I plan to derive elsewhere the expressions for the intensity and entropy of
radiation progressing in a diathermic medium, as well as the theorem for the increase
of total entropy in nonstationary radiation processes.
4.5.3 Numerical Values
§11. The values of both universal constants h [Planck constant] and k [Boltzmann
constant] may be calculated rather precisely with the aid of available
measurements. F. Kurlbaum,
24 designating the total energy radiating into air from
1 cm
2 of a black body at temperature t
∘
C in 1 s by S t , found that:
S 100 À S 0 ¼ 0:0731 Á
watt
cm 2 ¼ 7:31 Á 10
5
Á
erg
cm 2 Á sec
ð4:218Þ
From this one can obtain the energy density of the total radiation energy in air at
the absolute temperature 1:
4 Á 7:31 Á 10
5
3 Á 10
10
Á 373
4
À 273
4
À
Á¼ 7:061 Á 10
À15
Á
erg
cm 3 Á deg
4
ð4:219Þ
On the other hand, according to Eq. (4.216) the energy density of the total radiant
energy for θ ¼ 1 is:
u
Ã
¼
Z 1
0
u dν ¼
8πh
c 3
Z 1
0
ν
3 dν
e hν=k À 1
ð4:220aÞ
u
Ã
¼
8πh
c 3
Z 1
0
ν
3 e
Àhν=k
þ e
À2hν=k
þ e
À3hν=k
þ . . .
dν
ð4:220bÞ
And by term wise integration:
u
Ã
¼
8πh
c 3 Á 6
k
h
4
1 þ
1
24
þ
1
34
þ
1
44
þ ⋯
¼
48πk
4
c 3 h
3
Á 1:0823
ð4:220cÞ
If we set this equal to 7.061 Á 10
À15 , then, since c ¼ 3 Á 10
10 cm/s, we obtain:
k
4
h
3
¼ 1:1682 Á 10
15
ð4:221Þ
24 F. Kurlbaum, Wied. Ann. 65 (1898), p. 759.
4.5 On the Law of Distribution of Energy in the Normal Spectrum, By Max Planck,. . .
189