Editing Carnot heat engine (section)

==Carnot cycle==
{{main|Carnot cycle}}
[[File:Carnot cycle pV diagram.svg|upright=1.6|thumb|Figure 1: A Carnot cycle illustrated on a [[PV diagram]] to illustrate the work done.]]
[[File:Carnot cycle ST diagram.svg|upright=1.6|thumb|Figure 2: A Carnot cycle acting as a heat engine, illustrated on a temperature-entropy diagram. The cycle takes place between a hot reservoir at temperature {{math|{{var|T}}{{sub|H}}}} and a cold reservoir at temperature {{math|{{var|T}}{{sub|C}}}}. The vertical axis is temperature, the horizontal axis is entropy.]]

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

# '''Reversible [[isothermal]] expansion of the gas at the "hot" temperature, {{math|{{var|T}}{{sub|H}}}} (isothermal heat addition or absorption).''' During this step ({{mvar|A}} to {{mvar|B}}) the gas is allowed to expand and it does work on the surroundings. The temperature of the gas (the system) does not change during the process, and thus the expansion is isothermic. The gas expansion is propelled by absorption of heat energy {{math|{{var|Q}}{{sub|H}}}} and of entropy {{math|Δ{{var|S}}{{sub|H}} {{=}} {{var|Q}}{{sub|H}} / {{var|T}}{{sub|H}}}} from the high temperature reservoir.
# '''[[Isentropic process|Isentropic]] ([[Reversible adiabatic process|reversible adiabatic]]) expansion of the gas (isentropic work output).''' For this step ({{mvar|B}} to {{mvar|C}}) the piston and cylinder are assumed to be thermally insulated, thus they neither gain nor lose heat. The gas continues to expand, doing work on the surroundings, and losing an equivalent amount of internal energy. The gas expansion causes it to cool to the "cold" temperature, {{math|{{var|T}}{{sub|C}}}}. The entropy remains unchanged.
# '''Reversible isothermal compression of the gas at the "cold" temperature, {{math|{{var|T}}{{sub|C}}}} (isothermal heat rejection)''' ({{mvar|C}} to {{mvar|D}}). Now the gas is exposed to the cold temperature reservoir while the surroundings do work on the gas by compressing it (such as through the return compression of a piston), while causing an amount of waste heat {{math|{{var|Q}}{{sub|C}} < 0}} (with the [[Heat|standard sign convention for heat]]) and of entropy {{math|Δ{{var|S}}{{sub|C}} {{=}} {{var|Q}}{{sub|C}}/{{var|T}}{{sub|C}} < 0}} to flow out of the gas to the low temperature reservoir. (In magnitude, this is the same amount of entropy absorbed in step 1. The entropy decreases in isothermal compression since the multiplicity of the system decreases with the volume.) In terms of magnitude, the recompression work performed by the surroundings in this step is less than the work performed on the surroundings in step 1 because it occurs at a lower pressure due to the lower temperature (i.e. the resistance to compression is lower under step 3 than the force of expansion under step 1). We can refer to the first law of thermodynamics to explain this behavior: {{math|Δ{{var|U}}{{=}} {{var|W}}+{{var|Q}} }}.
# '''Isentropic compression of the gas (isentropic work input)''' ({{mvar|D}} to {{mvar|A}}). Once again the piston and cylinder are assumed to be thermally insulated and the cold temperature reservoir is removed. During this step, the surroundings continue to do work to further compress the gas and both the temperature and pressure rise now that the heat sink has been removed. This additional work increases the internal energy of the gas, compressing it and causing the temperature to rise to {{math|{{var|T}}{{sub|H}}}}. The entropy remains unchanged. At this point the gas is in the same state as at the start of step 1.