where M is the molecular weight of the salt in solution, [theta] the
absolute temperature, and R a constant which has the value 8.32
joules, or nearly 2 calories, per degree C. It is necessary to
consider two cases, corresponding to the curves CB and AB in fig. 1,
in which the solution is saturated with respect to salt and water
respectively. To facilitate description we take the case of a salt
dissolved in water, but similar results apply to solutions in other
liquids and alloys of metals.
(a) If unit mass of salt is separated in the solid state from a
saturated solution of salt (curve CB) by forcing out through a
semi-permeable membrane against the osmotic pressure P the
corresponding volume of water V in which it is dissolved, the heat
evolved is the latent heat of saturated solution of the salt Q
together with the work done PV. Writing (Q + PV) for L, and V for (v"
- v') in equation (1), and substituting P for p, we obtain