You received an unsolicited proposal from a self-declared inventor who is seekin

Question

You received an unsolicited proposal from a self-declared inventor who is seeking investors for the development of his latest idea: a device that uses heat extracted from the ground by a heat pump to boil water into steam that is used to heat a home and to power a steam engine that drives the heat pump. This procedure is potentially very lucrative because, after an initial extraction of energy from the groin, no fossil fuels would be required to keep the device running indefinitely. Would you invest in this idea? State your conclusion clearly and present detailed arguments to support it.

Explanation / Answer

You would not invest in this idea because this breaks the second law of thermodynamics =p. Additionally, this is an example of a "Perpetual motion machine of the second kind", which can spontaneously convert thermal energy into work. This also breaks the conservation of energy. You cannot make or destroy energy. The amount of energy extracted from the ground cannot exceed the amount of energy used to extract it. If you consider this, then at best, you will have a machine that will constantly fuel the heat pumping, but you will not have the extra heat to heat your house. (Additionally, you can't even have a machine that will constantly pump the fuel up and power the pump because Carnot once said something like "There are no perfect heat engines that convert heat to work 100%" (actually, Kelvin might have said that...). Anyways, basically, you cannot turn heat into work without heat loss (imagine the Carnot engine diagram, where a Hot Heat Reservoir can be utilized by a pump to do Work and spit out heat into a Cold Reservoir. You cannot remove the Cold reservoir because there will always be heat loss due to friction of some sort). In summary, you can only remove an amount of energy less than the amount of energy used to drive the pump. Otherwise, you would be creating energy, which violates the energy conservation law. I am not quite sure how to explain why it takes an equal amount of energy to pump out a certain amount of energy though..sorry. Hope this helps!

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