TITLE.PM5

BASIC CONCEPTS OF THERMODYNAMICS 15

dharm
M-therm/th2-1.pm5

Pressure exerted by an Ideal Gas :

Let us consider a quantity of gas to be contained in a cubical vessel of side l with perfectly

elastic wall and N represent the very large number of molecules in the vessel. Now let us consider

a molecule which may be assumed to have a velocity C 1 in a certain direction. The velocity can be

resolved into three components u 1 , v 1 , w 1 parallel to three co-ordinate axes X, Y and Z which are

again assumed parallel to the sides of the cube as shown in Fig. 2.1.

Fig. 2.1

Thus, C 12 = u 12 + v 12 + w 12.

Let this molecule having mass m strike wall surface ABCD of the cube with velocity u 1.

Since the collision is perfectly elastic, the molecule will rebound from this surface with the same

velocity u 1. Therefore,

The momentum of the molecule before it strikes the face ABCD = mu 1

The momentum of the molecule after impact = – mu 1.

Hence change of momentum at each impact in direction normal to the surface

ABCD = mu 1 – (– mu 1 ) = 2mu 1

After striking the surface ABCD, the molecule rebounds and travels back to the face EFGH,

collides with it and travels back again to the face ABCD covering 2l distance. This means molecule

covers 2l distance to hit the same face again. Hence the time taken by the same molecule to strike

the same face ABCD again is^2

1

l

u

.

Therefore, the rate of change of momentum for one molecule of the gas

==

2

2

1

1

1

mu^2

l

u

mu

l