  The partition function and the one- and two-body distribution functions are
evaluated for two hard spheres with different sizes constrained into a
spherical pore. The equivalent problem for hard disks is addressed too. We
establish a relation valid for any dimension between these partition functions,
second virial coefficient for inhomogeneous systems in a spherical pore, and
third virial coefficients for polydisperse hard spheres mixtures. Using the
established relation we were able to evaluate the cluster integral $b_{2}(V)$
related with the second virial coefficient for the Hard Disc system into a
circular pore. Finally, we analyse the behaviour of the obtained expressions
near the maximum density.

Statistical Mechanics