An ideal gas enclosed in a volume V is composed of N identical particles in equilibrium at temperature T.
(a) Write down the N-particle classical partition function Z in terms of the single-particle partition function ζ, and show that Z it can be written as
ln(Z)=N(ln (V/N) + 3/2ln(T)+σ (1) where σ does not depend on either N, T or V .
(b) From Equation 1 derive the mean energy E, the equation of state of the ideal gas and CV .
An ideal gas enclosed in a volume V is composed of N identical particles in equilibrium...
1. N identical particles of mass m is confined to move only about a surface of area A, and thus can be considered as a “two-dimensional gas.” In the classical limit what is the single particle partition function of one of the particles in this ideal two-dimensional gas? What is the partition function of the N particle gas? What is the mean thermal energy of this gas, and what is the entropy of this gas?
Answer a total of any THREE out of the four questions. Put the solution to each problem in a separate blue book and put the number of the problem and your name on the front of each book. If you submit solutions to more than three problems, only the first three problems as listed on the exam will be graded. Some possibly useful information: Sterling's asymptotic series: N In N-N + 1 ln(2nN] In N! N → oo, as 2...
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