A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX II 191

Planck arrives at this result on dynamical grounds in the following

manner. Conceiving a monatomic gas as an aggregate of particles with

three effective degrees of freedom, and representing the co-ordinates of

a particle by x, y, z, and its velocity components by u, v, 2V, the condition

diagram is a six-dimensional one in which the position and

momentum of a point representing a particle are given as x, y, z, mu,

?nv, mw {m being the mass of a molecule). According to the Maxwell

Law the number of molecules whose representative points lie within

the limits x, y, z, mu, mv, mw, and x + dx . . . m{w + dw) is—

^^g~ kr dxdydzdudvdw . . (15)

where N is number of molecules in a gram-molecule, « the energy of

a molecule in condition xyz. u, v, w, due to its position and velocity,

and A is a number given by the equation —

I = A U *T dxdydzdudvdw.

If one puts e = \m{if" -f v- -t- w"-), it follows that—

I / w \l

1 \21tUy)

V being the volume of the gas.

Now, according to Planck's view, instead of the differential element

of the six-dimensional diagram which occurs in (15), we ought to introduce

a finite element having a value G, definite in size for a system of

definite molecules. The form and position of these " elementary

regions "

would, as in the two-dimensional case, be bounded by the

"surfaces" or loci of equal energy. If we number these regions i, 2,

3, . . . n, we can say that a fraction /i of the representative points lie

in region i, etc., 7^ in region n, where—

J^ G

'" m^

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