Gas laws and the simple kinetic theory of matter
An introduction to the kinetic theory of matter has been given in chapter 13. On this theory a gas consists of a vast number of molecules moving with random high velocities, colliding with one another, and bouncing off the walls of the containing
vessel. A force is thus set up on the walls, which is given by the rate of change of momentum as they bounce off. The pressure of the gas is the value of this force per unit area. Calculations based on the inetic theory in conjunction with the experimental
results known as Boyle’s L harles’s L aw, and the Pressure Law showthat the absolute thermodynamic te pera ure of a perfect gas is proportional to the average kinetic energy of its mole les. Tf se calculations are dealt with in more advanced texts, so a brief descripti n only WI be given here.Boyle’s law. At constant temperat re, the average kinetic energy of the molecules is constant. If the volume of a fixed ass of gas is halved it can be shown by geometry that the number of molecular i pacts per second per unit area of wall surface is doubled: in other words, the p essure is doubled. This confirms the experimental result that the pressure of a fi d mass of gas at constant temperature is inversely proportional to the volume.
Raising the t perature of a fixed mass of gas at constant volume increases the average kin ic energy of the molecules so that they make more frequent impacts with t walls at higher velocity. Thus the rate of change ofmomentum on impact is Increased with consequent increase in pressure.
If the p essure of a fixed mass of gas is to remain constant as the temperature is raised t e rate of change of momentum of the molecules on impact with the walls must remain constant. Since the velocity of the molecules will increase with temperature, the change in momentum will be greater, and to keep the rate of change the same it will be necesssary to make fewer impacts per second. Thus the volume must increase so that the molecules have to travel further between collisions with the walls. As we have seen, this condition applies if the volume varies as the thermodynamic temperature.