Page:Elementary Text-book of Physics (Anthony, 1897).djvu/247

§ 222] upon the sidos of the vessel are so numerous that their effect is that of a continuous constant force or pressure.

The entire independence of the molecules is assumed from the fact that, when gases or vapors are mixed, the pressure of one is added to that of the others ; that is, the pressure of the mixture is the sum of the pressures of the separate gases. It follows from this, that no energy is required to separate the molecules; in other words, no internal work need be done to expand a gas. This was demonstrated experimentally by Joule (§ 215).

The action between two molecules, or between a molecule and a solid wall, must be of such a nature that no energy is lost; that is, the sum of the kinetic energies of all the molecules must remain constant. Whatever be the nature of this action, it is evident that when a molecule strikes a solid stationary wall it must be reflected back with a velocity equal to that before impact. If the velocity be resolved into two components, one parallel to che wall and the other normal to it, the parallel component remains unchanged, while the normal component is changed from + u, its value before impact, to $$-u,$$ its value after impact. The change of velocity is therefore $$2u,$$ and if $$\theta$$ represent the duration of impact, the mean acceleration is $$\frac{2u}{\theta},$$ and the mean force of impact $$p = m\frac{2u}{\theta},$$ where $$m$$ represents the mass of the molecule.

Since the effect of the impacts is a continuous pressure, the total pressure exerted upon unit area is equal to this mean force of impact of one molecule multiplied by the number of molecules meeting unit area in the time $$\theta.$$ To find this latter factor, we suppose the molecules confined between two parallel walls at a distance $$s$$ from each other. Any molecule may be supposed to suffer reflection from one wall, pass across to the other, be reflected back to the first, and so on. Whatever may be the effect of the mutual collisions of the molecules, the number of impacts upon the surface considered will be the same as though each one preserved its rectilinear motion unchancred, except when reflected from the solid walls. The time required for a molecule moving with a velocity $$u$$