Peoples Physics Book Version-2

19.2. Molecular Kinetic Theory of a Monatomic Ideal Gas http://www.ck12.org

FIGURE 19.2

Illustration x-direction atom from above.

According to Newton’s second law, the force imparted by the single particle on the wall is

F=

∆p

∆t

= 2 mvx×

vx

2 L

=

mvx^2

L

Now, since there aren(a very large number) atoms present, the net force imparted on the wall will be

Fnet=n×

m(vx^2 )avg

L

Where thevx^2 is averaged over allnatoms.

Now let us attempt to relate this to the state variables we considered last chapter. Recall that pressure is defined as
force per unit area:

P=

F

A

Since the area of the wall in question isL^2 , thepressureexerted by the gas atoms on it will equal:

Pnet=

Fnet

A

=n

m(vx^2 )avg

L×L^2

=n

m(vx^2 )avg

L^3

Since, for a cubical box, volumeV=L^3 , the formula above can be reduced to:

Pnet=n

m(vx^2 )avg

V

or,

PnetV=nm(vx^2 )avg [1]