Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation Page: 11
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CALCULATING ENTROPIES FROM EXPERIMENTAL DATA 11
by E++,4e and let Eo be the corresponding energy at 00 K., the gas
being in the ideal state. As the energy of the molecules in a given
state is their number times the energy per molecule, it follows that
Ef+,+e- E$= OpoAo + p AAo e-j1/kT + pe2Aoe-2/kT+ ... = A0, pi i e-e/T
Eliminating A0 between equations (22) and (23),
2 D Pie je-eilkT
Er+,+e-- EOO= N (24)
Differentiating equation (24) with respect to T,
dT kT2 pe-e/ pe-ilk (25)
Equation (25) gives the sum of the rotational, vibrational, and
electronic heat capacities of the gas. The total heat capacity at
constant pressure is obtained by adding this sum to 5/2 R=4.969,
the heat capacity at constant pressure of an ideal monatomic gas.
The entropy of the gas, excluding translational entropy, is defined
d dE,+,+, d In T, (26)
0+,+- s= fT dEr+ +6
Sr+,+S-O d'd in T. (27)
Writing Q for 1 pie-'elkt, equation (24) becomes
E?+,+,- E = Nk T2 d i= R T2 d in Q(28)
B=Nkc being the gas constant per mole. Therefore,
r+,+,-So= d R T d n d in T, (29)
= -R T d/ T d In T, (30)
o [ Td dT)n Q dT o (31)
=R[lnQ+Td 7 Q]T, (31)
=R [InQ-ln Qo+T dn o T ,
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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/m1/15/: accessed April 23, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.