Key points (a) Expansion work is proportional to the external pressure. (b) Free expansion
(against zero pressure) does no work. (c) The work of expansion against constant pressure is
proportional to that pressure and to the change in volume. (d) To achieve reversible expansion,
the external pressure is matched at every stage to the pressure of the system. (e) The work of
reversible, isothermal expansion of a perfect gas is a logarithmic function of the volume.