Prove that James Joul's Paddle experiment does not work backward because the entropy of the universe would be less than 0. (include a diagram of the PV state and the experiment)

The partition function of a hypothetical system is given by In Z = «TªV where a is a constant. Evaluate the mean energy E, the pressure P, and the entropy S.

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Homework 4 For a system of N identical non- interacting particles in a box each having two energy levels 0 and E. Find their fundamental entropy (sigma) and the total energy of the system (U).

Gibbs definition of entropy is S=-kΣP,In(P)- what is the distribution at O K that allows this distribution to be consistent with the Third B Law of Thermodynamics? One state as a probability of 1, and all others are zero. Two states have probabilities of 0.5, and all others are zero. All states are populated with exactly equal probabilities. The states are populated with completely random probabilities.

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system of three particles can possess four energies 0, E, 2E, and 4E with degeneracy 1,3,5,6respectivelya) Find the expression of the partition function of the systemb) Find the expressions of the Free energy and the entropy if E =kBT

(a) Answer the following questions about entropy-volume relationships: (i) For a general system, use the Helmholtz free energy as an intermediary to express the derivative () in terms of a T. derivative of the pressure P with respect to temperature T. (ii) Assuming an ideal gas, evaluate your derivative of P, and finally integrate () to determine the volume dependence of the av entropy S of the classical ideal gas. (iii) Comment on your result, and in particular on how an alternative understanding of the S(V) dependence can be achieved on the basis of spatial multiplicity considerations.

the ideal gas? Do you expect these assumptions to work better for a dilute or dense gas? Explain. What are the two major assumptions that are made in deriving the partition function for 90

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