Prelecture 31: Slide 3

Since a difference in temperature is key to the operation of all heat engines, it is common to represent the operation of an engine through one of its cycles using the diagram shown

Here we see heat flowing from a hot reservoir through the working substance of the engine, usually a gas, to a cold reservoir. The engine converts some of this heat to mechanical work, usually by the expansion and compression of the gas during a complete cycle.

We can apply the first law of thermodynamics to the engine to determine that the heat that flows from the hot reservoir into the engine must be equal to the sum of the work done by the engine and the heat that flows out of the engine into the cold reservoir.

In order to keep the temperature of the hot reservoir constant, energy must be continually added to it. For example, if a certain amount of energyis extracted each cycle, then an equivalent amount of energymust also be supplied to the reservoir to maintain its temperature. This is the energy cost to drive the engine. The engine then does work. Consequently, it is natural to define the efficiency of the engine as the ratio of the work done by the engine to the heat that has to be extracted from the hot reservoir.

On the next slide, we will show that the second law of thermodynamics places a limit on how large this efficiency can be. We will find that this limit is determined by the temperature difference of the reservoirs.