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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


and for irreversible changes

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