Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation Page: 17
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CALCULATING ENTROPIES FROM EXPERIMENTAL DATA 17
corresponding to a single vibrational degree of freedom. The entropy
is computed as follows:
S0 Teh/kT (h)2
S= R foT (eh-pkT)2 dT (47)
Replacing hv/k T by x leads to
S/ (e - 12e dx. (48)
Equation (48) is integrated by parts with the result that
S:= R x-i-1n (l-e-) ]vkT(49)
So[hv/kt 1-n (l-e-hIkT). (50)
Equation (50) gives the entropy associated with a single vibrational
degree of freedom. Linear molecules composed of n atoms have
3n-5 vibrational degrees of freedom and nonlinear molecules com-
posed of n atoms have 3 n - 6 vibrational degrees of freedom. All
of these are not necessarily active at 298.160K., and the corresponding
vibration frequencies are not necessarily distinct; in fact, the converse
usually is true, and more than one degree of freedom may be assigned
to a fundamental vibration frequency. Throughout this bulletin vi-
bration frequencies are given in wave numbers or reciprocal centi-
meters and are designated by the symbol w. There may be written,
3n-5 Fhc (
for linear molecules and
S 3n6 LkT -In 1-e kT (52)
e kT- 1
for nonlinear molecules. Values of the individual summation items
may be found from available tables (208, 309, 374, 375) which give
S as a function of T' so that but little computation is neces-
As mentioned before, quantity S should be evaluated by the method
described for treating spectroscopic data. Fortunately, in most
instances only the lowest electronic state is occupied at 298.160, so
that this term reduces to R In po, in which po is the quantum weight.
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Kelley, K. K. Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation, report, 1950; Washington D.C.. (https://digital.library.unt.edu/ark:/67531/metadc12637/m1/21/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.