Bose gas — UPSC IFoS 2015 Physics PYQ

Derive an expression for the total number of particles N in an ideal Bose gas at any temperature T. Hence, obtain the relation N_0 = N \left[ 1 - \left( \frac{T}{T_0} \right)^{\frac{3}{2}} \right] for the number of particles N_0 in the ground state at T < T_0, the Bose-Einstein condensation temperature, and draw N_0 versus T curve.