Adiabatic process and the Carnot cycle

A process with no heat exchange with the surroundings is adiabatic (Q = 0); fast processes are close to it. From the first law A = –ΔU: if the gas expands and does work its internal energy falls and it cools; if it is compressed quickly it heats up. A heat engine converts the internal energy of fuel into mechanical work; it has three parts: a working substance (gas or steam), a heater (T₁) and a cooler (T₂). In one cycle the working substance takes heat Q₁ from the heater, gives Q₂ to the cooler and does work A = Q₁ – Q₂. The efficiency is η = A/Q₁ = (Q₁ – Q₂)/Q₁ (×100% for percent). The Carnot cycle is an ideal reversible cycle of two isotherms and two adiabats; its efficiency does not depend on the working substance: η = (T₁ – T₂)/T₁, with temperatures in kelvin (T = t + 273). So to raise the efficiency one raises T₁ and lowers T₂; the efficiency is always below 1 (100%). Carnot’s theorem: for given T₁ and T₂ no engine has an efficiency greater than that of the Carnot cycle.