In a classical gas of hard spheres (of diameter \(D\) ), the spatial distribution of the particles is no longer uncorrelated. Roughly speaking, the presence of \(n\) particles in the system leaves only a volume \(\left(V-n u_{0}ight)\) available for the \((n+1)\) th particle; clearly, \(u_{0}\) would be proportional to \(D^{3}\). Assuming that \(N v_{0} \ll V\), determine the dependence of \(\Omega(N, V, E)\) on \(V\) (compare to equation (1.4.1)) and show that, as a result of this, \(V\) in the ideal-gas law (1.4.3) gets replaced by \((V-b)\), where \(b\) is four times the actual volume occupied by the particles.