- Carnot Cycle Definition: The Carnot cycle is a thermodynamic cycle that achieves maximum efficiency by converting heat into work through reversible processes.
- Cycle Efficiency: The efficiency of the Carnot cycle depends solely on the temperatures of the hot and cold reservoirs, not on the working fluid.
- Work Done: In the Carnot cycle, work done during expansion and compression determines the net work output.
- Reversible Processes: The Carnot cycle consists of four reversible processes—two isothermal and two adiabatic.
- Reversed Carnot Cycle: The reverse Carnot cycle is a refrigeration cycle where heat is absorbed from a low-temperature reservoir and rejected to a high-temperature reservoir.
Carnot Cycle
The Carnot cycle is a reversible heat-engine cycle between one hot reservoir and one cold reservoir. It has two isothermal legs and two adiabatic (isentropic) legs. No real engine between those two temperatures can beat its thermal efficiency.
Carnot thermal efficiency is 1 minus the cold-reservoir absolute temperature divided by the hot-reservoir absolute temperature (kelvin or rankine, not celsius). The live page had that ratio inverted. The cycle is the upper bound for any engine between those two reservoirs.
The working fluid does work on the expansion legs. Work is done on the fluid on the compression legs. Net work out is expansion work minus compression work, equal to heat in minus heat out.
Reversible legs give the least compression work and the most expansion work for those two temperatures. A real plant always has friction, finite temperature difference and other irreversibilities, so it stays below the Carnot limit.
Engineers use the reversible cycle as a limit, then add the irreversibilities of the real plant. Rankine, Otto and vapour-compression machines are those modified cycles, not Carnot machines.
The Carnot cycle has four reversible processes: two isothermal and two adiabatic, in this order:
A piston-cylinder sketch of the four legs:
STEP 1 – 2
(Reversible Isothermal Expansion, Th = Constant)
TH is both the gas temperature and the hot-reservoir temperature. The cylinder head is in thermal contact with that reservoir.
Expansion would cool the gas. The reservoir supplies heat so the temperature stays at T_H.
That heat input is Qh, not a temperature increment dT.
STEP 2 – 3
(Reversible adiabatic expansion temperature drop from TH to TL)
Insulation replaces the hot reservoir, so the expansion is adiabatic and isentropic. The gas temperature falls from Th to Tl.
Reversible plus adiabatic means isentropic in closed-system engineering thermodynamics: no heat and no internal irreversibility.
STEP 3 – 4
(Reversible Isothermal Compression, Tl = constant)
At state 3 the cold sink at Tl replaces the insulation. Compression work would heat the gas; the sink takes that heat so temperature stays at the sink value.
Heat rejected to the sink on this isothermal compression is Ql.
STEP 4 – 1
(Reversible adiabatic compression temperature increases from Tl to Th)
Insulation replaces the sink. Adiabatic compression raises the gas temperature from Tl to Th and returns the fluid to state 1.
Net Work Done
On the p-V plot, expansion work is the area under 1-2-3.
Compression work is the area under 3-4-1.
Net work is the enclosed area 1-2-3-4-1.
Importance of the Carnot Cycle
Heat engine efficiency depends on the maximum and minimum temperature of the cycle:
Carnot’s theorem: all reversible engines between the same two reservoirs have the same efficiency, and no irreversible engine between those reservoirs can do better. The working fluid does not appear in eta = 1 – T_L/T_H.
Raising T_H or lowering T_L raises that limit. Superheated steam helps a Rankine plant by raising the mean heat-addition temperature; it does not turn the plant into a Carnot engine.
Carnot Cycle and Second law of thermodynamics:
A heat engine must reject some heat to a colder sink (Kelvin-Planck). Heat does not flow by itself from the sink to the source (Clausius). A reversed Carnot plant can move heat uphill only if a net work input is supplied.
Reversed Carnot Cycle
The Carnot cycle run backwards is the Carnot refrigerator or heat pump. Heat and work arrows reverse:
Thus,
- Heat taken from the cold reservoir is Ql
- Heat dumped to the hot reservoir is Qh
- Net work input is Wnet-in. Refrigerator COP is Q_L/W = T_L/(T_H – T_L) on the kelvin scale.
The Reversed Carnot cycle uses the same four states as the power Carnot Cycle, traversed the other way.
History of Carnot Cycle
Nicolas Leonard Sadi Carnot published the cycle in 1824 in Reflexions sur la puissance motrice du feu. Later writers recast his argument in kelvin temperatures and entropy. Heat is energy transfer driven by a temperature difference.
