Work

The mechanical work, W, performed upon a gas is given by

$W=-\underset{\alpha }{\overset{\beta }{\int }}pdV$

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, where the system evolves through a succession of equilibrium states, one has

$dW=-pdV$

and for irreversible changes

$dW>-pdV$