Page:Encyclopædia Britannica, Ninth Edition, v. 7.djvu/238

220 DIFFUSION ture to the lime, or from the lime to the mixture, in such a manner that the conditions of the system differ only by infinitesimal quantities at the corresponding stages of the direct and the inverse processes. The same thing may be done at lower temperatures by means of potash or soda. If one of the gases can be condensed into a liquid, and if during the condensation the pressure is increased or the temperature diminished so slowly that the liquid and the mixed gases are always very nearly in equilibrium, the separation and mixture of the gases can be effected in a reversible manner. The same thing can be done by means of a liquid which absorbs the gases in different proportions, provided that we can maintain such conditions as to temperature and pressure as shall keep the system in equilibrium during the whole process. If the densities of the two gases are different, we can effect their partial separation by a reversible process which does not involve any of the actions commonly called chemical. We place the mixed gases in a very long horizontal tube, and we raise one end of the tube till the tube is vertical. If this is done so slowly that at every stage of the process the distribution of the two gases is sensibly the same as it would be at the same stage of the reverse process, the process will be reversible, and if the tube is long enough the separation of the gases may be carried to any extent. In the Philosophical Magazine for 1876, Lord Kayleigh has in- yestigated the thermodynamics of diffusion, and has shown that if two portions of different gases are given at the same pressure and temperature, it is possible, by mixing them by a reversible process to obtain a certain quantity of work. At the end of the process the two gases are uniformly mixed, and occupy a volume equal to the sum of the volumes they occupied when separate, but the temperature and pressure of the mixture is lower than before. The work which can be gained during the mixture is equal to that which would be gained by allowing first one gas and then the other to expand from its original volume to the sum of the volumes ; and the fall of temperature and pressure is equal to that which would be produced in the mixture by taking away a quantity of heat equivalent to this work. If the diffusion takes place by an irreversible process, such as goes on when the gases are placed together in a vessel, no external work is done, and there is no fall of temperature or of pressure during the process. We may arrive at this result by a method which, if not so instructive as that of Lord Kayleigh, is more general, by the use of the physical quantity called by Clausius the Entropy of the system. The entropy of a body in equilibrium is a quantity such that it remains constant if no heat enters or leaves the body, and such that in general the quantity of heut which enters the body is where <p is the entropy, and 6 the absolute temperature. The entropy of a material system is the sum of the entropy of its parts. In reversible processes the entropy of the system remains un changed, but in all irreversible processes the entropy of the system increases. The increase of entropy involves a diminution of the available energy of the system, that is to say, the total quantity of work which can be obtained from the system. This is expressed by Sir W. Thomson by saying that a certain amount of energy is dissipated. The quantity of energy which is dissipated in a given process is equal to 0o(fo-0i) where fa is the entropy at the beginning, and fa that at the end of the process, and is the temperature of the system in its ultimate state, when no more work can be got out of it. When we can determine the ultimate temperature we can calculate the amount of energy dissipated by any process ; but it is sometimes difficult to do this, whereas the increase of entropy is determined by the known states of the system at the beginning and end of the process. The entropy of a volume v t of a gas at pressure p l and temperature 0! exceeds its entropy where its volume is v, and its temperature by the quantity Hence if volumes t and v 2 of two gases at the same temperature and pressure are mixed so as to occupy a volume t j + 1- 2 at the same temperature and pressure, the entropy of the system increases during the process by the quantity p I V Z Since in this case the temperature does not change during the pro cess, we may calculate the quantity of energy dissipated "by multi plying the gain of entropy by the temperature, and we thus. find for the dissipation 2^i log v i-^ + pv z log - 1 + r 2 , or the sum of the work which would be done by the two portions of gas if each expanded under constant temperature to the volume ! + ,. It is greatest when the two volumes are equal, in which case it is l-386.pt>, where p is the pressure and v the volume of one of the portions. Let us now suppose that we have in a vessel two separate portions of gas of equal volume, and at the same pressure and temperature, with a movable partition between them. If we remove the partition the agitation of the molecules will carry them from one side of the partition to the other in an irregular manner, till ulti mately the two portions of gas will be thoroughly and uniformly mixed together. This motion of the molecules will take place whether the two gases are the same or different, that is to say, whether we can distinguish between the properties of the two gases or not. If the two gases are such that we can separate them by a reversible process, then, as we have just shown, we might gain a definite amount of work by allowing them to mix under certain conditions ; and if we allow them to mix by ordinary diffusion, this amount of work is no longer available, but is dissipated for ever. If, on the other hand, the two portions of gas are the same, then no work can be gained by mixing them, and no work is dissipated by allowing them to diffuse into each other. It appears, therefore, that the process of diffusion does not involve dissipation of energy if the two gases are the same, but that it does if they can be separated from each other by a reversible process. Now, when we say that two gases are the same, we mean that we cannot distinguish the one from the other by any known reaction. It is not probable, but it is pos sible, that two gases derived from different sources, but hitherto supposed to be the same, may hereafter be found to be different, and that a method may be discovered of separating them by a reversible process. If this should happen, the process of interdiffusiou which we had formerly supposed not to be an instance of dissipation of energy would now be recognized as such an instance. It follows from this that the idea of dissipation of energy depends on the extent of our knowledge. Avail able energy is energy which we can direct into any desired channel. Dissipated energy is energy which we cannot lay hold of and direct at pleasure, such as the energy of the confused agitation of molecules which we call heat. Now, confusion, like the correlative term order, is not a property of material things in themselves, but only in relation to the mind which perceives them. A memorandum-book does not, provided it is neatly written, appear confused to an illiterate person, or to the owner who understands it thoroughly, but to any other person able to read it appears to be inextricably confused. Similarly the notion of dis sipated energy could not occur to a being who could not turn any of the energies of nature to his own account, or to one who could trace the motion of every molecule and seize it at the right moment. It is only to a being in the

intermediate stage, who can lay hold of some forms of