A system of physical chemistry - Index of

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A system of physical chemistry - Index of

APPENDIX 1

Thus the number, unrestricted as to

direction, with speeds between c,

and ^2, is—

4tN 727/87:^^6

rci

Cl

^2 ^ ^-3C2/2c-2 _ ^^

Expression (6) can be much simplified by introducing instead of the

speed c the ratio which this speed bears to the maximum probability

. speed c. 71

Call this ratio x so that—

c=

Jl^.c.x

and hence dc =

J^.c. dx.

On introducing these expressions into

(6) we find after a little rearrangement

that the number of molecules whose speed ratios lie

between x-^ and x rises to a maximum value i/e (or

Fig. 14,

0-37 approximately) when x = i ; the curve then descends asymptoti-

cally to the axis of x, y reaching as low a value as 0*02 when x = 2*5,

showing that all but a very small fraction of the molecules have speeds

at any moment less than two and a half times the maximum probability

speed (which corresponds to x equal to unity) or practically twice the

r-m-s-speed. In fact, the fraction of the molecules whose speed ratios

165

(6)

(7)

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