I) We consider atoms of rubidium in the gaseous state. The molar mass of rubidium is M-87 g/mol. 1) At T-900 K, the rubidium acts like and ideal gas. At this temperature the free energy F is given by h2 F = -kBT In Z where Z = with z = N! V and A = (; 1/2 N being the number of 2TmkBT particles of the gas and m the mass of one particle. a) Explain the presence of the N! in the equation. b) Derive the expression of F as a function of T and the number of particles per unit volume, n=N/V. c) Show that u = T In(nA) where 7 is a quantity that you will express as a function of T.

I) We consider atoms of rubidium in the gaseous state. The molar mass of rubidium is M-87 g/mol. 1) At T-900 K, the rubidium acts like and ideal gas. At this temperature the free energy F is given by h2 F = -kBT In Z where Z = with z = N! V and A = (; 1/2 N being the number of 2TmkBT particles of the gas and m the mass of one particle. a) Explain the presence of the N! in the equation. b) Derive the expression of F as a function of T and the number of particles per unit volume, n=N/V. c) Show that u = T In(nA) where 7 is a quantity that you will express as a function of T.