It is shown that the usual derivation of the heat capacity of an ideal free-electron gas is made invalid by the use of a divergent series. A plausible argument is offered to indicate that these series are asymptotic expansions which provide good approximations through their first few terms. The usual procedure is modified by the replacement of an infinite series by its first two terms plus a remainder whose bounds are estimated as being negligible to the accuracy required; a rigorous derivation of the well-known temperature dependence of the electronic heat capacity of an ideal Fermi gas results.
Weinstock, R. (1969, June 26). Heat capacity of an ideal free-electron gas: A rigorous derivation. Am. J. Phys., 37(12), 1273-1279. Retrieved September 30, 2014, from http://dx.doi.org/10.1119/1.1975299
%0 Journal Article %A Weinstock, Robert %D June 26, 1969 %T Heat capacity of an ideal free-electron gas: A rigorous derivation %J Am. J. Phys. %V 37 %N 12 %P 1273-1279 %8 June 26, 1969 %@ 0002-9505 %U http://dx.doi.org/10.1119/1.1975299
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