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Carnot engine efficiency is:

[itex]\eta_{work} = 1 - \frac{T_c}{T_h}[/itex]

Carnot refrigeration efficiency is:

[itex]\eta_{cool} = \frac{ T_c }{T_h-T_c}[/itex]

[itex]\eta_{cool} = \frac{ 1 }{\frac{T_h}{T_c} - 1}[/itex]

Simple multiplication should give me the efficiency where both the engine and the refrigeration share the same hot and cold reservoirs:

[itex]\eta_{combined} = \frac{ 1 - \frac{T_c}{T_h} }{\frac{T_h}{T_c} - 1}[/itex]

Combining this we get:

[itex]\eta_{combined} = \frac{T_c}{T_h}[/itex]

This is a rather strange result. It seems as though we could maximize the efficiency of energy consumption if we simply balanced heat engine work with refrigeration and relied on very

Though, [itex]\frac{T_c}{T_h}[/itex] is also the fraction of input energy into the Carnot engine that gets dumped out as heat. So that balances it out I guess.

Maybe its basically a fancy way to slow down the transfer of heat from hot to cold.

Maybe that's what "thermal insulators" actually are - a mass assembly of very tiny Carnot heat engines and refrigerators

[itex]\eta_{work} = 1 - \frac{T_c}{T_h}[/itex]

Carnot refrigeration efficiency is:

[itex]\eta_{cool} = \frac{ T_c }{T_h-T_c}[/itex]

[itex]\eta_{cool} = \frac{ 1 }{\frac{T_h}{T_c} - 1}[/itex]

Simple multiplication should give me the efficiency where both the engine and the refrigeration share the same hot and cold reservoirs:

[itex]\eta_{combined} = \frac{ 1 - \frac{T_c}{T_h} }{\frac{T_h}{T_c} - 1}[/itex]

Combining this we get:

[itex]\eta_{combined} = \frac{T_c}{T_h}[/itex]

This is a rather strange result. It seems as though we could maximize the efficiency of energy consumption if we simply balanced heat engine work with refrigeration and relied on very

**small**ambient temperature differences. That's very counter-intuitive.Though, [itex]\frac{T_c}{T_h}[/itex] is also the fraction of input energy into the Carnot engine that gets dumped out as heat. So that balances it out I guess.

Maybe its basically a fancy way to slow down the transfer of heat from hot to cold.

Maybe that's what "thermal insulators" actually are - a mass assembly of very tiny Carnot heat engines and refrigerators

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