394 THE QUANTUM THEORY
diatomic molecules (including hydrogen) have a cv close to 5R/2. It was not yet
recognized by Maxwell that this is the value prescribed by the equipartition theo-
rem for a rigid dumbbell molecule; that observation was first made by Boltzmann
[B5]. The equipartition theorem was therefore very helpful, yet, on the whole, the
specific heat of gases remained a murky subject.
Things were getting worse. Already before 1900, instances were being found in
which cv depended (weakly) on temperature [W4], in flagrant contradiction with
classical concepts. No wonder these results troubled Boltzmann. His idea about
the anomalies for the specific heats of solids could not work for gases. Molecules
in dilute gases hardly stick together! In 1895 he suggested a way out: the equi-
partition theorem is correct for gases but does not apply to the combined gas-
aether system because there is no thermal equilibrium: 'The entire ether has not
had time to come into thermal equilibrium with the gas molecules and has in no
way attained the state which it would have if it were enclosed for an infinitely
long time in the same vessel with the molecules of the gas' [B6].
Kelvin took a different position; he felt that the classical equipartition theorem
was wrong. He stuck to this belief despite the fact that his attempts to find flaws
in the theoretical derivation of the theorem had of course remained unsuccessful.
'It is ... not quite possible to rest contented with the mathematical verdict not
proved and the experimental verdict not true in respect to the Boltzmann-Max-
well doctrine,' he said in a lecture given in 1900 before the Royal Institution [K2].
He summarized his position by saying that 'the simplest way to get rid of the
difficulties is to abandon the doctrine' [K3].
Lastly, there was the position of Rayleigh: the proof of the equipartition theo-
rem is correct and there is thermal equilibrium between the gas molecules and the
aether. Therefore there is a crisis. 'What would appear to be wanted is some
escape from the destructive simplicity of the general conclusion [derived from
equipartition]' [R4].
Such was the state of affairs when Einstein took on the specific heat problem.
20b. Einstein
Until 1906, Planck's quantum had played a role only in the rather isolated prob-
lem of blackbody radiation. Einstein's work on specific heats [El] is above all
important because it made clear for the first time that quantum concepts have a
far more general applicability. His 1906 paper is also unusual because here we
meet an Einstein who is quite prepared to use a model he knows to be approxi-
mate in order to bring home a point of principle. Otherwise this paper is much
like his other innovative articles: succinctly directed to the heart of the matter.
Earlier in 1906 Einstein had come to accept Planck's relation (Eq. 19.11)
between p and the equilibrium energy U as a new physical assumption (see Sec-
tion 19d). We saw in Section 19a that Planck had obtained the expression