greater than that of air. M. Drion has since made very careful experiments upon several volatile liquids, and among them liquid sulphurous acid and chloride of ethyle. From these he has constructed the following table. True coefficient of expansion for 1°C. Tempe- Chloride of Sulphurous Tempe- Chloride of Sulphurous We may perhaps conclude that the coefficient of expansion of a liquid is very great at those temperatures at which the substance can only exist in the liquid state under very great pressure. 58. Contraction of liquids from their boiling points. Views perhaps analagous to those we have just mentioned induced Gay Lussac to compare the contraction of different liquids reckoned from their respective boiling points, and he obtained the following result for alcohol and sulphuret of carbon. Table of the contraction of alcohol and sulphuret of carbon for successive intervals of 5°C, reckoned from their boiling points, the volumes at these points being equal to 1000. It thus appears that the contractions of alcohol and sulphuret of carbon, reckoned in this way, are as nearly as possible the same. Pierre and Kopp have both verified this law of Gay Lussac, and the former has shewn 1. That amylic, ethylic, and methylic alcohol follow nearly the same law of contraction, or, in other words, equal volumes of these liquids at their respective boiling points will preserve their equality at all temperatures equidistant from these points. 2. That the same law holds true for the bromides and iodides of ethyle and methyle; 3. And in one or two other cases: but that in general two liquids formed by the combination of a common principle with two different isomorphous elements follow different laws of contraction starting from their respective boiling points. 59. In conclusion, if we compare this chapter with the preceding we shall be led to the following result: 1. Solids have a much smaller coefficient of expansion than liquids. 2. The coefficient of expansion of liquids increases with the temperature. 3. The coefficient of expansion of a liquid which only preserves its state under intense pressure is probably very great. CHAPTER IV. Dilatation of Gases. 60. Before commencing the subject of this chapter it may be well to draw attention to the following experiment and law. A B Fig. 13. Fig. 14. 30 Inches. Let there be a tube shaped as in the accompanying figures, of a uniform bore throughout, and let it contain at the atmospheric pressure (equal, let us say, to 30 inches of mercury) a volume of air AB. If this air be shut out from the atmosphere by mercury, then the surfaces B and D of the mercury in the two limbs of the tube will be at the same level, since the pressure upon the surface at B is supposed equal to that of the atmosphere pressing at D. Now if additional mercury be poured into the tube until there is a difference of 30 inches between the levels B' and C', then it is evident that the air A'B' exists under the pressure of two atmospheres; for we have not only the column of mercury C'D' = 30 inches tending to press this air into less volume, but we have in addition the pressure of the atmosphere upon the surface C', which is also equal to 30 inches of mercury. Hence we have the air in Fig. 14 existing at a pressure double of that in Fig. 13. Now it is a well-known fact that the space occupied by the air in Fig. 14 will be one-half of that occupied by it in Fig. 13; and generally, "provided the temperature remains the same, the volume which a gas occupies is inversely proportional to the pressure under which it exists; or, in other words, its density is proportional to its pressure." This is known as the law of Boyle or Marriotte. 61. But if the temperature be increased, the air will on this account alone tend to expand, and one of two things will happen. 1. If we wish to keep the air always occupying the same space we must employ additional pressure; 2. If we wish to keep it exerting the same pressure we must allow it to occupy additional space. Our subject thus naturally divides itself into two parts. In one of these we determine the relation between the pressure and temperature of a gas whose volume is constant, and in the other we determine the relation between the volume and temperature of a gas whose pressure is constant. If we imagine Boyle's law to hold rigidly for gases, then the two cases are connected with each other in a very simple manner. For if a gas whose volume is V and pressure P at o°C has at ° and under the same pressure the volumn V', then it is clear that were it constrained to V V occupy its old volume its pressure would be P x Either of the methods would in this case present us with precisely the same proportional change for increase of temperature, this being in the one case change of volume, and in the other change of elasticity; but it has been deemed right to determine the change by both methods, and we shall see in the sequel that the two values thus found are not precisely the same. 62. The fact of the dilatation of gas may be easily proved by filling a bladder nearly full of air, tying its orifice, and heating it; it will then soon appear to be quite full, the contained air having expanded by heat under the constant pressure of the atmosphere. Dalton in this country and Gay Lussac in France were the first who investigated the law of expansion of gases with any considerable success, and they were both led to the conclusion that all gases expand equally for equal increments of temperature. With regard, however, to the precise law which connects together volume and temperature, there was a difference in the result obtained by these two philosophers. According to Gay Lussac, the augmentation of volume which a gas receives when the temperature increases 1o is a certain fixed proportion of its initial volume at o°C; while according to Dalton, a gas at any temperature increases in volume for a rise of 1° by a constant fraction of its volume at that temperature. Gay Lussac's law may be expressed as follows. Let Vo, Vt denote the volumes at o°C and 1° of a certain quantity of gas existing at the pressure P, then these two volumes are connected with one another by means of the following formula V1 = V2 {I + at}; where a is the coefficient of expansion, nearly the same for all gases, which it is the object of experiment to determine. From this equation we derive at once the relation between the temperature and the density (density being represented by the mass contained in unit of volume) of air whose pressure remains constant. For let D denote the mass of air that occupies unit of volume at o°C; this mass will at t° occupy a volume equal to 1 + a t, and hence the mass of unit volume or the density at this temperature will be D The dilatation of gases has since been investigated by Rudberg, Dulong and Petit, Magnus, and Regnault, and the result of their labours leaves little doubt that Gay Lussac's method of expressing the law is much nearer the truth than Dalton's. It has also been ascertained that the coefficient |
