The Clausius statement of the second law says it is impossible to construct a device that operates in a cycle and produces no effect other than transferring heat from a lower-temperature body to a higher-temperature body. What would be the coefficient of performance of such an impossible device?
Explanation
The Clausius statement forbids the spontaneous transfer of heat from a cold object to a hot object. A hypothetical device that could do this would require zero work input (W_in = 0). Since the Coefficient of Performance (COP) is defined as the desired heat transfer divided by the work input, a non-zero heat transfer with zero work input would result in an infinite COP.
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