Work

The mechanical work, W, performed upon 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. The mechanical work done by the gas has the opposite sign (a common source of mistakes).

For reversible changes,

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

and for irreversible changes

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