Pressure-volume work

For expansion or compression against a constant external pressure, w = −pₑₓ(V_f − V_i) = −pₑₓΔV.

In expansion ΔV is positive, so w is negative (the system does work); in compression ΔV is negative, so w is positive.

A reversible process proceeds through a series of equilibrium states, with the external pressure differing from the internal pressure only infinitesimally at every step.

Reversible isothermal expansion of an ideal gas: w_rev = −2.303 nRT log(V_f/V_i).

Reversible expansion does more work on the surroundings than an irreversible expansion between the same two states.

Free expansion is expansion into a vacuum (pₑₓ = 0), so no work is done; for an ideal gas ΔU is also zero because it has no intermolecular attractions.

For isothermal changes of an ideal gas ΔU = 0, so q = −w: irreversible q = pₑₓ(V_f − V_i), reversible q = 2.303 nRT log(V_f/V_i), free expansion q = 0.

Work of 1 L bar equals 100 J.