2.3 (a)A classical harmonic oscillatorp?, Kq?H+2m2is in thermal contact with a heat bath at temperature T. Calculate thepartition function for the oscillator in the canonical ensemble andshow explicitly that• (E) = kgT, ((E – (E))²) = k¿T² 2.6 (a), (b)(a) Show that, if the kinetic energy of a particle with mass m, momentum pis E = p²/2m, the single particle partition function can be written Z1 =V/23, where 1 = /h²/2nmkgT is the thermal wavelength. The canonicalpartition function for the ideal gas will then beVNZNN!23N(b) Use Stirling's approximation to show that in the thermodynamic limitthe Helmholtz free energy of an idealgasisVA = -NkgT |InN23

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2.3 (a) A classical harmonic oscillator p? Kq? + 2 H 2m is in thermal contact with a heat bath at temperature T. Calculate the partition function for the oscillator in the canonical ensemble and show explicitly that (E) = kgT, ((E – (E))²) = kỷT² %3D |