4.2 Heat engines  (Page 2/6)

Heat engines operate by carrying a working substance through a cycle. In a steam power plant, the working substance is water, which starts as a liquid, becomes vaporized, is then used to drive a turbine, and is finally condensed back into the liquid state. As is the case for all working substances in cyclic processes, once the water returns to its initial state, it repeats the same sequence.

For now, we assume that the cycles of heat engines are reversible, so there is no energy loss to friction or other irreversible effects. Suppose that the engine of [link] goes through one complete cycle and that $Q_{\text{h}},Q_{\text{c}},$ and W represent the heats exchanged and the work done for that cycle. Since the initial and final states of the system are the same, $\text{Δ}{E}_{\text{int}}=0$ for the cycle. We therefore have from the first law of thermodynamics,

so that

The most important measure of a heat engine is its efficiency ( e )    , which is simply “what we get out” divided by “what we put in” during each cycle, as defined by $e=W_{\text{out}}\text{/}{Q}_{\text{in}}.$

With a heat engine working between two heat reservoirs, we get out W and put in $Q_{\text{h}},$ so the efficiency of the engine is

Here, we used [link] , $W=Q_{\text{h}}-Q_{\text{c}},$ in the final step of this expression for the efficiency.

Summary

• The work done by a heat engine is the difference between the heat absorbed from the hot reservoir and the heat discharged to the cold reservoir, that is, $W=Q_{\text{h}}-Q_{\text{c}}.$
• The ratio of the work done by the engine and the heat absorbed from the hot reservoir provides the efficiency of the engine, that is, $e=W\text{/}{Q}_{\text{h}}=1-Q_{\text{c}}\text{/}{Q}_{\text{h}}.$

Conceptual questions

Problems