A system of physical chemistry - Index of

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A system of physical chemistry - Index of

1 64

A SYSTEM OF PHYSICAL CHEMISTRY

and the point density in the is region given by (3). Hence the number

sought is—

47rN 7^7/8^^. f2^-3c2/2c2 _ ^^ . . . (4)

The expression (4) has, for a given value of the differential element of

speed, dc, its maximum value for a value of c which makes—

a maximum. By the il*sual methods of the calculus it appears that this

value of ^ is : J'^c or o-8i6?; so that there are more molecules at an

instant possessing speeds within, say, one foot per second of this speed

than of any other assigned speed. That is, o*8i6? is the speed with

" maximum probability ".

We can now deal with the fallacious inference mentioned above.

Let us consider a velocity with speed c and a definite direction whose

direction angles are a, ^S, and 7. The velocity has then the components—

c cos a, c cos fi, c cos y.

Now, undoubtedly, there are more molecules whose velocities have

components between

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