Work done by a heat engine (15-24)

Review

Let’s apply the first law of thermodynamics, Equation 15-2, to the generic engine shown in Figure 15-14. In one cycle of the engine it takes in an amount of energy $Q_{\mathrm{H}}$ from the hot reservoir in the form of heat and sends an amount of energy $\vert Q_{\mathrm{C}}\lvert$to the cold reservoir in the form of heat, so the net quantity of heat that goes into the engine is $Q = Q_{\mathrm{H}} - \vert Q_{\mathrm{C}}\vert$. In that same cycle the engine does an amount of work $W$. Because the engine goes through a cycle that returns it to its initial state at the beginning of the cycle, there is zero net change in its internal energy: $\Delta{U} = 0$. So the first law of thermodynamics, $\Delta{U} = Q - W$, becomes

$0 = Q_{\mathrm{H}} - \vert Q_{\mathrm{C}}\vert - W$

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