Heat engines and their efficiency

Every heat engine has three parts: a heater at temperature T₁ (it gives heat Q₁), a working substance (usually a gas) and a cooler at T₂ < T₁ (it takes heat Q₂). The working substance changes state in repeating cycles: it takes Q₁ from the heater, does work and gives the remaining Q₂ to the cooler. The useful work is A = Q₁ – Q₂ and the efficiency is η = A/Q₁ = (Q₁ – Q₂)/Q₁ (·100 %). Heat must always be given to the cooler (second law), so η < 1 always. The French engineer S. Carnot found the greatest efficiency for an ideal engine, whose cycle consists of two isotherms and two adiabats (the Carnot cycle): η_max = (T₁ – T₂)/T₁ (T in kelvins). To raise the efficiency, raise the heater temperature or lower the cooler temperature; if T₁ = T₂ the engine can do no work.