4 1 8 D O C . 4 2 7 Q U A N T U M T H E O R Y O F I D E A L G A S
427. “On the Quantum Theory of the Ideal Gas”[1]
[Einstein 1925i]
Presented 29 January 1925
Published 5 March 1925
In: Preußische Akademie der Wissenschaften (Berlin). Physikalisch-mathematische
Klasse. Sitzungsberichte (1925): 18–25.
Stimulated by a derivation of Planck’s radiation formula originating from Bose,
which consistently supports itself on the light-quantum hypothesis, I recently pos-
tulated a quantum theory for ideal
gas.1)
[2]
This theory seems legitimate when one
starts out from the conviction that a light quantum (disregarding its polarization
property) differs from a monatomic molecule essentially only in that the quantum’s
mass at rest is vanishingly small. But because the presupposition of this analogy is
certainly not accepted by all
researchers,[3]
and furthermore, because the statistical
method used by Mr. Bose and me is certainly not beyond doubt but rather just
seems justified a posteriori by its success in the case of
radiation,[4]
I looked for
other considerations on the quantum theory of ideal gas that are as free of arbitrary
hypotheses as possible. These considerations shall be communicated in the follow-
ing. They provide an effective support for the theory postulated earlier, even though
the results attained do not yield a full substitute for that theory. Here it is a matter
of establishing considerations in the field of gas theory by a method and with re-
sults largely analogous to those in the field of radiation theory leading to Wien’s
displacement law.
§1. Posing the Problem
For an ideal gas, let volume V of one mole, temperature T, and mass m of the
molecule be given. What is sought is the statistical law of velocity distributions,
hence the analogue to Maxwell’s distribution law. Therefore, an equation of the
type
. (1)
1)
These Proc[eedings] XXII, p. 261, 1924.
[p. 18]
dn ρ( L, κT, V, m)------------------------------
Vdp1dp2dp3
h3
- =