(a) For a dilute gas, the pair distribution function g(r) may be approximated as
g(r)≃exp{−u(r)/kT}.
Show that, under this approximation, eqn. (3.7.17) takes the form
NkTPV≃1−2πn∫0∞f(r)r2dr,
where f(r)[=exp{−u(r)/kT}−1] is the so-called Mayer function; see eqn. (9.1.6).
(b) What form will this result take for a gas of hard spheres, for which
u(r)=∞for r≤σ=0otherwise?
Compare your result with that of Problem 1.4.