Although expressions like = -(d lnq)/dbeta, where is the average value of 8 and

Question

Although expressions like = -(d lnq)/dbeta, where is the average value of 8 and q is the molecular partition function are useful for manipulations in statistical thermodynamics and for the derivation of thermodynamic functions in closed formulas, they are sometimes more trouble than they are worth in practical applications. When given together with a table of energy levels, it is often much better to calculate the following sums by explicit summations: q = Sj expt-ßsj]; q1 = betaepsilon exp[-beta epsilonj];q = (betaepsilonj)2 exp[-betaepsilonj] Derive expressions for internal energy, heat capacity at constant volume, and entropy in terms of q, q1, and q11. Calculate by this technique the electronic contribution to CV,m of Mg vapour at 5000K, using:

Explanation / Answer

In thermodynamics, the internal energy is one of the two cardinal state functions of the state variables of a thermodynamic system. It refers to energy contained within the system, while excluding the kinetic energy of motion of the system as a whole and the potential energy of the system as a whole due to external force fields. It keeps account of the gains and losses of energy of the system.

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