Question

A crucial step in obtaining the Fermi-Dirac and Bose-Einstein statistic is the equivalence shown below: nmax [la-»* = [TECH kno Convince yourself of this identity by showing it is valid in a case where each of 3 energy levels can host up to two particles, thus nk 0.1,2; k= 1, 2, 3. 1. Consider a gas on non-interacting magnetic molecules. Consider that when a magnetic field is applied, these molecules can align parallel or antiparallel to the field and the energy in each case is Et = -ImH and E = HmH. If M is the number of molecules and N is the number of those aligned parallel to the field a. Find an expression for the canonical partition function (N.M.T) assuming the molecules are distinguishable b. Calculate the chemical potential as a function of N. An and H. c. Using the grand-partition function calculate the fraction of molecules with magnetic moment parallel to the field as a function of u kun and H d. Find an expression for the canonical partition function O(N.MT) assuming the particles are indistinguishable Hint for c: you can use the binomial expansion: (x + y) = ER R -"y"

Answer 1

- HH' ↑ Single fpartlele pardifionfmudien Q(N, M,T) = 9) ĕ AP where A = since Q Hebnatz free Emergy AMHB :- kgT Mn(eMF. IInQ = - katlm{. T,V 1BM Hm HB © Grand -portition fn : Z =še M=0 BM Mинр M:0 t.. %3D Scanned Mith CamScanner z\z