

[russ_watters]

I'm not sure that's correct (but I'm no expert in thermo). The OP says this at the end of his post:

That would violate the 2nd law of thermo.

This is a perpetual motion machine, and @jrmdescribed why it won't work. Thread locked.

 

[Dale]

I was reading about heat pumps and it made me wonder… would the following process be physically possible…?

No. That would violate the second law of thermodynamics.

400% COP (coefficient of performance) means 1 kilowatt hour of electricity consumed by the heat pump delivers 4 kilowatt hours of heat … …the stirling engine operates at 32% efficiency… for every 4 kilowatt hours of heat supplied, 1.28 kilowatt hours of mechanical energy is generated.

The COP of a heat pump and the efficiency of a heat engine both depend strongly on the temperatures of the hot and cold reservoirs. For this calculation you need to go back and check the sources for the temperatures corresponding to each of these numbers. You will find that the Stirling engine numbers are for a much bigger temperature difference than the heat pump numbers.