Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation Page: 10
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10 CONTRIBUTIONS TO DATA ON THEORETICAL METALLURGY
equation (19) are shown in column 2 of table 1, where they may be
compared with the values in column 3 based upon low-temperature
heat-capacity data. The agreement is seen to be highly satisfactory.
TABLE 1.-Entropies of rare gases at 298.160
Substance S298.16 S .6 Substance S298.1 S2.16
(theor.) (exp.)Substance (theor.) (exp.)
Argon --------------- 36. 99+0. 01 36. 95==0. 2 Neon..---------------..... 34. 950. 01 35. 01+10. 10
Helium .......-------------- 30. 130. 01 Radon .--------------. . 42. 10=t0.01
Krypton ------------- 39.20=0. 01 39. 17=L-0. 10 Xenon-------------- ............... 40. 54=0. 01 40. 7-0. 3
Other examples could be given from the list of monatomic metal
gases. The comparison, however, would require the use of vapor-
pressure data in computing the values based upon heat capacities.
There is no objection to such procedure, but the validity of equations
(18) and (19) is now so well-established that Kelley (270) has employed
the calculation in the reverse sense, rectifying the vapor-pressure
data for metal gases by means of the theoretical entropies. Inci-
dentally, the experimental justification of Tetrode's value of So does
not depend on data for monatomic gases alone, and a variety of checks
may be given for gases which are not monatomic, as the translational
portions of their entropies also conform to equations (18) and (19).
For some examples see table 4.
The other contributions to the entropy will now be considered.
Let E1 be the sum of the rotational, vibrational, and electronic
energies of a molecule and let A0 and A, be the numbers of molecules
in two energy states so and el. Then, according to the Maxwell-
Boltzman distribution law,
= e kT (20)
e being the natural logarithmic base, k the gas constant per molecule,
and T the temperature in degrees Kelvin. Suppose Ao refei s to the
lowest energy state of the molecule and A1, A2, A3, etc., to
the successively higher energy states, and for convenience suppose
all the energies, e, now are referred to that of the lowest state as a
zero base, which obviously leaves the magnitude of the exponent in
equation (20) unchanged. Then, considering 1 mole of gas
(Avogadro's number of molecules, N), it follows that
N= Ao+ Aoe-'1/kT+ Aoe-E/kT+ . . . (21)
For a group of states, pi in number, whose energies are so nearly alike
that they may be considered together, the corresponding terms in
equation (21) may be replaced by piAoe-ei/kT or, Igeneral,
N= poAo+piAoe-l1/kT+ p2Aoe-E2/kT+ . . = Aoe. pe-'E/kT. (22)
The quantity pi is termed the quantum weight or the a priori probabil-
ity of the state of energy ei. Let the sum of the rotational, vibrational,
and electronic energies of 1 mole of gas at any temperature be denoted
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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/m1/14/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.