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 8 1
nitude, approach the saturation density, and since according to (41) the degeneracy
influences the pressure substantially, if the present theory is correct, a not inconsid-
erable quantum influence will make itself felt in the equation of state; in particular,
one will have to examine whether the deviations from the Van der Waals law of cor-
responding states can be explained this
way.*)
[20]
In addition, it must also be expected that the diffraction phenomenon mentioned
in the foregoing section, which at low temperatures does, of course, generate an ap-
parent enlargement of the true molecular volume, influences the equation of state.
A case exists in which nature has possibly essentially realized a saturated ideal
gas, namely, in conduction electrons in the interior of metals. The electron theory
of metals is known to have explained with remarkable quantitative approximation
the relation between electrical and thermal conductivity (Drude-Lorentz formula)
under the assumption that in the interior of metals there are free electrons that con-
duct electricity as well as heat. Despite this great success, that theory is currently
not deemed appropriate, among other things because it cannot account for free
electrons not making any noticeable contribution to the metal’s specific heat. This
difficulty, however, disappears when one applies the present theory of gases. For,
from (39) it follows that the saturation concentration of (moving) electrons at a nor-
mal temperature is about equal to , so that only a vanishingly small pro-
portion of the electrons could contribute toward the thermal energy. The mean ther-
mal energy per electron participating in the thermal motion is roughly half as large
as according to the classical molecular theory. If only very small forces are there to
keep the immobile electrons in their resting positions, it is also understandable that
they would not be participating in the electric conduction. It is even possible that
an absence of these weak binding forces at very low temperatures could occasion
superconductivity. The thermal forces would never be comprehensible on the
grounds of this
theory[21]
as long as the electron gas is treated as an ideal gas. Such
an electron theory of metals should not be underpinned by a Maxwell velocity dis-
tribution, of course, but rather by the distribution of a saturated ideal gas according
to the present theory; from (8), (9), and (11) the result for this special case is:
. (42)
Thinking this theoretical possibility through, one encounters the difficulty that
in order to explain the measured conductivity of heat and electricity by metals one
*)
This is not the case, as I later found out by comparison against experience. The sought
influence is obscured by other kinds of molecular
interactions.[22]
5.5 10–5 ⋅
dW const.
E1 /2dE
eκT
E
-------
1 –
----------------- =
[p. 13]