2 The Steam Engine

Carnot spent much time thinking about steam engines. Steam engines are conceptually simple devices though complex in practice. Basically a steam engine is a cylinder fitted with a piston and several valves. One valve opens, letting hot steam into the cylinder. The piston is pushed outward. This step is essentially done at constant temperature, the temperature of the hot steam. The steam valve is then closed, but the piston allowed to continue moving outward. As it does, the steam cools. This step is basically adiabatic. The piston then starts to move back into the cylinder. As it does so a second valve opens and the now much cooler steam is pushed out of the cylinder. The temperature of the steam remains mainly unchanged in this step. The second valve then closes, but the piston continues to move inward until it returns to its original position. That step results in adiabatic heating of the residual steam, returning it to its original temperature.

The important thing to realize about this process is that it is cyclical. The piston returns to its original position and original conditions once each cycle. The net process is that hot steam is taken in, work is done, and cool steam is pushed out. Carnot realized that the process was cyclical. Further he understood that the steam was taken from a boiler and that the cool steam could be run through a condenser and the resulting liquid returned to the boiler. In principle no water would ever be lost.⁸All that happened in a steam engine was that (a) heat from the boiler went into the engine, (b) work was done by the engine, and (c) heat was extracted from the spent steam and the water recycled. We can abstract this process as shown in Figure 1

Figure 1: Heat and Work in a Steam Engine

The hot reservoir at a temperature $T_2$ represents the boiler. An amount of heat $q_2$ is taken from in by the hot steam and sent to the engine. In the course of one cycle the engine does an amount of work w. The spent steam is reconverted to water in a condenser at a temperature $T_1$ by the extraction of heat $q_1$. The process then repeats.

This cyclic process is today known as a Carnot cycle in honor of Sadi Carnot.