Work

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

$W = - \int_\alpha^\beta p ~dV$

where $α$ and $β$ are points in state space, p is the pressure and V is the volume.

For reversible changes

$\left.dW\right.=-p~dV$

and for irreversible changes

$\left.dW\right. > -p~dV$