D O C . 3 8 5 Q U A N T U M T H E O R Y O F I D E A L G A S I I 3 7 9
of this wave field, insofar as it corresponds to the energy region ΔE examined by
us above.
These considerations cast light on the paradox pointed out at the end of my first
paper.[15]
In order for two wave trains to be able to interfere noticeably, they must
virtually coincide with respect to V and ν. For that, according to (35), (36), and
(37), it is necessary that ν as well as m virtually coincide for both gases. The wave
fields[16]
assigned to two gases of noticeably different molecular mass therefore
cannot interfere with each other noticeably. From this it can be concluded that, ac-
cording to the theory presented here, the entropy of a gas mixture is composed just
as additively as the one for the mixture’s components, in accordance with the clas-
sical theory, at least as long as the components’ molecular weights differ somewhat
from one another.
§ 9. Comment about the Viscosity of Gases at Low Temperatures
From the observations of the previous section, it seems as if a wave field were
associated with every process of motion, just like the optical wave field is associ-
ated with the motion of light quanta. This wave field—whose physical nature is still
unknown for now—must in principle be detectable by the corresponding motion
phenomena. Thus a beam of gas molecules going through an aperture should expe-
rience a diffraction analogous to that of a ray of light. In order for such a phenom-
enon to be observable, the wavelength λ should be somewhat comparable to the di-
mensions of the aperture. From (35), (36), and (37) it then follows for velocities
which are small compared to c
(38)
For gas molecules, which move at thermal velocities, this λ is always extraordinar-
ily small, mostly considerably smaller, even, than the molecule’s diameter σ. It in-
itially follows from this that it would be out of the question to observe this diffrac-
tion with manufacturable apertures or screens.
It appears however that, at low temperatures, λ evidently becomes of the order
of magnitude of σ for hydrogen and helium gases; and it does, in fact, seem as if
the influence that we would expect according to the theory manifests itself in the
friction coefficient.
Namely, if a swarm of molecules moving at velocity ν met another molecule,
which for the sake of convenience we shall imagine as immobile, then this is com-
parable to the case of a train of waves of given wavelength λ met a lamella of
diameter 2σ. A (Fraunhofer) diffraction effect occurs that is the same as the one
λ
V
ν
---
h
mv
------ -. = =
[p. 11]