In an adiabatic process, the system is insulated from the surroundings and heat absorbed or released is zero.

For an adiabatic process of an ideal gas - `PV^gamma=C=` Constant `........(1)`

where `gamma` is the ratio of specific heats (ordinary or molar) at constant pressure and at constant volume.

`gamma=(C_p)/(C_v)`

Thus if an ideal gas undergoes a change in its state adiabatically from (`P_1, V_1`) to (`P_2, V_2`) :

`P_1V_1^gamma=P_2V_2^gamma......(2)`

The work done in an adiabatic change of an ideal gas from the state (`P_1, V_1, T_1`) to the state (`P_2, V_2, T_2`).

`W=int_(V_1)^(V_2)PdV`

`W=Cint_(V_1)^(V_2)(dV)/(V^gamma)`

`W=C/(1-gamma)xx[1/(V_2^(gamma-1)) -1/(V_1^(gamma-1))]......(3)`

`W=1/(1-gamma)[(P_2V_2^gamma)/(V_2^(gamma-1)) -(P_1V_1^gamma)/(V_1^(gamma-1))]`

`W=1/(1-gamma)(P_2V_2 - P_1V_1)`