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

- =