D O C . 2 8 3 Q U A N T U M T H E O R Y O F I D E A L G A S 2 8 1
, (17)
where ν represents the number of moles, R the constant of the equation of state for
the ideal gases. This result about the absolute value of the entropy is in agreement
with well-known findings of quantum statistics.[10]
According to the theory given here, Nernst’s theorem for ideal gases[11] is satis-
fied. Our formulas however do not permit direct application to extremely low tem-
peratures, because we presumed in their derivation that the ’s change only rela-
tively infinitely little when s changes by 1. Yet one immediately perceives that the
entropy must vanish at absolute zero. For, then all the molecules are located in the
first cell; however, for this state there is just a single distribution of the molecules
in the sense of our counting. From this the correctness of the assumption directly
follows.
§5. The Divergence from the Gas Equation of the Classical Theory
Our findings regarding the equation of state are contained in the following
equations:[12]
(18) (comp. (6a))
(19) (comp. (7a) and (15))
(20) (comp. (9) and (13))
. (21) (comp. (8))
We now want to reformulate and discuss these results. From the considerations
contained in § 4 it emerges that the quantity , which we want to denote as λ, is
smaller than 1. It is a measure for the “degeneracy” of the gas. We can now write
(18) and (19) in the form of double summations, thus
(18a)
, (19a)
S νR lg e5 /2--------(
V
h3n
2πmκT3 /2) =
pν s
n
αν
-------
ν
¦e1
=
E
3
2
--pV -
c¦---------------
s2 /3
eαs
1 –
-
s
= =
αs A
cs2 /3
κT
----------- -+=
c
Es
s2 /3
-------- -
h2
2m©
-------§
4
3
--πV¹ -
·
2 3 /–
= =
[p. 266]
e–A
n
cs2 /3τ
κT
–---------------
sτ
¦λτe
=
E c /3λτe
/3τ –cs2
κT
------------------
sτ
¦s2
=