At the same time (1879) as Pictet was working on the liquefaction of gases in Switzerland, Cailletet, in Paris, was occupied on the same subject, and his results, although not so convincing as Pictet's, still showed that the majority of gases, previously unliquefied, were capable of passing into a liquid state. Cailletet subjected gases to a pressure of several hundred atmospheres in narrow thick-walled glass tubes (fig. [25]); he then cooled the compressed gas as far as possible by surrounding it with a freezing mixture; a cock was then rapidly opened for the outlet of mercury from the tube containing the gas, which consequently rapidly and vigorously expanded. This rapid expansion of the gas would produce great cold, just as the rapid compression of a gas evolves heat and causes a rise in temperature. This cold was produced at the expense of the gas itself, for in rapidly expanding its particles were not able to absorb heat from the walls of the tube, and in cooling a portion of the expanding gas was transformed into liquid. This was seen from the formation of cloud-like drops like a fog which rendered the gas opaque. Thus Cailletet proved the possibility of the liquefaction of gases, but he did not isolate the liquids. The method of Cailletet allows the passage of gases into liquids being observed with greater facility and simplicity than Pictet's method, which requires a very complicated and expensive apparatus.
The methods of Pictet and Cailletet were afterwards improved by Olszewski, Wroblewski, Dewar, and others. In order to obtain a still lower temperature they employed, instead of carbonic acid gas, liquid ethylene or nitrogen and oxygen, whose evaporation at low pressures produces a much lower temperature (to -200°). They also improved on the methods of determining such low temperatures, but the methods were not essentially altered; they obtained nitrogen and oxygen in a liquid, and nitrogen even in a solid, state, but no one has yet succeeded in seeing hydrogen in a liquid form.
The most illustrative and instructive results (because they gave the possibility of maintaining a very low temperature and the liquefied gas, even air, for a length of time) were obtained in recent years by Prof. Dewar in the Royal Institution of London, which is glorified by the names of Davy, Faraday, and Tyndall. Dewar, with the aid of powerful pumps, obtained many kilograms of oxygen and air (the boiling point under the atmospheric pressure = -190°) in a liquid state and kept them in this state for a length of time by means of open glass vessels with double walls, having a vacuum between them, which prevented the rapid transference of heat, and so gave the possibility of maintaining very low temperatures inside the vessel for a long period of time. The liquefied oxygen or air can be poured from one vessel into another and used for any investigations. Thus in June 1894, Prof. Dewar showed that at the low temperature produced by liquid oxygen many substances become phosphorescent (become self-luminous; for instance, oxygen on passing into a vacuum) and fluoresce (emit light after being illuminated; for instance, paraffin, glue, &c.) much more powerfully than at the ordinary temperature; also that solids then greatly alter in their mechanical properties, &c. I had the opportunity (1894) at Prof. Dewar's of seeing many such experiments in which open vessels containing pounds of liquid oxygen were employed, and in following the progress made in researches conducted at low temperatures, it is my firm impression that the study of many phenomena at low temperatures should widen the horizon of natural science as much as the investigation of phenomena made at the highest temperatures attained in the voltaic arc.
[33] The investigations of S. Wroblewski in Cracow give reason to believe that Pictet could not have obtained liquid hydrogen in the interior of his apparatus, and that if he did obtain it, it could only have been at the moment of its outrush due to the fall in temperature following its sudden expansion. Pictet calculated that he obtained a temperature of -140°, but in reality it hardly fell below -120°, judging from the latest data for the vaporisation of carbonic anhydride under low pressure. The difference lies in the method of determining low temperatures. Judging from other properties of hydrogen (see Note [34]), one would think that its absolute boiling point lies far below -120°, and even -140° (according to the calculation of Sarrau, on the basis of its compressibility, at -174°). But even at -200° (if the methods of determining such low temperatures be correct) hydrogen does not give a liquid even under a pressure of several hundred atmospheres. However, on expansion a fog is formed and a liquid state attained, but the liquid does not separate.
[34] After the idea of the absolute temperature of ebullition (tc, Note [29]) had been worked out (about 1870), and its connection with the deviations from Mariotte's law had become evident, and especially after the liquefaction of permanent gases, general attention was turned to the development of the fundamental conceptions of the gaseous and liquid states of matter. Some investigators directed their energies to the further study of vapours (for instance, Ramsay and Young), gases (Amagat), and liquids (Zaencheffsky, Nadeschdin, and others), especially to liquids near tc and pc; others (Konovaloff and De Heen) endeavoured to discover the relation between liquids under ordinary conditions (removed from tc and pc) and gases, whilst a third class of investigators (van der Waals, Clausius, and others), starting from the generally-accepted principles of the mechanical theory of heat and the kinetic theory of gases, and assuming in gases the existence of those forces which certainly act in liquids, deduced the connection between the properties of one and the other. It would be out of place in an elementary handbook like the present to enunciate the whole mass of conclusions arrived at by this method, but it is well to give an idea of the results of van der Waals' considerations, for they explain the gradual uninterrupted passage from a liquid into a gaseous state in the simplest manner, and, although the deduction cannot be considered as complete and decisive (see Note [25]), nevertheless it penetrates so deeply into the essence of the matter that its signification is not only reflected in a great number of physical investigations, but also in the province of chemistry, where instances of the passage of substances from a gaseous to a liquid state are so common, and where the very processes of dissociation, decomposition, and combination must be identified with a change of physical state of the participating substances, which has been elaborated by Gibbs, Lavenig, and others.
For a given quantity (weight, mass) of a definite substance, its state is expressed by three variables—volume v, pressure (elasticity, tension) p, and temperature t. Although the compressibility—[i.e., d(v)/d(p)]—of liquids is small, still it is clearly expressed, and varies not only with the nature of liquids but also with their pressure and temperature (at tc the compressibility of liquids is very considerable). Although gases, according to Mariotte's law, with small variations of pressure, are uniformly compressed, nevertheless the dependence of their volume v on t and p is very complex. This also applies to the coefficient of expansion [= d(v)/d(t), or d(p)/d(t)], which also varies with t and p, both for gases (see Note [26]), and for liquids (at tc it is very considerable, and often exceeds that of gases, 0·00367). Hence, the equation of condition must include three variables, v, p, and t. For a so-called perfect (ideal) gas, or for inconsiderable variations of density, the elementary expression pv = Ra(1 + at), or pv = R(273 + t) should be accepted, where R is a constant varying with the mass and nature of a gas, as expressing this dependence, because it includes in itself the laws of Gay-Lussac and Mariotte, for at a constant pressure the volume varies proportionally to 1 + at, and when t is constant the product of tv is constant. In its simplest form the equation may be expressed thus:
pv = RT;
where T denotes what is termed the absolute temperature, or the ordinary temperature + 273—that is, T = t + 273.
Starting from the supposition of the existence of an attraction or internal pressure (expressed by a) proportional to the square of the density (or inversely proportional to the square of the volume), and of the existence of a real volume or diminished length of path (expressed by b) for each gaseous molecule, van der Waals gives for gases the following more complex equation of condition:—
(p + a / v2 )(v - b) = 1 + 0·00367t;