in general move in straight lines, except when two approach very near to each other. In consequence of this linear motion it must often happen that a molecule of vapour strikes against the surface of the liquid; in this case, under favourable conditions, it may be held there by cohesion. In the liquid, too, the molecules are not at rest, but are in as brisk motion as in the vapour, but not in straight lines. In consequence of this motion it may happen that a liquid particle gets out of the range of the forces of cohesion and passes again into the vapour. There is, therefore, a continuous interchange of molecules between liquid and vapour, and, since there is equilibrium, as many molecules must on the average pass from the vapour into the liquid as from the liquid into the vapour. On considering that this equilibrium between liquid and vapour extends also to temperature, we see that not only as much mass but also as much energy necessarily passes from the liquid to the vapour as from the vapour to the liquid. The same number of molecules therefore carry over the same amount of energy from the one state of aggregation to the other, and this is only possible if the energy of a molecule is as great in the liquid as in the vapour. In this theorem we have to remember that we are not dealing with kinetic energy only, but in the case of liquid molecules with the sum of their kinetic and potential energy. This equilibrium will only be maintained, however, when the vapour has a certain density, so that there is a sufficient number of molecules to bombard the surface of the liquid. Such a vapour is called a saturated vapour. If liquid is introduced into a vessel in which there is at first no vapour of this substance, vapour at once begins to form in consequence of the heat present. Molecules detach themselves from the liquid surface and move about as molecules of vapour in the free space above. Such a separation of a molecule from the liquid left behind takes place the more easily the greater the energy which the escaping molecule possesses. With the molecules that have darted off, therefore, the liquid loses a sum of energy which is greater than that which on the average falls to these molecules, and thus for those that are left behind there remains a less amount of energy than they possess hitherto on the average. It is thus explained on our theory that a liquid cools by vaporisation. The heat that has disappeared has gone in doing the work of expansion. 21. Absorption and Adsorption Quite the same state of things occurs when a gas or vapour is dissolved in a liquid which is not of the same substance as occurs in the phenomenon of absorption. In this case the gaseous substance throngs into the liquid in consequence of the motion of its molecules, and is held fast by the attraction exerted on it by the liquid; and this process goes on until equilibrium between evaporation and condensation occurs. On the absorption of a gas by a liquid, heat is developed which is greater in amount than the latent heat of vaporisation. As the latter is equal to the sum of the kinetic energy of the molecules of the gas and the potential energy required to overcome the cohesion in the liquefied gas, it follows that still more energy than this is required to separate the gas from the liquid which has absorbed it. Hence there is no doubt as to the existence of an attraction of the gas by the liquid. If the force with which the liquid, when in the state of a saturated solution, retains the gas were as great as if the liquid were pure, the number of the molecules of gas absorbed by the liquid would be exactly proportional to the number of molecules remaining above it in the gaseous state, and Henry's law, that the mass of gas absorbed increases proportionally to the acting pressure, would hold strictly. But as this supposition cannot be accurate when large masses are absorbed, Henry's law can only approximately represent the truth. A rise of temperature also increases the energy of the molecules in the absorbed gas; they will, therefore, at a higher temperature come oftener into a position of being able again to escape from the liquid. Therefore the higher the temperature the less gas will be absorbed, as observation has taught. Molecules of a gas can also be held fast by a solid body just as by a liquid, porous bodies especially being able to condense considerable masses of gas. In other cases the mass condensed increases with the extent of surface of the body, and we must therefore assume that only the surface layers are active in causing condensation by the attractive forces they exert. On this account it has been thought necessary to introduce a new name and designate the phenomenon as Adsorption when the condensation is caused by a solid body. It differs, however, in nothing else from absorption in liquids; on the contrary, everything that has been stated about absorption can be ascribed to adsorption without further remark. One such fact is that by adsorption also can considerable heat be developed, as, for instance, in Döbereiner's lamp, on the condensation of hydrogen by spongy platinum. 41 CHAPTER III MAXWELL'S LAW 22. Unequal Distribution of Molecular Speed THE mean value of the molecular speed given in § 13 is not the arithmetic mean of all the different values of the speeds with which individual molecules move. The magnitude G-by which the mean value in question is denoted— has been defined in § 10 to be such that the mean energy of the molecules which strike against the wall would be unaltered if all of them possessed this same speed G instead of their actually different speeds. From this it results that with that equalised distribution the gaseous medium retains the same energy and exerts the same pressure as with its actual unequal distribution. So long as we are concerned only with the calculation of the pressure and energy, therefore, it is sufficient to ascribe this mean speed to all molecules. But if we wish to investigate more nearly the character of the gaseous state, we have to ask ourselves whether a difference in the values of the speeds is possible, and, further, how these different speeds are actually distributed among the molecules. That the equilibrium of a swarm of gaseous molecules in no way depends on the speed of all the molecules being the same, and that, on the contrary, there must really be a non-uniform distribution of speed among the molecules, can be seen without calculation. For it is easy to prove that if all the molecules had exactly equal speeds at any moment, this distribution of speed would be at once disturbed, and in place of it a non-uniform distribution would be established. Consider, for instance, the case of a moving particle being struck perpendicularly to the direction of its motion and so that the direction of the blow passes through its centre of mass; then the striking particle will cede part of its speed to the struck particle, which, as it experiences no resistance in the direction of the path it has thus far traversed, will retain its own motion undiminished, and, therefore, receiving in addition a further speed from the striking particle, will move more quickly than before the collision, and in changed direction, while the other moves more slowly, since it must lose speed. This example shows that in such an aggregation of molecules as we assume in gaseous bodies in our theory the speeds of the individual molecules cannot be equal in the state of equilibrium. Equilibrium can, therefore, only consist in a condition of continuous interchange of speed between every pair of colliding particles, every particle now gaining and now losing, its velocity being now big and now little, and changing as often in direction as in magnitude. It is for this continuous change of motion of the particles as they dash about that we have to investigate the law. 23. The Applicability of the Calculus of The attempt to deduce a law for something that is subject only to chance may seem singular and strange, but this should not deter us from undertaking a research which touches the very core of the kinetic theory. This theory, indeed, seeks for the cause of regular phenomena and regular properties of gaseous media in irregular tumultuous motions of the molecules. We have here to look at the observed facts, not as direct necessary consequences of unchangeable laws as is usual, but as the result of a large number of elementary processes which are subject to no law but that of chance. And yet all phenomena occur in unchangeable regularity. This is certainly a very uncommon position, but it is by no means unwarranted, and it is also not in the least limited to this theory only. During every chemical reaction |