A system of physical chemistry - Index of

ATOMIC HEAT OF SOLIDS 29

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

p

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

2

= I H—

y

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

state.

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.

no

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