2.6 (a), (b)• (a) Show that, if the kinetic energy of a particle with mass m, momentum pp²/2m, the single particle partition function can be written Z1 =V/23, where 1 =partition function for the ideal gas will then beis E =Vh2/2nmkgT is the thermal wavelength. The canonicalVNZNN! 23N• (b) Use Stirling's approximation to show that in the thermodynamic limitthe Helmholtz free energy of an ideal gas isA = -NkgT In (V+1N23

Given, the kinetic energy E=p22m and λ=h22πmkBT

(a) Show that, if the kinetic energy of a particle with mass m, momentum p is E = p2/2m, the single particle partition function can be written Z, = V/23, where 1 = /h? /2nmkgT is the thermal wavelength. The canonical partition function for the ideal gas will then be %3D %3D VN ZN N!23N • (b) Use Stirling's approximation to show that in the thermodynamic limit the Helmholtz free energy of an ideal gas is V A = -NkgT In N23

(a) Show that, if the kinetic energy of a particle with mass m, momentum p is E = p2/2m, the single particle partition function can be written Z, = V/23, where 1 = /h? /2nmkgT is the thermal wavelength. The canonical partition function for the ideal gas will then be %3D %3D VN ZN N!23N • (b) Use Stirling's approximation to show that in the thermodynamic limit the Helmholtz free energy of an ideal gas is V A = -NkgT In N23