THE FREE PATH IN A GAS Let us regard each molecule of a gas, for simplicity, as a small round shot. These shot travel with a velocity which, as we have seen, is something like 2 kilometres a second in hydrogen, and about half a kilometre a second in air. Each shot travels on in a straight line until it strikes some sort of target, after which its speed is changed and its direction of motion altered. Some molecules strike the target formed by the boundary of the vessel containing the gas; their impact gives rise to the pressure on the boundary which we have just discussed. If the molecules were mere points, this would be the only target; each molecule would travel on until it hit the boundary, since the chance of two points hitting one another would be infinitesimal. Actually the molecules are of finite size, and although this size is small, we cannot legitimately disregard the possibility of molecules hitting one another; indeed each molecule in a flask of air under normal conditions hits other molecules several million times for each time it hits the boundary. If the diameter of each molecule is two molecules cannot pass so close that their centres are at a distance less than a of one another without a collision taking place, so that each molecule can be regarded as forming a target of area ire If there are v molecules per unit volume, the number in a small layer of thickness t and cross section S is vtS, and these form a target of total area This quantity is pro portional to t, and for a certain value of t it becomes equal to S. When t has this value, the target formed by the combined mole cules precisely fills up the whole area S, so that no molecule can get through without a collision. The value of t which makes equal to S is so that in travelling through a layer of this thickness in the gas each molecule will collide with some other molecule and have its speed and direction of motion changed.
The foregoing simple calculation requires adjustment in several respects; in particular we must allow for the possibility of the molecules "covering" one another in their motion, so that the area of the total target is substantially less than the sum of the areas of the targets presented by the separate molecules. An
exact calculation, first given by Maxwell, shows that the distance 1 which a molecule is likely to travel before colliding with another molecule is given by In ordinary air the length of the average free path is about 0.000006cm. or a four-hundred-thousandth part of an inch. Since the molecule of air travels at a rate of 5o,000cm. a second, it must describe 8,000 million free paths every second, and so col lides with 8,000 million other molecules in each second of its existence.
Conduction of Heat.—During the description of any free path the energy of a molecule remains unchanged, although it may gain or lose energy at a collision with another molecule. Consider the motions of molecules in a gas in which the tem perature is not uniform. Let one layer AB of the gas be at a temperature T, while another parallel layer A'B' at a distance 1 (equal to the free path of the molecules) is at a temperature T'.
Owing to the difference of temperature, the average energies of the molecules in the two layers will be different ; let them be E,E' respectively. A molecule which starts from a collision at A and describes the free path AA' before collision at A' is likely to have the energy E appropriate to the layer AB, while one which describes the free path B'B in the reverse direction is likely to have the energy E' appropriate to the layer A'B'. If the temperature T is higher than T', E will be greater than E', so that more energy is carried from the hot layer AB to the cold layer A'B' than travels in the reverse direction, and there is a resultant flow of heat energy from the hot parts of the gas to the cold. In this way the kinetic theory explains the conduction of heat in a gas.