A system of physical chemistry - Index of


A system of physical chemistry - Index of


The Ratio y for Gases, and the number " "

of effective Degrees of Freedom.

It may easily be shown [cf. Meyer's Kinetic Theory of Gases, p. 140


seq.) that the ratio ^ or y can be expressed approximately in the form—


= I H—


where n is the number of degrees of freedom of the gas molecule. In

the case of monatomic gases the value of y is i'666, and this is the

quantity which is obtained on putting « = 3 in the above expression.

That is, a monatomic gas molecule possesses three degrees of freedom,

in respect of translation only. This agrees with the conclusion we

came to above (though, of course, it must be remembered that the actual

number of degrees is possibly greater than this, i.e. degrees in virtue of

rotation, but for some unknown reason only some are effective in regard

to heat capacity, for after all an atom is not a point in the mathematical

sense). In the case of a diatomic molecule the value of y, found by

experiment, is in many cases i -4, and this will correspond to putting

« = 5 in the above equation. In triatomic gas molecules y = 1*3 in

general, and this makes n = 7. These numbers are certainly less than

the actual number of degrees of freedom possessed by di- and triatomic

gases, as is indeed shown by the fact that there are some diatomic

gases with as small a value as 1*29 for y (iodine vapour) and some

triatomic gases, e.g. CS2, for which y = i'2. Further, the values of y

are not constant but vary with the temperature. The whole problem of

the number of degrees of freedom is, therefore, in a very unfinished


The doubt which exists, in the case of polyatomic molecules, regarding

the true number of degrees of freedom, takes away from the

force of the criticism levelled against the principle of the equipartition,

on the ground of the lack of agreement between observed and calculated

molecular heats. The soundest criticism of the principle rests on the

experimental observation that the molecular heat varies with the temperature,

whilst the principle leads us to expect it to be constant, matter how many degrees of freedom be present.


Atomic Heat of Solids.

Since the equipartition principle is considered to hold equally well

for all '^tates of matter, the term ^RT must represent the kinetic energy

per degree of freedom of i gram-mole of any system at the temperature

T. In solid elements— the metals— it is generally agreed that the

gram-molecule and gram-atom are identical,

so that in such a case

•|RT is the kinetic energy per degree of freedom for each gram-atom,

R being put equal to I'gSs cals. The orientation of the atom of a

metal is such, that it is free to vibrate in any direction which can be

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