Work

The mechanical work, W, performed in compressing a gas is given by

$W=-\int _{\alpha }^{\beta }p~dV$

where $\alpha$ and $\beta$ are points in state space, p is the pressure and V is the volume.

For reversible changes

$\left.dW\right.=-PdV$

and for irreversible changes

$\left.dW\right.>-PdV$