Consider a classical ideal gas of N indistinguishable, non-interact...

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Consider a classical ideal gas of N indistinguishable, non-interacting, particles confined to a region of three dimensional space by a harmonic potential V(r). This might be a model for a gas of atoms in a magnetic trap. The single particle Hamiltonian is then, a) [10 pts] Compute the average total energy E of the gas as a function of temperature T. Compute the total specific heat C. b) [10 pts] Compute the density of particles n(I) at position r. Note, n(r) should be nor- malized SO that j dr = N. c) [5 pts] What is the root mean square distance (r2) of particles from the origin? d) [5 pts] What is the pressure of the gas p(r) at a position r? e) [10 pts] What is the chemical potential of the gas H(I) at position r?

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