# Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation Page: 16

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16 CONTRIBUTIONS TO DATA ON THEORETICAL METALLURGY

At 298.160 K. and 1 atmosphere pressure, and with I in c. g. s. units,

this last equation reduces to

2098.16=3/2 R In M+R In I+S+Se+215.019. (41)

Equations (40) and (41) are valid for diatomic gases composed of un-

like atoms and also for gases composed of unsymmetrical, linear,

polyatomic molecules. For diatomic gases composed of like atoms

and gases composed of symmetrical, linear, polyatomic molecules

equations (40) and (41) must be reduced by R In 2, as shown by

Tetrode (481). The more general expressions are

S= 3/2 R In M+5/2 R In T+R In V+R In I- R In o-+S+S'+166.625, (42)

and

S29816= 3/2 R In M+R In I - R In a +S'+S'+215.019, (43)

in which a, called the symmetry number, has the values 2 or 1, depend-

ing on whether the diatomic molecules or linear, polyatomic molecules

are symmetric or unsymmetric.

The expression analogous to equation (39), but for gases composed of

rigid, nonlinear, polyatomic molecules, is

Sr= 3/2 R In (111213)1/3 T+So, (44)

in which I, 12, and 13 are the principal moments of inertia, T is the

absolute temperature, and So is a constant having the value

83/2 r7/2k3/2e3/2

R In h3 =267.686. Substituting equations (18) and (44) in

equation (38), and introducing the term -R In a as before, leads to

S= 3/2 R In M+3 R In T+R In V+1/2 R In 111213- R In a + S+S+ 256.613.

(45)

Also

S298.16= 3/2 R In M+ 1/2 R In 11213-R In a+S,+S,+310.668 (46)

for 1 atmosphere pressure. The symmetry number, a, is to be con-

sidered as the number of permutations of the atoms that can be ob-

tained solely by rotations of the molecule in such ways as to leave its

appearance unchanged. If all the atoms in a molecule are different

a= 1. For diatomic molecules composed of like atoms, or symmetrical,

linear, polyatomic molecules such as O= C = O and N- C- C N, a=2.

Pyramidal molecules such as NH3 have a=3, but if the atoms are all

in the same plane, as for BC13, then a= 6. Tetrahedral molecules like

CH4 have a= 12 but CH3C1 has a=3. Molecules like SF6, in which

the S atom is at the center and the F atoms at the midfaces of a cube,

have a - 24.

In computing S' it is assumed that the vibrations are purely har-

monic, in which case equation (15) may be taken as the specific heat

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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/m1/20/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.