The most efficient cycle of operations for a reversible heat engine. Published in 1824 by N. L. S. Carnot, it consists of four operations on the working substance in the engine: (1) Isothermal expansion at thermodynamic temperature T1 with heat q1 taken in. (2) Adiabatic expansion with a fall of temperature to T2. (3) Isothermal compression at temperature T2 with heat q2 given out. (4) Adiabatic compression with a rise of temperature back to T1. According to the Carnot principle, the efficiency of any reversible heat engine depends only on the temperature range through which it works, rather than the properties of the working substances. In any reversible engine, the efficiency (η) is the ratio of the work done (W) to the heat input (q1), i.e. η = W/q1. As, according to the first law of thermodynamics, W = q1 − q2, it follows that η = (q1 − q2)/q1. For the Kelvin temperature scale, q1/q2 = T1/T2 and η = (T1 − T2)/T1. For maximum efficiency T1 should be as high as possible and T2 as low as possible.