Investigate the chemical potential μ upon a change in volume. We will use the fact that
F=U−TS and μ=∂F∂N. We will compute μ(Vf)−μ(Vi)

Take N=20 moles (which is 20 times Avagodro's number of particles), T=300 K, Vi=0.01 m^3,Vf=0.02 m^3
For a gas with an excluded volume: U=32NkT+const S=Nkln⁡(V−bN)+const

If b=9 × 10-29 m^3, compute µ(Vf)- µ(Vi)