52 OUTLINES OF PHYSICAL CHEMISTRY
appeared, that is, the period of liquefaction is nil, and under a pressure of about 75 atmospheres there is no distinction between the liquid carbon dioxide and the gaseous carbon dioxide — that is, the critical state has been reached: temperature 31°, pressure 74*6 atmospheres, volume 0-00578 to 0-00821.
At temperatures higher than 81° no liquefaction can take place, and the curve represents entirely the gaseous condition.
Van der Waals's Equation. — If the behaviour of a gas is not exactly represented by hyperbola-isotherms, and by the equation pv = rt, this is probably due to two causes :
1. The apparent volume of a gaseous mass is partly occupied by the material of the molecules. The free space in which the molecular movements can take place is
2. The attraction which exists between the gaseous molecules is very much weakened by the distance across which it acts ; however, it is not nil, and for the gaseous state just as for the other states of matter we must assume either a surface tension or a certain degree of cohesion. There exists, therefore, a certain force, caused by the molecular attractions, which, in conjunction with the external pressure, tends to stop the expansion of a gaseous mass and limit its volume. Van der Waals assumes that this supplementary forcd is inversely propor- tional to the square of the volume occupied by the gas, and
its general expression is ^
1 According to I, Traube, and in agreement with Van der Waals's ideas, the value of b would correspond to the vibratory volumes of the atoms contained in the gaseous molecule, and would generally be 4 to 3*5 times as great as the sum of the material volumes occupied by the atom-nuclei.
2 It is generally admitted that gases, like liquids, have a certain surface tension ; the molecules of the very thin surface layer are attracted by the neighbouring molecules, and there is no counter- balancing attraction from without. Now if we increase the total volume of the gas n times, then there will be, in a certain definite
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