3 8 0 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

produced by an aperture of the same size. Large diffraction angles appear when λ

is of order of magnitude σ or larger. Thus, in addition to a collision deflection due

to mechanics, there would then also be mechanically incomprehensible deflections

of the molecules with the same frequency of occurrence as the other deflection,

which reduce the free path length. Close to that temperature therefore there will oc-

cur a quite sudden accelerated drop in the viscosity as the temperature drops. An

estimate for that temperature, according to the relation , yields 56° for H,

40° for He. These are very rough estimates, of course; they can be replaced by more

exact calculations. This is a new interpretation of the experimental results for

hydrogen obtained by P. Günther at Nernst’s instigation on the dependence of the

viscosity coefficient on temperature, for which Nernst has already conceived an ex-

planation in quantum

theory.*)

[17]

§10. Equation of State of Saturated Ideal Gas. Remarks on the Theory of the

Equation of State for Gases and on the Electron Theory of Metals

In §6 it was shown that the degeneracy parameter λ for an ideal gas at equilibri-

um with a “condensed substance” is equal to 1. The concentration, energy, and

pressure of that portion of the molecules endowed with motion are then, according

to (18b), (22), and (15), determined by T alone. The equations

(39)

(40) [18]

(41)

hence apply. Here:

η means the concentration in moles,

N the number of molecules per mole,

M the mole mass (molecular weight).

One finds with the aid of (39) that real gases do not attain such density values,

that the corresponding ideal gas would be saturated. However, the critical density

of helium is only about five times smaller than the saturation density η of an ideal

gas at the same temperature and the same molecular weight. For hydrogen the cor-

responding ratio is about 26. Since real gases exist at densities that, in order of mag-

*)

Comp. W. Nernst, Proceed[ings] 1919, VIII, p. 118. – P. Günther, Proceed[ings] 1920,

XXXVI, p.

720.[19]

λ σ =

η

n

NV

------- -

2.615

Nh3

------------ -( 2πmκT)3 /2 1.12 10–15( MRT)3 /2 ⋅ = = =

E

n

---

1.348

2.615

------------- κT ⋅ =

p

1.348

2.615

-------------RTη. =

[p. 12]