Page:The American Cyclopædia (1879) Volume XI.djvu/729

 MOLECULE 711 assumed apparatus is a possible form of air thermometer, which is the most accurate mea- sure of temperature we employ ; and thus it appears that our best practice is in harmony with our theory. Evidently, if we could re- duce the temperature of the confined gas in- definitely, we should at last bring the molecules to rest. They would then exert no pressure, and the mercury column in our barometer would fall to its lowest level. This condition would be theoretically the absolute zero, and our air thermometer shows what the relation of this point must be to our ordinary standard of temperature, the centigrade scale. Begin- ning with the apparatus in the condition de- scribed above, the temperature of the air being that of melting ice or C., and the tension 273 millimetres, let us heat it to the temperature of boiling water, 100 C. We know by experi- ment that if the volume of the air is kept con- stant the mercury column, which measures the tension, would rise to 373 millimetres. Hence, under the conditions assumed and according to our method of graduating thermometers, each centigrade degree corresponds to one millime- tre in the height of this mercury column. If the instrument is now cooled through 100 0., that is, if the temperature is reduced again to C., the mercury column will of course fall 100 millimetres ; and therefore if cooled 373 C., that is, 273 below the centigrade zero, the tension should become nothing. Or if, accord- ing to our mode of estimating temperature by the air thermometer, we define a centrigrade degree as a difference of temperature, which at any part of the scale determines in a confined mass of gas a difference of tension equal to ^ F of the tension at the temperature of melting ice, then the absolute zero of heat is at 273 on the scale so defined. Such a definition, however, gives us no positive knowledge of the relations of the absolute zero to natural phenomena, as a simple consideration will show. Starting from the self-evident proposi- tion that the quantity of heat liberated by burning fuel under constant conditions is pro- portional to the amount of fuel burned, we may use the weight of some combustible of con- stant nature, like hydrogen, as a measure of quantities of heat. Now taking the case we have assumed of a confined mass of air having a tension of 237 millimetres at the temperature of melting ice, we can say in general that, so far as accurate observations have been made, equal increments of heat measured by the fuel standard cause equal increments of tension, and equal decrements of heat equal decrements of tension. Moreover, it would be possible in a given case to calculate from experimental data, at least approximately, the amount of combus- tible which would be required to increase the tension of a confined mass of air one milli- metre ; and the theory of the air thermometer, our standard of temperatures, is based on the conclusion that twice this amount of combus- tible would increase the tension two milli- metres, three times the amount three millime- tres, and so on. If this is true indefinitely, and if the tension actually increases or dimin- ishes by a constant quantity, through all parts of the scale, on the addition or subtraction of the same quantity of heat (measured by the fuel standard), then we have real knowledge of the relations of the absolute zero. We can say of a mass of matter that it contains as much heat as would be generated by burning a given weight of hydrogen gas, and that if this limited amount of heat were removed its temperature would be reduced to absolute zero. But unfortunately the accurate experi- ments on the expansion of gases by heat have been confined within such narrow limits of temperature, and our means of connecting the observed effects with the amount of fuel burned, the only legitimate measure of thermal differ- ences, are so indirect, that we must generalize very cautiously; and it is possible that the law to which our observations appear to point would totally fail when the differences of tem- perature became extreme. Still there are several independent phenomena which seem to confirm this law, and indicate that the absolute zero, as defined above, is a reah'ty and not an assumption. But even as an assumption the absolute zero is on many accounts a more con- venient point to count from than the tem- perature of melting ice. By adding 273 to temperatures expressed in centigrade degrees, we obtain what we may call the absolute temperature; and we find by experiment, as our theory requires, that the tension of a con- fined mass of any gas is proportional to the absolute temperature thus expressed. This is a modern way of expressing the law discov- ered by Charles that equal changes of tempera- ture cause the same relative changes of volume or tension in all aeriform bodies. Thus it is that the molecular theory explains, and indeed predicts, the mechanical condition of aeriform bodies. We have only been able to give the general features of the reasoning. The mathe- matical demonstration of the several theorems is based on a beautiful application of the doc- trine of averages in the calculus of probabil- ities, and for this we must refer the mathemat- ical reader to the classical works of Clausius. Let us next consider some of the qualities or relations of molecules of different kinds, which can be deduced by a similar course of reasoning. In the first place, it is evident that if equal volumes of two gases contain the same number of molecules, the relative weights of these molecules must be the same as the rela- tive weights of the equal gas volumes. Thus, a cubic centimetre of oxygen weighs 16 times as much as a cubic centimetre of hydrogen under the same conditions ; and if there is in each cubic centimetre the same number of mo- lecules, each molecule of oxygen must weigh 16 times as much as each molecule of hydro- gen. In general, the number which expresses the specific gravity of a gas with reference to