Page:The American Cyclopædia (1879) Volume XI.djvu/728

710 MOLECULE very greatly. Indeed, this must result from the fortuitous collisions, which will cause velo- city to accumulate sometimes in one molecule and sometimes in another, while contiguous molecules suffer a corresponding loss. When we come to consider next the mutual action between masses of different substances, con- sisting therefore of unlike molecules having different weights, the problem becomes more difficult, because we have now to deal with the collisions of unequal masses. Still the same laws as before give us the key to the solution ; and it has been shown by Maxwell and Boltz- mann that in all cases, when the condition of equilibrium is reached, the mean value of the moving power of the molecules of any masses must be equal. That is, in general, when any two bodies have the same temperature, wV 2 =m'V' 2 , m and m! representing the weights of the several molecules of the two bodies, while V 3 and V' 2 represent the mean of the squares of the velocities in each sys- tem. If the molecular weights are equal, then of course the mean velocities must be equal, as just stated; but if the weights are unequal, then the lighter molecules will have on the average a greater velocity. In any case V : V'= Vw>' Vm; and since we can determine the relative values of the molecular weights, we can calculate the ratio between these mean values of the molecular velocities, assuming of course that the two substances compared are of the same temperature. For example, as the molecules of oxygen gas are 16 times heavier than those of hydrogen gas, the mean value for the velocity of the hydrogen molecules at any given temperature will be four times as great as that for the oxygen molecules. It thus appears that temperature is a condition determined by molecular motion, and that the mean value of $7V 2 is the same for all bodies at the same temperature, a defi- nite value corresponding to each temperature, and becoming greater or less as the temper- ature rises or falls. This product is the true measure of temperature, and, as will soon ap- pear, this measure corresponds to that obtained with an air thermometer. We know as yet but little in regard to the molecular structure either of solids or liquids, but the three great laws which define the aeriform condition of matter may be shown to be necessary conse- quences of the mode of motion which our theory assigns to the molecules of gases. Gas molecules, as we have seen, move with perfect freedom until their motion is altered by colli- sions either with each other or against some surface ; and our theory refers the pressure of a gas against the surfaces with which it is in contact to a very rapid succession of small im- pulses which produce the effect of a continuous pressure. Now if a mass of oxygen, for exam- ple, is confined in a vessel, each of the oxygen molecules must on an average strike the sides of the vessel the same number of times ; and so long as the temperature is constant, it must strike with an impulse of the same average momentum. Hence each must contribute an equal share to the whole pressure, and this pressure must be proportional to the number of oxygen molecules in the vessel, or in other words to the density of the gas. Next let us assume that we have two similar vessels of equal capacity containing different gases, both at the same temperature and tension, one filled for example with hydrogen and the other with oxygen gas. According to our theory, if the temperatures are the same, the moving power of the hydrogen and oxygen molecules must be the same; that is, ^mV 2 = iw'V' 2 , as above. Hence mV : m'V'=V' : V, or the momentum of the two kinds of mole- cules, which is the measure of the pressures they exert, must be inversely proportional to their respective velocities. But, on the other hand, the swifter molecules will strike the sides of the vessels a greater number of times in a second, the number of impulses in a given time being proportional to the respective veloci- ties; or n : n'=V : V. Hence, nmV=n'm'V- that is, each molecule of hydrogen will pro- duce in a given time the same effect as each molecule of oxygen, the less momentum being compensated by the greater frequency of the impulses. But if the molecule of hydrogen thus becomes the mechanical equivalent of the molecule of oxygen in producing pressure, then the same effect can be produced in the two vessels only by the same number of mole- cules. In other words, equal volumes of two gases at the same temperature and tension must contain the same number of molecules ; and this is the very important law first an- nounced by Avogadro and afterward confirmed by Ampere. Next consider what must be the effect on a confined mass of gas of an increase of temperature. Assume that we begin with a closed vessel filled with air at the tempera- ture of melting ice, and with a tension mea- sured by a column of mercury 273 millimetres high in a connecting barometer. An increase of temperature will augment the velocity of the molecule, and the effect of each molecu- lar impulse upon the exposed surface of mer- cury will be increased in proportion to the velocity ; but besides this, each molecule will now strike the mercury a greater number of times in a second, greater again in proportion to its velocity, so that the part of the pressure due to each molecule will vary as the square of the velocity. As the total effect is but the ag- gregate of these molecular impulses, and the number of molecules acting is assumed to be constant, it is evident that the mercury col- umn, which is the measure of the pressure or tension of this confined gas, must rise in pro- portion as the product wV 2 increases ; and since, as we have seen, all gas molecules are mechanically equivalent, the effect must be the same whether our vessel be filled with air or with any other gas. Now this product is our theoretical measure of temperature, and the