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
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
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
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
. (1)
These Proc[eedings] XXII, p. 261, 1924.
[p. 18]
dn ρ( L, κT, V, m)------------------------------
- =
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