Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 29

a) Calculate the free energy Calculate the Gibbs poten-

tial G is the Legendre transform of F with respect

to V.

b) If the molecules of type A are called the solvent, and those

of type B the solute. Consider two solutions with the same solvent

(type A) and different concentrations of solute (type B molecules)

separated by a partition through which solvent molecules can pass but

solute molecules cannot (see Figure P.4.56). There are particles in

volumeV(or in volume2V), and and particles in volume

V on the left and right of the membrane, respectively. Calculate the

pressure differenceacross the membrane at a given temperature and

volume. Assume that the concentrations of the solutions are small;

i.e.,

and

4.57 Clausius–Clapeyron (Stony Brook)

Derive the Clausius–Clapeyron equation for the equilibrium of two

phases of a substance. Consider a liquid or solid phase in equilibrium

with its vapor.

Using part (a) and the ideal gas law for the vapor phase, show that the

vapor pressure follows the equation ln Make reasonable

assumptions as required. What is B?

a)

b)