Transcription of Solutions to problems for Part 2
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Solutions to problems for Part 2
1 Solutions to problems for Part 2 Sample Quiz ProblemsQuiz Problem 1. Write down the equation for the thermal de Broglie wavelength. Explain its importance in thestudy of classical and quantum =h 2 mkBT(1)This is of the formh/pT, wherepT= (2 mkBT)1/2is an average thermal momentum. Define the average interparticlespacing of a gasLc= (V/N)1/3. If > Lcquantum effects become important in the thermodynamics. Quiz Problem 2. Why are the factors 1/N! and 1/h3 Nintroduced into the derivation of the partition function ofthe ideal classical gas?SolutionThe factor 1/N! is needed to account for the fact that when an intergration is carried out over all phase space forNparticles, all permutations of the particle identities is included. For indentical particles this must be removed. Thefactor 1/h3 Ntakes account of the Heisenberg uncertainty principle which states that the smallest phase space volumethat makes sense is ( h/2)3.
fugacity z= e as temperature T!0, for both the non-relativistic and ultra-relativistic Bose gas. Solution. For the Bose gas as temperature goes to zero, the internal energy contribution dominates. As temperature goes to zero all of the particles that are added go into the ground state, so the chemical potential goes to the ground state energy.
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