PNEUMATICS 243 to 100 C. The general characters of the curves obtained for hydrogen, nitrogen, olefiant gas, and marsh gas remain the same as at the ordinary temperature ; that is, with the exception of hydrogen, the product pv decreases to a minimum and then increases indefinitely. The position of the minimum changes with the temperature. Thus for olefiant gas and carbonic acid gas (whose properties were also studied at these higher temperatures), the pressure at which the minimum occurs increases with the temperature, while in the case of nitrogen and marsh gas this critical pressure decreases as the temperature rises. Probably at some temperature higher than 100 olefiant gas and carbonic acid gas would begin to behave like nitrogen, and all would appear to tend more and more, as the tem perature rises, to the condition of which hydrogen is the type. That is, the deviation from the Boylean law up to tlie minimum point woxild steadily decrease until finally the curve would cease to 0-20 0-15 0-10 + O05 05 O-IO 0-lti have a marked minimum. For any one gas, the higher the tem perature the less the curvature at the minimum point ; and the comparison of different gases seems to indicate that the curvature is greater for the more easily liquefiable gas. At sufficiently high temperatures the law of compressibility for all gases approximates to the relation P( V - a) = constant, where P is the pressure, V the volume, and a a constant. Hydrogen follows this law very closely at the ordinary temperature of the air, as the straightness of its representative curve shows at a glance. Amagat has further discussed by means of his results the law of dilatation of gases. This law is named Charles s law, after the discoverer of it. Stated simply, it is that at constant pressure every gas expands by the same fraction of itself for a given rise from a given temperature. Charles did not publish his results ; and it was not till fifteen years later, when Dalton and Gay-Lussac, working independently, rediscovered it, that the law became generally known. Their results were published in 1801 l and 1802 2 respec tively; and it is upon the authority of the latter, who accidentally became acquainted with the fact, that the law is now named after Charles. The careful measurements of Magnus, 3 Kegnault, 4 Jolly, and others have established that there is an appreciable difference in the coefficients of expansion for the different gases. The difference is slight for the so-called permanent gases air, nitrogen, oxygen, hydrogen, and marsh gas ; but for the more easily lique fiable gases it is quite marked. The mean coefficient of expansion for air between C. and 100 C. and at the ordinary atmospheric pressure is 003665 per degree, and the value for any one of the gases just mentioned does not certainly differ from this by one-half per cent. 5 This may be expressed by the formula where K is a constant and T the tempera ture measured from absolute zero, which is 274 C. below the freezing point of water (see HEAT). When T is constant, we have by Boyle s law the product pv also constant. Hence we may combine the two laws in the form where R is a constant. We thus see that, Boyle s law being assumed to be true at all temperatures, Charles s law, if true for any given pressure, is true for every other pressure. Further, if v is kept constant the rate of increase of log p with temperature will be expressed by the same number as the rate of increase of log v when p is kept constant. Ex periment has fully verified this conclusion to as close an approximation as Boyle s and Charles s laws themselves are fulfilled. The rate of increase of log v with tempera ture, or, what is the same thing, the ratio of the rate of increase of the volume to the original volume, is given by the formula and this is the measure of the coefficient of expansion at temperature T. Hence the coefficient of expansion diminishes as the temperature rises, a conclusion also in accordance with experiment so long as we are dealing with gases which nearly obey Boyle s and Charles s laws. We have seen, however, that even in the case of Amngat s hydrogen the departure from Boyle s law is very marked results. at the higher pressures ; and therefore we cannot expect a closely numerical agreement between the results of experi ment and the results of calculation from the above formula. Thus, it is not surprising that practically the coefficient of expansion should be affected by the pressure, as Amagat s experiments clearly show, although in the equation deduced above the pressure does not enter. In the following table given by Amagat, the second column contains the mean coefficients of expansion of hydrogen between 17 and 60 C. at the pressures given in the first 1 Memoirs of the Philosophical Society of Manchester, vol. v. 2 Annales de Chimie, xliii. , An X. 3 Pogg. Ann., Iv. , 1841. 4 Mem. de I Acad., xxi. 5 The first who really gave accurate values of these quantities was
Rudberg.