Answer Happy

Please only answer question iv.)
b) An isolated system consists of N distinguishable atoms, each of which has three states available to it: one with energy ( and two with energy ε. i) Show that the number of microstates of the system with n particles in total in the upper two states is N! 12= 2n n!(N − n)??" [4 marks] ii) Find an expression for the entropy of the system in terms of the energy, and hence find the temperature of the system. [6 marks] iii) From your expression for the temperature as a function of energy, find and sketch an expression for the average energy as a function of temperature, commenting on the high- and low-temperature limits. Discuss how this compares to the expression (E) = Nɛ(1 + EFB)-1 which is obtained if there is only one excited state. (5 marks] = iv) Two sets of these atoms, Nį and N2 respectively, are brought into thermal contact with one another, while still being isolated from the surroundings. Their combined energy is E = ne. After reaching equilibrium, the average number of excited atoms in the first system is ni. Find an expression for ni. [5 marks]