Define the isobaric partition function

\[
Y_{N}(P, T)=\frac{1}{\lambda^{3}} \int_{0}^{\infty} Q_{N}(V, T) e^{-\beta P V} d V
\]

Show that in the thermodynamic limit the Gibbs free energy (4.7.1) is proportional to \(\ln Y_{N}(P, T)\). Evaluate the isobaric partition function for a classical ideal gas and show that \(P V=N k T\). [The factor of the cube of the thermal deBroglie wavelength, \(\lambda^{3}\), serves to make the partition function dimensionless and does not contribute to the Gibbs free energy in the thermodynamic limit.]