Gas compression heat pump
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Gas compression heat pumps using the Stirling cycle are commonly used to liquefy air in order to produce liquid nitrogen, oxygen, argon, etc. for industrial purposes.
In a Carnot heat engine, e.g. a steam engine, we are usually interested in producing work (e.g. electrical energy) out of heat. The Second law of thermodynamics makes that rather difficult and puts severe restrictions on the efficiency of such a process. Only part of the heat available, say, from burning fuel can be transformed into useful work, and the rest must be dumped in a cold reservoir (e.g. the river).
In a heat pump the desired product is heat. There is no restriction on transforming work (electricity) into heat. That means that in an electrical heater 100 joules (watt-seconds) of electricity will give 100 joules of heat. In a heat pump we can do more. We can use the electrical power to run the heat pump to move existing heat about.