Consider a rod, at an angle 
to the normal of a wall,
with its centre-of-mass velocity 
along the normal direction,
of mass m and angular velocity 
about an
axis parallel to the wall but perpendicular to the rod. Suppose
one end of the rod, with normal component of velocity
is infinitesimally close to the wall and undergoes an instantaneous energy conserving collision; the momentum transfer from the rod to the wall can be easily found to be:
Since both and independently obey Gaussian distribution
with their variances given by the equipartition of the thermal energy,
it follows, from Eq.(40), that 
also obeys a Gaussian distribution:
with a variance 
. The pressure
can then be integrated to give:
which is the required result. Although derived by kinetic theory, this result must of course correspond to that found from an appropriate free energy derivative. Accordingly it remains applicable to rods in solution (rather than in vacuo), so long as p is interpreted as an osmotic pressure.
