This process can be also expressed
mathematically. For a such a process, ΔQ = 0.
Therefore...
0 = ΔU + ΔW
Any work done by the system is done at the expense of the internal energy. Any work done on the system serves to increase the internal energy.
For an ideal gas changing from conditions ( P1, V1, T1 ) to ( P1, V1, T1 ) is an adiabatic process,
P1V1γ = P2V2γ and
T1V1γ-1 = T2V2γ-1
where *γ = cp / cn
*cp is just simply the specific heat of a gas at a constant pressure, and cv is just simply the specific heat at a constant volume. For more information, see Specific Heats of Gases.