Carnot cycle

A Carnot cycle (English: kar-NOH, French: [kaʁno]) is an ideal thermodynamic cycle proposed by French physicist Sadi Carnot in 1824 and expanded upon by others in the 1830s and 1840s. By Carnot's theorem, it provides an upper limit on the efficiency of any classical thermodynamic engine during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference through the application of work to the system.

In a Carnot cycle, a system or engine transfers energy in the form of heat between two thermal reservoirs at temperatures TH and TC (referred to as the hot and cold reservoirs, respectively), and a part of this transferred energy is converted to the work done by the system. The cycle is reversible, merely transferring thermal energy between the thermal reservoirs and the system without gain or loss. When work is applied to the system, heat moves from the cold to hot reservoir (heat pump or refrigeration). When heat moves from the hot to the cold reservoir, the system applies work to the environment. The work W done by the system or engine to the environment per Carnot cycle depends on the temperatures of the thermal reservoirs per cycle such as W = QH(TH − TC)/TH, where QH is heat transferred from the hot reservoir to the system per cycle.

Stages

A Carnot cycle is an idealized thermodynamic cycle performed by a Carnot heat engine, consisting of the following steps:

In this case, since it is a reversible thermodynamic cycle (no net change in the system and its surroundings per cycle)

Q

H

T

H

=

−

Q

C

T

C

.

{\displaystyle {\frac {Q_{\text{H}}}{T_{\text{H}}}}=-{\frac {Q_{\text{C}}}{T_{\text{C}}}}.}

This is true as QC and TC are both smaller in magnitude and in fact are in the same ratio as QH/TH.

Pressure–volume graph

When a Carnot cycle is plotted on a pressure–volume diagram (Figure 1), the isothermal stages follow the isotherm lines for the working fluid, the adiabatic stages move between isotherms, and the area bounded by the complete cycle path represents the total work that can be done during one cycle. From point 1 to 2 and point 3 to 4 the temperature is constant (isothermal process).