The Carnot Cycle

The Carnot cycle describes an ideal, reversible cycle between an inexhaustible hot energy reservoir and an inexhaustible cold reservoir. This cycle is important because it sets the theoretical limit on the amount of work that can be provided by a given amount of energy for the hot reservoir.

Carnot imagined a gaseous substance being put through several cyclic stages. He believed that the particular gas or liquid used in the cycle didn't matter; however, some substances will work more efficiently than others. We assume that the gas being used is an ideal gas; that is, it follows the law that pressure times volume is proportional to temperature.

The Carnot cycle consists of four stages:

A to B: An isothermal (constant-temperature) expansion of the gas. The temperature is maintained at the level of the hot reservoir.

B to C: An adiabatic (no heat flow Q - insulated from surroundings) expansion that lowers the temperature

from Thot to Tcold. This is where the work of the cycle is done; as the gas expands, it pushes a piston or turns a turbine.

C to D: An isothermal compression maintained at the temperature of the cold reservoir. Normally, this compression would add heat, but instead the heat is siphoned away into the cold reservoir.

D to A: An adiabatic compression that brings the temperature of the gas back up to the level of the hot reservoir.

The work done each cycle is the area inside of the lines.

The thermal efficiency of the Carnot cycle is e= 1 - (Thot / Tcold), which means that the hotter the hot reservoir and the colder the cold reservoir, the more efficient the engine is. In order to get 100% efficiency, the cold reservoir would have to be absolute zero, which is impossible; therefore, efforts are usually concentrated on making the hot reservoir warmer. For example, using a larger furnace for a steam engine or more explosive fuel for an internal combustion engine can increase efficiency.