7 Diatomic gases
This chapter is a slight diversion, and could well be omitted at a first reading. However,
the studyofdiatomic Maxwell–Boltzmanngases proves tobe a ratherinterestingone.
It will reinforce the ideas of energy scales, introduced in Chapter 2, and illustrate
further the concept ofdegrees offreedom. Furthermore the rotation ofmolecular
hydrogen(H 2 )gasholdsafew quantum surprises. Throughout thechapter we shall
assume, as is realistic, that MB statistics applies. Thequantum surprises are not
concernedwith‘degeneracy’,i.e. whether FD or BE corrections needbemadetothe
statistics. Rather theyare todowiththeindistinguishabilityofthe two H atoms which
make up the H 2 molecule.7.1 Energycontributionsindiatomicgases
As outlinedinthe previous chapter,ifthe partitionfunction ofour MBgasis evaluated
then all its thermal properties can be calculated. So far we have treated explicitlyonly
amonatomic gas such as helium. What now about a polyatomic gas?
The problemisquite tractable, withonebasic assumption. Thisisthat the various
forms of possessingenergyare independent. To explain what this means, consider
the contributions to the energy of a polyatomic gas molecule. The molecule can
have energy due to translationalmotion,due to rotation,due tointernalvibrations
and (exceptionally) due to electronic excitation. If these energycontributions are
independent, then it means, for example, that the state of vibration does not influence
the possible energies oftranslation. In other wordsthe one-particle states canbe
described simplyas havingenergies
ε=εtrans+εrot+εvib+εelec (7.1)so that each mode of possessing energy can be considered separately from the
others.
Thisis an approximation only,butitisagoodone. Translation,i.e. motion ofthe
centre of mass, is accurately independent of the internal degrees of freedom of the
molecule,i.e. motion aroundthe centre ofmass andexcitedelectronic states. One
might expect a smallcouplingbetween vibration androtationalstates;for example,
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