To study the amount of this flow of heat, let us fix our attention on the molecules which cross a unit area PQ, halfway between the two layers AB, A'B'. Half of these will cross PQ in one direction and half in the other. If there are molecules per unit volume each travelling with an average velocity c, then -vc molecules will cross in each direction per unit time. The stream which crosses in the direction AA' will transport energy lvcE across the unit area ---4 in the direction AA', while the other stream will transport energy IvcE' in the reverse direction. The net transport of energy across the plane in unit time is accordingly The foregoing simple discussion needs correction, since the free paths which cross the plane PQ are not, in general, perpendic ular to PQ. A simple mathematical investigation shows that the necessary correction consists in multiplication by a factor so that the net transport of energy is where E,E' are the values of E in layers at a distance 1 apart. By definition of v and E, vE is the total energy per unit volume at A, and this is equal to p T, where p is the density and Cy is the specific heat of the gas at constant volume. Thus in place of formula (8), the net transport of energy in unit time may be taken to be If x is a co-ordinate measured perpendicular to PQ in the direction AA', we may put and the flow of heat-energy per unit area per unit time is seen to be In the theory of heat the flow of heat is given by expression (io) where is the coefficient of conduction of heat. Thus the
kinetic theory explains the conduction of heat and predicts for the coefficient of conduction the value given by formula (I 1). This value needs minor adjustments of various kinds, and these result in 6 assuming a value substantially larger than that given by equation (II).
Viscosity.—The phenomenon of gaseous viscosity can be dis cussed in a very similar way. We now suppose the layers AB and A'B' of the gas to be moving parallel to PQ with different veloc ities v,v' so that molecule in the layer AB is likely to have momen tum my parallel to AB. We no longer investigate the transfer of energy E across the plane PQ, but the transfer of momentum my. As in formula (8) the net transfer per unit time is K=ipcl. (12) This is accordingly the value of the coefficient of viscosity predicted by the kinetic theory. In terms of the coefficient of viscosity K, the coefficient of conduction of heat .6 can be ex pressed in the form Diffusion.—The phenomenon of diffusion can be treated in a very similar manner. We consider a mixture of two gases G, and supposing that the proportion of G, in the mixture is 0 at AB and is 0' at A'B'. The chance of a molecule which describes a free path AA' being a molecule of is 0, so that the mass of the gas G, which is carried by each molecule describing such a free path is, on the average equal to Om. As in formula (8), the net transport of across the plane PQ per unit time is Svc (Om —0'm') or