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1. A system consist of two particles,each of which has two possible quantum stats with energies Eo and 2Eo .Write the complete expression for the partition function if: (a) The particle are distinguishable. (b) The particle obey Maxwell-Boltzmann statistics. (c) The particle obey Fermi-Dirac statistics. (d) The particle obey Bose-Einstein statistics. 2.When a closed cubic box of volume V is heated to temperature T, the walls will emit and absorb electromagnetic radiation . When the radiation is in equilibrium with the walls, an equal amount of radiation is emitted and absorbed by the walls, and the radiation forms standing waves in the box. A standing wave of frequency and wave vector k is composed of photons of energy and momentum p= k .Photons are massless bosons.Since photons are continuously emitted and absorbed by the walls , the number of photons in the box continuously change. Since photons are massless , the chemical potential is zero. (a)Find the average number of photons with momentum p. (b)find the heat capacity of the photon gas. 3.A one-dinmensional Debye solid with N lattice sites coupled harmonically to their nearest neighbors has a Hamiltonian of the form 2 1 2 N pl 1 2N H k (ql ql 1 ) 2 2 i 0 2m 2 i 0 4. Show that the entropy for Bose-Einstein and Fermi-Dirac gas(neglecting spin) can be written in the form S k b ( n pl ln n pl 1 n pl i 0 ln( 1 n pl )) where the top sign hold for Bose-Einstein particles and the bottom sign holds for Fermi-Dirac particles.