Simultaneously with Rankine and Clausius, Prof. William Thomson was engaged in researches in thermo-dynamics (1850). He was the first to express the principle of Carnot as adapted to the modern theory by Clausius in the now generally quoted propositions:[109]
1. When equal mechanical effects are produced by purely thermal action, equal quantities of heat are produced or disappear by transformation of energy.
2. If, in any engine, a reversal effects complete inversion of all the physical and mechanical details of its operation, it is a perfect engine, and produces maximum effect with any given quantity of heat and with any fixed limits of range of temperature.
William Thomson and James Thompson showed, among the earliest of their deductions from these principles, the fact, afterward confirmed by experiment, that the melting-point of ice should be lowered by pressure 0.0135° Fahr, for each atmosphere, and that a body which contracts while being heated will always have its temperature decreased by sudden compression. Thomson applied the principles of energetics in extended investigations in the department of electricity, while Helmholtz carried some of the same methods into his favorite study of acoustics.
The application of now well-settled principles to the physics of gases led to many interesting and important deductions: Clausius explained the relations between the volume, density, temperature, and pressure of gases, and their modifications; Maxwell reëstablished the experimentally determined law of Dalton and Charles, known also as that of Gay-Lussac (1801), which asserts that all masses of equal pressure, volume, and temperature, contain equal numbers of molecules. On the Continent of Europe, also, Hirn, Zeuner, Grashof, Tresca, Laboulaye, and others have, during the same period and since, continued and greatly extended these theoretical researches.
During all this time, a vast amount of experimental work has also been done, resulting in the determination of important data without which all the preceding labor would have been fruitless. Of those who have engaged in such work, Cagniard de la Tour, Andrews, Regnault, Hirn, Fairbairn and Tate, Laboulaye, Tresca, and a few others have directed their researches in this most important direction with the special object of aiding in the advancement of the new-born sciences. By the middle of the present century, the time which we are now studying, this set of data was tolerably complete. Boyle had, two hundred years before, discovered and published the law, which is now known by his name[110] and by that of Marriotte,[111] that the pressure of a gas varies inversely as its volume and directly as its density; Dr. Black and James Watt discovered, a hundred years later (1760), the latent heat of vapors, and Watt determined the method of expansion of steam; Dalton, in England, and Gay-Lussac, in France, showed, at the beginning of the nineteenth century, that all gaseous fluids are expanded by equal fractions of their volume by equal increments of temperature; Watt and Robison had given tables of the elastic force of steam, and Gren had shown that, at the temperature of boiling water, the pressure of steam was equal to that of the atmosphere; Dalton, Ure, and others proved (1800-1818) that the law connecting temperatures and pressures of steam was expressed by a geometrical ratio; and Biot had already given an approximate formula, when Southern introduced another, which is still in use.
The French Government established a commission in 1823 to experiment with a view to the institution of legislation regulating the working of steam-engines and boilers; and this commission, MM. de Prony, Arago, Girard, and Dulong, determined quite accurately the temperatures of steam under pressures running up to twenty-four atmospheres, giving a formula for the calculation of the one quantity, the other being known. Ten years later, the Government of the United States instituted similar experiments under the direction of the Franklin Institute.
The marked distinction between gases, like oxygen and hydrogen, and condensible vapors, like steam and carbonic acid, had been, at this time, shown by Cagniard de la Tour, who, in 1822, studied their behavior at high temperatures and under very great pressures. He found that, when a vapor was confined in a glass tube in presence of the same substance in the liquid state, as where steam and water were confined together, if the temperature was increased to a certain definite point, the whole mass suddenly became of uniform character, and the previously existing line of demarkation vanished, the whole mass of fluid becoming, as he inferred, gaseous. It was at about this time that Faraday made known his then novel experiments, in which gases which had been before supposed permanent were liquefied, simply by subjecting them to enormous pressures. He then also first stated that, above certain temperatures, liquefaction of vapors was impossible, however great the pressure.
Faraday’s conclusion was justified by the researches of Dr. Andrews, who has since most successfully extended the investigation commenced by Cagniard de la Tour, and who has shown that, at a certain point, which he calls the “critical point,” the properties of the two states of the fluid fade into each other, and that, at that point, the two become continuous. With carbonic acid, this occurs at 75 atmospheres, about 1,125 pounds per square inch, a pressure which would counterbalance a column of mercury 60 yards, or nearly as many metres, high. The temperature at this point is about 90° Fahr., or 31° Cent. For ether, the temperature is 370° Fahr., and the pressure 38 atmospheres; for alcohol, they are 498° Fahr., and 120 atmospheres; and for bisulphide of carbon, 505° Fahr., and 67 atmospheres. For water, the pressure is too high to be determined; but the temperature is about 775° Fahr., or 413° Cent.
Donny and Dufour have shown that these normal properties of vapors and liquids are subject to modification by certain conditions, as previously (1818) noted by Gay-Lussac, and have pointed out the bearing of this fact upon the safety of steam-boilers. It was discovered that the boiling-point of water could be elevated far above its ordinary temperature of ebullition by expedients which deprive the liquid of the air usually condensed within its mass, and which prevent contact with rough or metallic surfaces. By suspension in a mixture of oils which is of nearly the same density, Dufour raised drops of water under atmospheric pressure to a temperature of 356° Fahr.—180° Cent.—the temperature of steam of about 150 pounds per square inch. Prof. James Thompson has, on theoretical grounds, indicated that a somewhat similar action may enable vapor, under some conditions, to be cooled below the normal temperature of condensation, without liquefaction.