412 PRESSURE OF CONDENSED GASES. [196. cement. The cold bath was applied at the curvature. When pressure was requisite, it was obtained by the employment of two con FIG. 152. densing syringes; the first had a piston of an inch in diameter, the second one of only half an inch; these syringes were connected by a pipe, so that the first syringe forced the gas through the valves of the second; and the second syringe was then used to compress still more highly the gas which had already been condensed by the action of the first, with a pressure varying from ten to twenty atmospheres.* Natterer obtained a still more intense degree of cold than that produced by carbonic anhydride and ether in vacuo, by mixing liquid nitrous oxide with carbonic disulphide and placing the bath in vacuo; the lowest temperature which he has recorded is — 220° ( — 140° C.). Silicic fluoride, at this point, became a transparent solid, but liquid chlorine and carbonic disulphide preserved their fluidity. (Liebig's Ann. 1845, liv. 254.) (197) Pressure exerted by Condensed Gases.-In order to estimate the pressure of the condensed gas in the vessel in which it was contained, Faraday made use of small air-gauges, which he FIG. 153. enclosed in the tubes employed for the condensation (fig. 153). These gauges consisted of a somewhat conical capillary tube of glass, which was divided into parts of equal volume by introducing into the tube a globule of mercury shown at a, and causing it to occupy each part of the tube in succession: the length of the little cylinder into which the mercury was reduced in each portion of the tube was marked upon the glass with black varnish. The mercury was then transferred towards the widest extremity, * The temperatures recorded in these experiments are in all probability somewhat too high. They were estimated by means of a spirit thermometer, divided into degrees below 32° F., 'equal in capacity to those between 32° and 212°;' but the contraction of alcohol is more rapid at low than at high temperatures: at the lowest temperatures attained, the alcohol became somewhat viscid. 197.] FAILURE OF BOYLE'S LAW AT GREAT PRESSURES. 413 and the tube was sealed at its narrow end. A known quantity of air was thus included, and, by the compression which this air experienced in the course of the experiment (the volume being inversely as the pressure), the pressure of the gas under examination was easily calculated. It is remarkable that many of these condensed liquids expand upon the application of heat more rapidly than the gases themselves. It has been also found that Boyle's law (27), that the volume of a gas varies in the inverse ratio of the external pressure, is only approximately true in the ordinary gaseous state. The general law connecting pressure and volume, according to the recent experiments of Andrews on carbonic anhydride, is expressed by the equation v (1 − p v) =c, where v is the volume of the gas, p the external pressure, and c a constant for a given temperature. It follows that for homologous points, at which p v=p' v', in any two given isothermals, the ratio of the external pressures is constant (Phil. Trans. 1876, 444, 447). See also notes, pages 50 and 293.* Although indications of this departure from Boyle's law have been observed at common temperatures with some of the more condensible gases, such as sulphurous anhydride, sulphuretted hydrogen, cyanogen, and ammonia, it was most distinctly exhibited in the experiments of Cagniard de La Tour (Ann. Chim. Phys. 1822, xxi. 127, 178, and 1823, xxii. 410). De La Tour partially filled some strong glass tubes with water, with alcohol, with ether, and with some other liquids, furnished them with gauges, and sealed them hermetically. He then cautiously raised the temperature. The alcohol (density o'844), which occupied the capacity of the tube, gradually expanded to double its volume, and then suddenly disappeared in vapour, at a temperature of 497°7 (258°7 C.); it then had a pressure of about 119 atmospheres. Ether became gaseous at 392° (200° C.), in a space less than double its original volume, having a pressure of 37'5 atmospheres; whereas, if Boyle's law held good in these cases, calculating from the volume of vapour which a certain bulk of each liquid yields under the atmospheric pressure, ether should have exerted a pressure equal to about 190 atmospheres, and alcohol of at least 300. Water was found to become gaseous in a space equal to about four times its original volume, at a temperature of about 773° (412° C.), (that of melting zinc). So great was the solvent * The experiments of Fairburn and Tate on the pressure of superheated steam (Phil. Trans. 1860, 190) show that this diminution of elasticity near the point of condensation is very appreciable in the case of aqueous vapour. 414 EXPANSION OF LIQUIDS AND VAPOURS UNDER PRESSURE. [197. power of water on glass, at this high temperature, that the addition of a little sodic carbonate was necessary to diminish the action on the glass, which frequently gave way until this expedient was adopted. As the vapours cooled, a point was observed at which a sort of cloud filled the tube, and, in a few moments after, the liquid suddenly reappeared. It will be seen from the subjoined Table, that even after the liquid has wholly disappeared, the increase in the pressure of the vapour, as the temperature rises, is as rapid as before it had all volatilized, and indeed it continues to increase at a rate far greater than that which would be produced in air by an equal elevation of temperature. Atmospheric air, under a pressure of 375 atmospheres at 370° (188° C.) would at 482° (250° C.), have a pressure of 425, and at 617° (325° C.) of 48.6 atmospheres, whereas the corresponding pressures with ether were 863 and 1309 atmospheres. In the case of the two experiments with ether, the increase in pressure is greatest at first in the tube which contains At this point the liquid had entirely disappeared as vapour. 197.] CRITICAL POINT. 415 the smallest proportion of liquid; probably because the influence of cohesive attraction is more completely overcome in the tube which admits of the greatest distance between the particles of the vapour, though at higher temperatures the pressure increases less rapidly in this tube than in the other. Space must always be allowed for the full expansion of the liquid, otherwise the strongest vessels will give way. Andrews has observed, that on partially liquefying carbonic anhydride by pressure alone, in his apparatus, and gradually raising at the same time the temperature to 88° (31° C.), the surface of demarcation between the liquid and gas became fainter, lost its curvature, and at last disappeared. The space was then occupied by a homogeneous fluid, which exhibited, when the pressure was suddenly diminished or the temperature slightly lowered, a peculiar appearance of moving or flickering striæ throughout its entire mass. At temperatures above 31° C., no apparent liquefaction of carbonic anhydride or separation into two distinct forms of matter could be effected, even when a pressure of 300 or 400 atmospheres was applied, and, in consequence, Andrews calls temperature of 31° (or more accurately 30°92) the critical point for carbonic anhydride. If a quantity of carbonic anhydride at the temperature of 31°1 be submitted to pressure, its volume diminishes regularly until the pressure reaches 73 atmospheres ; a slight increase of pressure now causes a rapid diminution of volume, but without any appearance of liquefaction. If the experiment be repeated at higher temperatures, the pressure at which this sudden contraction takes place will be found to be higher and higher until at 48°1 the sudden contraction has disappeared, and the volume diminishes regularly as in the case of a permanent gas, though at a more rapid rate. Nitrous oxide gave analogous results.* From the foregoing experiments, it is obvious that there exists for every liquid a temperature at which no amount of pressure is sufficient to retain it in the liquid form. It is not surprising, therefore, that mere pressure, however great, should fail to liquefy many of the bodies which usually exist in the form of gases. The following Table embodies the results obtained by Faraday on the condensation and solidification of the gases. The solids were usually denser than the liquid portions from which they separated. *Information by letter from Dr. Andrews, since published as the Bakerian Lecture of 1869. (Proc. Roy. Soc. 1869, xviii. 42, and Phil. Trans. 1869, The diagram on the opposite page (fig. 154) shows the curves indicating the increase of pressure with the temperature, from Faraday's tables. In this diagram, the vertical lines represent the degrees of temperature on Fahrenheit's scale; the horizontal lines show the pressure in atmospheres exerted by the condensed gas. The numbers attached to each curve correspond to the gases in the following order : 1. Boric Fluoride. 2. Carbonic Anhydride. 5. Arseniuretted Hydrogen. 6. Hydriodic Acid. 7. Ammonia. 8. Cyanogen. 9. Sulphurous Anhydride. 10. Nitrous Oxide. II. Olefiant Gas. Faraday remarks, that as far as his observations go, 'it would appear that the more volatile a body is, the more rapidly does the force of its vapour increase by further addition of heat, commencing at a given point of pressure; for all these, for an increase of pressure from two to six atmospheres, the following number of degrees require to be added for the different bodies named:Water, 69° F.; sulphurous acid, 63°; cyanogen, 64°·5; ammonia, 60°; arseniuretted hydrogen, 54°; sulphuretted hydrogen, 56°5; muriatic acid, 43°; carbonic acid, 32°5; nitrous oxide, 30°. (Phil. Trans. 1845, 176.) The pressures indicated by the curves in fig. 154, after all, are probably only approximations. The experiments of Cagniard de La Tour show that under these enormous pressures the volume which the liquid bears to the space in which it is confined has a |