Carnot's theory describes the best efficiency that a heat engine can achieve, appropriately known as the Carnot efficiency. It is achieved by two isothermal processes (constant temperature) and two adiabatic processes (no heat energy in or out). The Carnot cycle is an ideal limit. Any real heat engine can only approximate it, but the Carnot efficiency is a useful goal, and the efficiency of a real heat engine is often compared to the Carnot efficiency as a standard.
Using physics we can derive Carnot’s equation for efficiency.
W = ∫PdV = (TH – TC)
QH = TH
n = ∆W/∆QH = 1 – TC/TH
∆W is the work done by the system
∆QH is the heat put into the system
TC is the absolute temperature of the cold reservoir
TH is the temperature of the hot reservoir
n is the efficiency
This final equation, n = 1 – TC/TH, is the theoretical maximum efficiency of a heat engine. It equals the difference in temperature between the hot and cold reservoir divided by the absolute temperature of the hot reservoir. This theorem is extremely useful in studying real engines and also refrigerators.