Eq. 3.3 unites statistical mechanics, in the guise of the partition function Q, with thermodynamics, namely the Helmholtz free energy A. If the free energy of a system is known, all other thermodynamic properties are determined, as discussed in Part II. In particular, the pressure is
while from Lecture 5, Q of an N-atom ideal gas is
Combining the above, the free energy of an ideal gas is
so from eq. 6.10
Once again, the detailed form of U(x) was implicitly fixed in the calculation. Eq. 6.11 came from
The kernel of the integral has no dependence upon 
, while the bounds
of each 
are V. There is a unique potential energy
corresponding to this kernel and bounds, namely 
for
within V, and 
for particles outside V. For this
there is no adsorption, nor any of the skin/surface effects
treated in problem 6-4.
