3. The classical partition function of a gas of noninteracting indistinguishable particles is written as d'r..d'ryd' pd PN exp{- N! Z= 2m where N is the number of particles of mass m, r, and p, are the position and the momentum of the ith particle, B = 1/(kpT), and Tis the temperature of the gas. The volume of the gas is V. (a) Find the analytic expression of the partition function of the gas. (b) Obtain the total mean energy E of the gas from the partition function. (c) Obtain the entropy S of the gas from the partition function and the total mean energy. Lexp(-x²xdx = Vz Hint:

3. The classical partition function of a gas of noninteracting indistinguishable particles is written as d'r..d'ryd' pd PN exp{- N! Z= 2m where N is the number of particles of mass m, r, and p, are the position and the momentum of the ith particle, B = 1/(kpT), and Tis the temperature of the gas. The volume of the gas is V. (a) Find the analytic expression of the partition function of the gas. (b) Obtain the total mean energy E of the gas from the partition function. (c) Obtain the entropy S of the gas from the partition function and the total mean energy. Lexp(-x²xdx = Vz Hint:

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