Prelecture 31: Slide 9

We conclude with a brief discussion of the main points of this prelecture.

First, we introduced the concept of the heat engine. In particular, we defined a heat engine as a device that extracts heat from a hot reservoir, does work and then exhausts heat to a cold reservoir. We defined the efficiency of the engine to be the ratio of the work done by the engine to the heat that was extracted from the hot reservoir. We applied the second law of thermodynamics to engine plus reservoirs to determine that there is a maximum efficiency for any engine that operates between two reservoirs. This maximum efficiency, called the Carnot efficiency, is equal to the ratio of the temperature difference between the reservoirs to the temperature of the hot reservoir.

Second, in order to calculate the efficiencies of heat engines, we restricted the possible processes in the engine cycle to those that are quasi-static, that is, those in which all changes are done slowly enough so that the working substance of the engine is essentially at equilibrium at all times, meaning that it has a well-defined pressure, temperature, volume, and entropy at all times. We could then represent any engine cycle on a PV diagram, in which the work done by the engine is represented as the area enclosed by the transitions that make up the cycle.

Finally, we introduced the Stirling cycle as our standard example of a heat engine. This cycle consists of two isothermic transitions (that is, at constant temperature) and two isochoric transitions (that is, at constant volume). We then calculated the efficiency of this engine, using an ideal gas as the working substance. We found that this efficiency was indeed less than the Carnot efficiency.