Adiabatic process

An adiabatic process is one in which no heat crosses the system boundary, Q = 0 — either because the walls are perfectly insulating or because the change happens too fast for heat to flow. The first law then reads ΔU = −W: a gas that expands must pay for the work out of its own internal energy and so cools, while a gas that is compressed has work piled into it and so heats.

For a reversible adiabatic change of an ideal gas, pressure and volume obey PVᵞ = const, equivalently TVᵞ⁻¹ = const, where γ = C_p/C_v is the adiabatic exponent. Because γ > 1, the adiabat is steeper on a PV diagram than the isotherm through the same point. The relation was first derived by Siméon Denis Poisson in 1823.

Adiabatic compression heats the air in a diesel engine enough to ignite fuel without a spark, and adiabatic expansion cools rising air parcels until their moisture condenses into cloud. A free expansion into vacuum is also adiabatic, but violently irreversible, with no smooth path on a PV diagram.

The relation PVᵞ = const was obtained by Poisson in 1823; the realisation that the speed of sound in air requires adiabatic, not isothermal, compression corrected Newton's estimate and confirmed the exponent γ in the early nineteenth century.