It will be noticed that the first four gases have almost the same coefficient of expansion: these gases are all very difficult of liquefaction, and it will be seen that the coefficient rapidly rises in the case of the other gases, which are easily liquefied. For purposes of ordinary calculation it is usual to adopt the coefficient of expansion of air as applicable to all gases. It will be obvious that since the volume of a gas is affected by alterations of temperature, it becomes necessary, when measuring the volume of a gas, to have regard to the particular temperature at which the measurement is made, and in order to compare volumetric measures they must be all referred to some standard temperature. standard temperature is by general consent o° C. Taking the fraction .003665, therefore, for the coefficient This I volume of a gas at o° becomes 1 + .003665 volumes at 1° Therefore the volume at t equals the volume at o° multiplied by I + .003665 t. Let v be the volume at t°, and v, the volume at o°, then v = v(I + .003665 t), and conversely the volume at o° equals the volume at ť divided by I + .003665 t― The vulgar fraction equivalent to .003665 is 275 273 volumes at o° become 273 + t at t°. What is known as the absolute temperature of a substance is the number of degrees above - 273° C. Taking this point as the zero, the absolute temperature of melting ice, for example, will be 273°. Charles' law, therefore, may be thus stated: The volume of any gas, under constant pressure, is proportional to the absolute temperature. The Relation of Gases to Pressure. The effect of increase of pressure upon a gas is to diminish its volume. The law which connects the volume occupied by a gas, with the pressure to which it is subjected, was discovered by Robert Boyle (1661), and is known as Boyle's Law. It may be thus stated: The volume occupied by a given weight of any gas is inversely as the pressure. The general truth of this law may readily be illustrated by subjecting a gas to varying pressures, and it will be seen that when the pressure is doubled the volume of gas is reduced to one-half, and so on. Just as in the case of the law of Charles, modern investigations have shown that the law of Boyle is not a mathematical truth. It is found not to be absolutely true of any gas, for, with the exception of hydrogen, all gases are more compressible than is demanded by the law. Hydrogen deviates from the law in an opposite sense, in that it requires a higher pressure than the law would indicate, in order to reduce a volume of it to a given point. These deviations from Boyle's law are explained by the operation of two causes ; first, the attraction exerted by gaseous particles upon each other; second, the fact that increased pressure diminishes the space between the molecules, and not the actual space occupied by the molecules of a gas. When the former cause predominates, the gas deviates from the law by being more compressible; in the case of hydrogen the second cause operates more powerfully. (See Kinetic Theory of Gases.) For ordinary purposes of calculation the law of Boyle may be regarded as true. As the volume of a given weight of gas is so intimately related to the pressure, and as the atmospheric pressure is variable, it becomes necessary, in all quantitative manipulation with gases, to know the actual pressure under which the gas is at the time of measurement, and to refer the volume to a standard pressure. The pressure that has been adopted as the standard is that of a column of mercury 760 mm. in height. (See Atmosphere.) If v equals the volume of gas measured at p pressure, and v。 the volume at the standard pressure, then In practice it is most usual to make both correction for tempe rature and pressure together; then 7, being the volume at the standard temperature and pressure, we get The Liquefaction of Gases.-Under certain conditions of temperature and pressure, the law of Charles and the law of Boyle both FIG. 1. - 10 completely break down. According to Similarly, according to the law of Boyle, 100 c.c. of a gas measured at the standard pressure should occupy 25 c.c. when exposed to a pressure of four additional atmospheres. If 100 c.c. of the gas sulphur dioxide be enclosed in one limb of a long U-tube, as shown in Fig. 1, the other limb being filled with air, and the two gases be simultaneously exposed to increased pressure by raising the mercury reservoir, it will be seen that at first the gases in both tubes are compressed equally. As the pressure approaches three atmospheres, however, the mercury will be seen * The student should familiarise himself with the method of calculating the changes of volume suffered by gases, by changes of temperature and pressure, by working out a number of examples such as the following: · 1. If 30 litres of gas are cooled from 25° to o°, what is the diminution in volume, the pressure being constant? Ans. 2.51 litres. 2. If a litre of air at o° weighs 1.293 grammes when the barometer is at to rise much more rapidly in the tube containing the sulphur dioxide, and when the mercury reservoir has been raised to such a height that the gases are subjected to four atmospheres, the sulphur dioxide will have completely broken down, and will be entirely converted into a few drops of liquid, which appear upon the surface of the mercury. The air meantime, in the other limb, will be found to occupy 25 c.c., as that gas at that pressure obeys Boyle's law almost absolutely. We see, therefore, that at a certain temperature and at a certain pressure the gas sulphur dioxide begins rapidly to depart from the laws of Charles and Boyle, and ultimately passes into the liquid condition. All known gases, when exposed to certain conditions of temperature and pressure, conditions which are special for each different gas, will pass from the gaseous to the liquid state; and as the point at which liquefaction takes place is approached, the departures from Boyle's law become more and more pronounced. The first substance, recognised as being under ordinary condi tions a true gas, that was transformed into the liquid condition was chlorine, which was liquefied in the year 1806 by Northmore. The true nature of this liquid was not understood until Faraday investigated the subject. In his earlier experiments Faraday's method consisted in sealing into a bent glass tube (Fig. 2) substances which, when heated, would yield the gas; the substances being contained in one limb of the tube, and the empty limb being immersed FIG. 2. in ice. The pressure exerted by the gas thus generated in a confined space was sufficient to cause a portion of it to condense to 760 mm., what will be the weight of a litre of air at 27°, the barometer standing at the same height? Ans. 1.177 grammes. 3. What will be the weight of a litre of air at 42° when the barometer stands at 735 mm.? Ans. 1.084 grammes. 4. Air at a temperature of 15° is enclosed in a vessel and heated to 93°. Compare the pressure of the enclosed air with that of the atmosphere. Ans. As 61: 48. 5. What will be the volume, at the standard temperature and pressure, of 500 c.c. of hydrogen, measured at 20°, and under a pressure of 800 mm.? Ans. .490 c.c. the liquid state, and the liquid collected in the cooled limb. In this way Faraday liquefied such gases as chlorine, sulphur dioxide, ammonia, cyanogen. In his later experiments Faraday compressed the gas by means of a small compression pump, and at the same time applied a low degree of cold, and by so doing he succeeded in liquefying carbon dioxide, hydrochloric acid, nitrous oxide, and other gases. There were a number of gases, however, which Faraday found it impossible to liquefy, such as hydrogen, oxygen, nitrogen, marsh gas, nitric oxide, carbon monoxide, &c. It became the custom to call these permanent gases, and this term was applied to them until the year 1877. In that year it was proved by Pictet, and independently by Cailletet, that under sufficiently strong pressure, and a sufficiently low degree of cold, the so-called permanent gases could in the same way be reduced to the liquid condition. Pictet's method was in principle the same as that employed by Faraday, the difference being that with the machinery at his disposal he was able to employ enormously increased pressure and a greater degree of cold. For the liquefaction of oxygen, a quantity of potassium chlorate was heated in a strong wrought-iron retort, to which was connected a long horizontal copper tube of great strength and small bore. At the extreme end of this tube there was a pressure gauge capable of indicating pressures up to 800 atmospheres, and a stopcock. The tube was cooled by being contained in a wider tube, through which a constant stream of liquid carbon dioxide, at a temperature of 120° to 140°, was caused to flow. The machinery employed to maintain this flow of liquefied carbon dioxide was somewhat elaborate, consisting of condensing and exhaust pumps for liquefying and rapidly evaporating sulphur dioxide, and similar condensing and exhaust pumps for liquefying and rapidly evaporating carbon dioxide: the sulphur dioxide being merely the refrigerating agent used to assist the liquefaction of the carbon dioxide. This machinery was driven by two eighthorse-power engines. As the potassium chlorate was heated and oxygen evolved, the internal pressure in the retort and copper tube rapidly rose, and its amount was indicated by the gauge. When the stop-cock upon the end of the tube was opened, liquid oxygen was forcibly driven out in the form of a jet. In the method employed by Cailletet, the pressure to which the gas is subjected is obtained by purely mechanical means. The |