A heat engine does work as a result of extracting energy as heat from the hot source and discarding some of it into the cold sink. Such an engine can also be used as a heat pump in which heat is extracted from a cold source; some work is done on the engine and thereby converted to heat which is added to that from the cold source before being discarded into the hot sink. (a) Assuming that the engine is perfect and that the heat transfers are reversible, use the Second Law to explain why it is not possible for heat to be extracted from the cold source and discarded into the hot sink without some work being done on the engine. (b) Assume that the hot sink is at temperature Th and the cold source at Tc, and that heat of magnitude |q| is extracted from the cold source. Use the Second Law to find the magnitude of the work |w| needed to make it possible for heat of magnitude |q| + |w| to be discarded into the hot sink.
A heat engine does work as a result of extracting energy as heat from the hot source and discarding some of it into the cold sink. Such an engine can also be used as a heat pump in which heat is extracted from a cold source; some work is done on the engine and thereby converted to heat which is added to that from the cold source before being discarded into the hot sink. (a) Assuming that the engine is perfect and that the heat transfers are reversible, use the Second Law to explain why it is not possible for heat to be extracted from the cold source and discarded into the hot sink without some work being done on the engine. (b) Assume that the hot sink is at temperature Th and the cold source at Tc, and that heat of magnitude |q| is extracted from the cold source. Use the Second Law to find the magnitude of the work |w| needed to make it possible for heat of magnitude |q| + |w| to be discarded into the hot sink.
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