Grand canonical ensemble

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Homework Statement


To calculate internal energy for a system of non interacting S.H.O's in 1 dimension at constant T & u(chem potential) using grand partition function


The Attempt at a Solution



L(Grnd prtition fn)= Summation(z^N)*[Z(TVN)] where z = fugacity , Z = partition fn of canonical ensemble . for Harmonic oscc E = (n+1/2)hw , so i substituted this in the grnd prtition fn , let it vary from n=0 to K , and N also varies from 1 to N , then i apply log form which i get a series of odd numbers for energy and (N1+N2+------+N) for the fugacity term and then differentiate with respct to beta which is 1/KT , and i dnt hve any term involving B , so i can't evaluate Cv , where is the problem .

I am taking U(internal energy) = -(d/dbeta)ln(L)
 

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