Physics

Problem

A heat pump keeps a room at

293\,\text{K}

by absorbing

3.5\times10^{4}\,\text{J}

of heat from outside air at

273\,\text{K}

each cycle. Assuming ideal reversible operation, determine the minimum work input required per cycle.

Intuitive explanation

A heat pump moves heat from cold to hot, but it can't do so for free—it needs work input. The key is using the coefficient of performance for an ideal (Carnot) heat pump, which relates the useful heat delivered to the work you must supply. Since both temperatures are fixed, you can find the theoretical minimum work by applying energy conservation and the second law of thermodynamics together.

Intuitive explanation

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