gypsum, charcoal, silica, and burnt magnesium. Neumann and Feddersen called the phenomenon thermo-diffusion. Osborne Reynolds, who used the name thermal transpiration, repeated Feddersen's experiments, and made a great number of actual measurements of the difference of pressure that was produced at the warmer side of the partition. In the above-mentioned memoir Maxwell has given a very simple explanation of the phenomenon on the basis of the kinetic theory of gases. His theory starts from the assumption that the number of particles of gas which collide with the walls of the containing vessel in unit time is proportional not only to the number N of molecules contained in unit volume but also to their mean speed ; and, when the area struck is taken equal to unity, this number is expressed by the product ΑΝΩ, as in a formula developed in § 37. If in unit volume on one side of the partition there are N1 molecules with the mean speed 1, and on the other N2 molecules with the mean speed 2, a unit area of the narrow openings in the wall will be met on one side by more molecules will pass over in the first direction than in the second, but fewer if There consequently ensues a flow of gas from that side on which the product NQ has the greater value towards that where the value is the smaller. Suppose now, first of all, as is the case at the beginning of an experiment, that there is the same pressure on both 1 Phil. Trans. clxx. pt. 2, 1879, p. 727; Wied. Beibl. vi. 1882, p. 455. sides of the partition; then between the values of N and there subsists the relation The flow of gas therefore proceeds in this case too from the side where there are the more molecules, i.e. where the gas is the denser, to the side where it is the less dense, just as in ordinary effusion; but while in this latter case the rarefaction is produced by lowering of pressure, in the case of thermal effusion just considered it is effected by warming. Hence the flow of a gas from a colder region to a warmer is a result of the theory no less than of experiment. The pressure therefore rises on the warmer side, and a force opposing the motion is brought into play by which a state of equilibrium is finally set up; and we have now to investigate under what circumstances this will happen. The flow must cease when In this case, between the values of the pressure on the two sides of the partition, must hold. Introducing into this equation the absolute temperature defined in § 15, and therefore putting in general, and in this particular case N ̧2 = N20,, N22 we find as the condition of the final state of equilibrium P1 P2 = √1: √/02. The thermal effusion therefore ceases as soon as the ratio of the pressures on the two sides of the partition has attained the value of the ratio of the square roots of the absolute temperatures. 39. Heat Effects Accompanying Effusion As effusion may arise from inequalities of temperature, so may it cause the temperatures at the two sides of a porous partition to be unequal. Cooling is produced at the side from which the flow takes place, while the other space into which the gas streams is warmed. The same action therefore occurs which has already been described in §§ 18, 19. Where the gas expands it cools, and where it is condensed it gets warmed. The explanation of this behaviour is also essentially that which has been given for the case in which it was assumed that the condensation was caused by the pushing down of a piston, the lifting of which made the gas to expand. The only difference consists in our having to take into account the encounters of the streaming particles with each other and with other particles instead of the collisions of the molecules against the piston. A particle which reaches the orifice from the interior of the receiver does not here meet particles at rest, but particles in motion that are proceeding in the same direction. In consequence of this the particle will be thrown back into the receiver, not with the same speed with which it arrived at the orifice, but with a much less speed, while the motion of the particle that streams out is increased. Thus the particles in the receiver lose part of their molecular energy during the flow, and the gas in the receiver therefore cools. On the other side of the partition the particles that escape from the orifice strike against particles that either are at rest or have lost in the larger space at least a part of their energy of flow by its transformation into heat. To these latter particles momentum is communicated by those which rush from the orifice with the full speed of the L. Natanson, Wied. Ann. xxxvii. 1889, p. 341. stream; the molecular motion therefore of the particles. in the space into which the flow occurs is increased, or, what is the same thing, the temperature in this region rises by reason of the flow. Both conclusions agree with the experimental observations made by Joule and others. CHAPTER IV IDEAL AND ACTUAL GASES 40. Inexactness of the Theoretical Laws ALTHOUGH all the laws which we have deduced from the kinetic neory of gases are in accordance with experiment, yet it must not, on the other hand, be overlooked that the agreement between observation and the strict results of theory has not proved to be absolutely complete and unexceptionable for any of the laws. In the case of Boyle's law respecting the pressure we have already had to remark that it holds good only approximately, and that every one of the gases shows deviations from this law, which, even if in most cases only small, are yet distinctly provable. This remark holds good also for all the other laws which follow from the theory. That Dalton's law with respect to the pressure of mixed gases suffers from the same deficiency as Boyle's cannot be doubted; from numerous observations. which Galitzine' has partly made by himself and partly drawn from other sources, the pressure of a mixture is sometimes greater and sometimes less than the sum of the pressures exerted by the components separately. There must therefore be present several causes of different kinds which act together and cause the deviations from the theoretical laws in either the one direction or the other. Just as incompletely do the experiments on the effusion of gases agree with the conclusions of theory. Neither does the speed of flow, as determined in Graham's and Bunsen's experiments, exactly correspond to the theoretical law, nor do the changes of temperature occur 'Das Dalton'sche Gesetz, Strassburg 1890; Wied. Ann. xli. 1890, p. 588; Gött. Nachr. 1890, p. 22. |