An adiabatic process is the process of quasi-static expansion or compression of a gas in a vessel with heat-insulated walls. This simulation illustrates the process of adiabatic compression or expansion of an ideal gas.

The first law of thermodynamics for an adiabatic process states that
A = -ΔU,
where ΔU is the change in internal energy of the gas. In an adiabatic process, the gas can produce work at the expense of the change in its internal energy. The internal energy of an ideal gas is proportional to its temperature. For one mole of mono-atomic gas,
U = 3/2RT = CvT,
where Cv = 3/2R is the molar specific heat of a mono-atomic gas at constant volume.

The molar specific heat of a mono-atomic gas at constant pressure is
Cp = Cv + R = 5/2R.

An adiabatic process can be represented on the (P,V) diagram by a set of curves as described by the Poisson equation
PV' = const, where
 γ = Cp . Cv
For a mono-atomic gas, γ = 5/3.

The work W produced by the gas in an adiabatic process is the function of the initial temperature T1 and final temperature T2.
W = Cv(T1 - T2)

Change the initial temperature T of the gas, and observe the ensuing changes on the adiabatic process' p(V) dependency graph.