Pressure Exerted by an Ideal Gas Collisions with a Wall

Pressure Exerted by an Ideal Gas Collisions with a Wall 

If we now consider an ideal gas made up of point particles, the particles cannot suffer collisions with each other and their velocities in the gas phase cannot change except after collisions with the walls of the container. The total transport of momentum in such a gas is by the individual molecules themselves. Let us calculate for such a gas the average pressure exerted on an element of wall surface dS. 

By Newton s laws, the net perpendicular force exerted on a surface element dS will be equal to the rate of change of momentum perpendicular to the wall 

The mean pressure is simply P = F/dS. But for our conservation principle to hold, Aj (momentum) of the wall must be equal to twice the component of perpendicular momentum brought by all the molecules striking the surface in the time At. Let us set up coordinate axes at the surface element dS and investigate the collisions (Fig. VII.3). 

Take a volume element in the gas dr whose spherical coordinates are r, 6, 4 with respect to the surface element dS. 

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