Start with the partition function and go from there. Becuase of the equivalence of ensembles in the thermodynamic limit, we can calculate the entropy using the ensemble that offers the most …

We will solve this problem using the canonical ensemble. Assuming the N systems in our collection are distinguishable, we can write the partition function of the entire system as a …

Grand canonical partition function. The constant of proportionality for the proba-bility distribution is given by the grand canonical partition function Z = Z(T, V, μ), e−β[H(q,p,N)−μN] , h3NN! where …

This problem (which appeared in the extra credit on Pset 6) is hard to solve using the microcanonical ensemble, but quite easy with the canonical ensemble. Try it.

Determine the equilibrium constant at 1565 from the partition function. The basic equation for the statistical thermodynamic calculation of the equilibrium constant is:

The problems below require you to use what you have learnt about the canonical and grand canonical paritition functions to derive a simple model for adsorbtion of atoms/molecules on a …

The partition function for an ideal gas of N atoms is approximately Z N = Z 1 N / N Show, for example by considering the power series expansion of e λ Z 1 where λ is equal to e μ / k B T, …

To begin solving the first step of this problem, identify the possible states of the system and their corresponding energies, as well as define the grand partition function using the expression for G.

3. Obtain the grand partition function of a classical system of particles, inside a container of volume V , given by the Hamiltonian 1 ~p2 i + u (~ri) : = H 2m in the representation of the …

To summarize the problem: a one-component open system can assume states characterized by composition N and quantum state N, j. The quantum state N, j has wave function N,j and …