Proof of the impossibility of perpetual motion of the second kind

In thermodynamics, proof of the impossibility of perpetual motion of the second kind refers to the proof given by German physicist Rudolf Clausius, sometime between 1850 and 1865, that if entropy did not increase, i.e. if the principle of entropy increase did not exist, in a system (body, working body, or working substance), in the operation of one cycle of a heat engine, or in many continuous cycles, quantified by the cycle integral, for any process that is in any way possible, that it would be possible to couple two heat engines together so as to make perpetual motion or rather perpetual motion of the second kind.

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