Undergrad 64% n.th + COP4 = more heat out of fuel than its calorific value?

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A CCGT generating power at 64% efficiency combined with a COP4 heat pump suggests a theoretical output of 256% thermal energy from the fuel's calorific value, raising questions about the source of the extra heat. The discussion highlights that while this seems counterintuitive, it is explained by the heat pump's ability to transfer environmental heat, not create energy. The concept of Coefficient of Performance (COP) is clarified as a measure of efficiency that can exceed 100%, which does not violate thermodynamic laws. The conversation also explores the potential for directly harnessing combustion temperatures to capture additional heat without electrical generation. Overall, the principles of energy transfer and thermodynamics are central to understanding these efficiencies.
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If a CCGT generates electrical power at 64% efficiency, and a heat pump generates 4 times the thermal power to electrical power, is that more heat energy out than the fuel has?
Something that has been on my mind a while.

If a CCGT generates electrical power at 64% efficiency, and a COP4 heat pump, powered by that generator, generates 4 times the thermal power to electrical power, wouldn't that mean we can get 256% heat out of the fuel's calorific value?

Maybe that is OK, but seems non-intuitive.

Where does the extra heat come from, or what am I not understanding?

I presume the answer is that because we're going from 'very hot' heat to colder heat, we can suck up some of the environmental heat? If so, is there not a more direct way to use the combustion temperature from a burning fuel to directly suck in extra heat from the environment, missing out the electrical generation bit?
 
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Short summary of @Llewelyn 's point: COP is like efficiency, but it is not efficiency. It is always way over 100%. That's not a violation of the laws of thermo. The energy isn't being created, just moved, and there are hard restrictions on the available temperature deltas.
 

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