A system of physical chemistry - Index of

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A system of physical chemistry - Index of

44

A SYSTEM OF PHYSICAL CHEMISTRY

... rr

we see that E, i.e. the total energy density, is

.

^,

that is—

^ 4-2 X 'ix\ X 10^ . ,, ergs

E,oabs = — ,„/ 4 K = -1'^

7 "061 X 10 —^.

1 *'^-

3 X ioi"(373* - 2734) c.c.

Now E = Ea^A,, or u^dv and Ea or u^ is given by Planck's

expression. Using Planck's expression in the form in which u^ occurs,

we — get

Ejo abs.

Uvdv = — iT-

^=0 ^* e^"!''

the term T being omitted in the final expression, since it is simply

unity. The integration may be effected by series, and we obtain

finally—

Eioabs. = —^ X 1-0823.

Setting this equal to the "observed" value of Eio abs.) ^^2.

7 •061 X io~^^, we obtain—

-y~„ = I 1682 X lO^^ . . . .

Further, Lummer and Pringsheim ( Fer/i. d. Deutsch. physik. GeselL,

2, 176, 1900) have determined the value of X^ax. T, where Xmax. is the

wave-length corresponding to the maximum value of Ex from a black

body radiating at a given temperature. The expression Amax. x T is

a constant independent of temperature as Wien has shown, the numeri-

cal value found by Lummer and Pringsheim being 0-294 cm. degrees.

Now, by differentiating Planck's formula (equation (2)) with respect

to X, and putting the differential equal to zero, when A = Amax. we

obtain—

f I ^ -V''/*'^^ma'=- = I

V s^Aniax. T/

whence Amax. x 1 = -—-?— r

4*965 1^

h 4*965i X 0294 ... ,

_„ ,

= ^-^-^

10-^^ = 4'866 x lo"" . . (4)

or T

k 3 X 10'"

By combining equations (3) and (4) we obtain finally —

A = 6"55 X 10"'-' erg/sec.

k = I '346 X \o~'^*'' erg/degree.

Millikan {Froc. Nat. Acad. Sci., 3, 314 (1917)) gives

(3)

as the

most accurate value of the charge e on an electron, the quantity

4*774 ± 0-005 X lo"^'* electrostatic units. Knowing this quantity and

the value of ejm, viz. 1-767 x 10''', and also knowing Rydberg's con-

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