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1) A rigid rotorwith moment of inertia Ihas energy levels EJ = J(J+ 1)¯h2/(2I) , where J= 0, 1,2, . . .andthere are 2J+ 1 states for each J(mJ = ? , ?J+ 1, . . . J ?1, J). Consider a system of N(distinguishable) such rotors.

(a) Find the partition function for the system and use it to find the internal energy of the system (written as a sum) as a functionof the temperature T.

(b) For high temperatures kT >>¯h2/Ithe sums found for the partition function and the internalenergy in part (a) can be approximated by integrals. In this limit find the internal energy and the heat capacity.

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