t S.1. A system of n identical spinless bosons of mass m is in a box of volume V = [3 at temperature T> 0. a) Write a general expression for the number of particles, n(E), having an energy between and + d in terms of their mass, the energy, the temperature, the chemical potential. the volume, and any other relevant quantities. b) Show that in the limit that the average distance, d. between the particles is very large compared to their de Broglie wavelength(i.e., d >> 2) the distribution becomes equal to that calculated using the classical(Boltzmann) distribution function. c) Calculate the 1st order difference in average energy between a system of N non- identical spinless particles and a system of N identical spinless boson when d >> . For both systems the cubical box has volume V = 13 and the particles has the mass m. S.2. a) Show that the number of photons in confilibrium