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

\[\left.dW\right.=-p~dV \]

and for irreversible changes

\[\left.dW\right. > -p~dV \]