Question

7.24. A simple model of a low-temperature solid is the following. Atoms interact with a repulsive pairwise potential energy of the form uj() constant x , where ry is the atom-atom separation distance and n is a constant, typically 9 or 12. For such solids, the Helmholtz free energy can be approximated as A(T, V, N)- 3NkBT ln(N/vyn b/T] [Shell et al., J. Chem. Phys. 118, 8821 (2003)]. Here m (n 2)/6 and b is a constant with units of [temperature] [volume]". Using this, find expressions for (a) the thermodynamic potentials E(S. Ч (b) the intensive heat capacities cvT, P) and cp(T, P), and the equation of state, and (T, P), and PCT, p), where ρ = N/ V.

Answer 1