A. (a) Consider a canonical ensemble having N particle, V volume and at T temperature. Write down the expression of partition function (QON,V,T)) of this canonical ensemble in terms of the microstate energy E. (b) Write down the expression for Helmhotz free energy (A) and pressure (P) in terms of Q(N,V.T). (c) Now, assume that for a system of dense gas you can write down the Q(N,V,T) as, 1 2amk,T QUN,V.T) N! (V-Nb)" e Treat a and b as constants. Get the expression for pressure (P) in terms of V, a, b, N, kg and T. Rearrange that expression to get a form where in the RHS of the equation will have NkgT. Identify the equation.
A. (a) Consider a canonical ensemble having N particle, V volume and at T temperature. Write down the expression of partition function (QON,V,T)) of this canonical ensemble in terms of the microstate energy E. (b) Write down the expression for Helmhotz free energy (A) and pressure (P) in terms of Q(N,V.T). (c) Now, assume that for a system of dense gas you can write down the Q(N,V,T) as, 1 2amk,T QUN,V.T) N! (V-Nb)" e Treat a and b as constants. Get the expression for pressure (P) in terms of V, a, b, N, kg and T. Rearrange that expression to get a form where in the RHS of the equation will have NkgT. Identify the equation.
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.36P
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