i.e. (ef. Note 1) 
ziet De ej es nea any: 
2 a6 ca 3 
Hence also 
Eee Sabine ok ae aan eee 
or 
d 
fae) SS oe ier oe en : 
.=(%) Fen ie 
If uw,’ were = u,’ instead of = '/, uw,” (strong collisions, cf. Fig. 15), 
then Z would have become = A+ '/, RT, c, ='*/, R=3B. 
All this applies to monatomic substances. In the case of multi- 
atomic (n-atomie) substances it is necessary to take besides the energy 
of the attractive forces A also the atomic energy A’ within the 
molecule into consideration, so that H becomes = L, 4 A + A’, 
Now L,=3RT, while A’ = 3(n—1)RT may be put, when 3(n—1) 
represents the number of supplementary degrees of freedom. We 
then find H=A-+ 3nRT, i.e. cy = 38nR = 6n (Neumann’s law) '). 
At low temperatures we have: 
SONG OR pees ty shore 
log (4 p* + 2) 
according to (c,), when we denote the factor 
(+FDO 
af 
by 4; hence because u,? gy? = (—o)? —, and thus '/, Nmu,? g? = 
m 
— Nm u* = 
2 
= Nf (l— 6)? = /- As 
1) It should be remembered that for gases H = A + 1/,R (3 + «) T may be put, 
in which « also represents the number of supplementary degrees of freedom (see 
among others Botrzmann, Gastheorie IJ, p. 124—125 and 128). But here u 
is simply = for multi-atomic molecules, so that for mon-atomic molecules n 
is still = 0, for di-atomie molecules however ” = 2, for tri-atomic ones» = 3, etc. 
Hence when the term A, which approaches 0, is neglected, and also the quantity 
e introduced by Botrzmann, referring to the potential energy of the intramolecular 
movements, H becomes =!/,RT(3 4 n) for gases, leading to cv =!/,R(8-+ n), 
2 
hence (with cpy—cy = R) to “= ô 
Cv d+ n 
correction quantity e to 3 +). 
. (Bottzmann adds the above mentioned 
