Carnot cycle

The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. It provides an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference (e.g. refrigeration) by the application of work to the system. It is not an actual thermodynamic cycle but is a theoretical construct.

Every single thermodynamic system exists in a particular state. When a system is taken through a series of different states and finally returned to its initial state, a thermodynamic cycle is said to have occurred. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine. A system undergoing a Carnot cycle is called a Carnot heat engine, although such a "perfect" engine is only a theoretical construct and cannot be built in practice. However, a microscopic Carnot heat engine has been designed and run.

Essentially, there are two systems at temperatures T_h and T_c (hot and cold respectively), which are so large that their temperatures are practically unaffected by a single cycle. As such, they are called "heat reservoirs". Since the cycle is reversible, there is no generation of entropy during the cycle; entropy is conserved. During the cycle, an arbitrary amount of entropy ΔS is extracted from the hot reservoir, and deposited in the cold reservoir. Since there is no volume change in either reservoir, they do no work, and during the cycle, an amount of energy T_hΔS is extracted from the hot reservoir and a smaller amount of energy T_cΔS is deposited in the cold reservoir. The difference in the two energies (T_h-T_c)ΔS is equal to the work done by the engine.

The Carnot cycle when acting as a heat engine consists of the following steps:

In this case,

or,

This is true as ${\displaystyle Q_{2}}$ and ${\displaystyle T_{2}}$ are both lower and in fact are in the same ratio as ${\displaystyle Q_{1}/T_{1}}$.

...
Wikipedia