Johannes Diderik van der Waals

“ For substances with a small polymerization heat the degree of association will continually decrease if we move along the border-curve on the side of the saturated vapour in the direction towards lower T. With this, it is perfectly compatible that for such substances the saturated vapour, e.g. under the pressure of one atmosphere, should show an almost normal density. Saturated vapour of water at 100° has a density which seems nearly 4% greater than the theoretical one, an amount which is greater than can be ascribed to the deviation from the gas-laws. ”

“ At any rate, as a solid body evaporates only on the surface, and solid gases are bad conductors of heat, further cooling will only take place very slowly, and will scarcely neutralize the influx of heat. If the pressure p3 is very small, it is perhaps practically impossible to reach T3; if so, T3 in the following lines will represent the temperature practically attainable. There is thus for every gas a limit below which it is not to be cooled further, at least not in this way. ”

“ If we confine ourselves to temperatures between Tc and T3, the gas will pass into a liquid if the pressure is sufficiently increased. When the formation of liquid sets in we call the gas a saturated vapour. If the decrease of volume is continued, the gas pressure remains constant till all the vapour has passed into liquid. The invariability of the properties of the phases is in close connexion with the invariability of the pressure (called maximum tension) . Throughout the course of the process of condensation these properties remain unchanged, provided the temperature remain constant ”

“ We must attribute extension to the molecules, and they will attract one another with a force which quickly decreases with the distance. Even those suppositions which reduce molecules to centra of forces, like that of Maxwell, lead us to the result that the molecules behave in mutual collisions as if they had extension—an extension which in this case is not constant, but determined by the law of repulsion in the collision, the law of the distribution, and the value of the velocities. ”

“ If we take the value 2Tc for T1, as we may approximately for air when we begin to work with the apparatus, we find for p1 about 8pc, or more than 300 atmospheres. If we take T1 = Tc, as we may at the end of the process, we find p1 = 2.5pc, or 100 atmospheres. The constant pressure which has been found the most favourable in Linde’s apparatus is a mean of the two calculated pressures. In a theoretically perfect apparatus we ought, therefore, to be able to regulate p1 according to the temperature in the inner spiral. ”

“ The pressure required to condense a gas varies with the temperature, becoming higher as the temperature rises. The highest pressure will therefore be found at Tc and the lowest at T3. We shall represent the pressure at Critical pressure. Tc by pc. It is called the critical pressure. The pressure at T3 we shall represent by p3. It is called the pressure of the triple point. The values of Tc and pc for different substances will be found at the end of this article. The values of T3 and p3 are accurately known only for a few substances. ”

“ As an approximate half-empirical formula for the calculation of the pressure, −log10 p/pc = f (Tc – T) /T) may be used. It would follow from the law of corresponding states that in this formula the value of f is the same for all substances, the molecules of which do not associate to form larger molecule-complexes. In fact, for a great many substances, we find a value for f, which differs but little from 3, e.g. ”

“ Its own expansion is sufficient, provided the initial Cooling by expansion. condition be properly chosen, and provided we take care, even more than in the former method, that there is no influx of heat. Those conditions being fulfilled, we may, simply by adiabatic expansion, not only lower the temperature of some substances down to T3, but also convert them into the liquid state. This is especially the case with substances the molecules of which contain few atoms.
Let us imagine the whole net of isothermals for homogeneous phases drawn in a pv diagram, and in it the border-curve. ”

“ When cp/cv = k (the limiting value of cp/cv for infinite rarefaction is meant) approaches unity, the isentropic curves approach the isothermals and vice versa. In the same way the critical point of the isentropic curves comes nearer to that of the isothermals. ”

“ According to the investigations of Sydney Young, this holds good with a high degree of approximation for a long series of substances. Important deviations from this rule for the values of vv/vl are only found for those substances in which the existence of association has already been discovered by other methods. ”

“ Thus it would follow from the given equation that pcvc/Tc = 3/8 pv/T, if the value of v is taken so great that the gaseous laws may be applied, whereas Sydney Young has found 1/3.77 for a number of substances instead of the factor 3/8. ”