Another method, which appears simpler at first sight, but re quires equivalent integrations, is to find a consistent expression for the entropy from those for H and V, by integrating (dH/T)—a(V/T)dP= dQ/T. The value of TcI).—H for the va pour is then equated to the Gibbs' function (i6) for the liquid. This necessarily gives the same result as integrating Clapeyron's equation in the form (12). It was also found that, if an equation of the van der Waals type, giving consistent values of H and V for the vapour, were combined with equation (II) for the liquid (instead of assuming the same equation for liquid and vapour), the combination would give much better results for L, and even for p itself, than Clausius' method. This afforded fur ther presumptive evidence in favour of (I I) as a suitable equation for the liquid.
The probability of this solution was first suggested by measure ments of the saturation volumes of water and steam in sealed tubes of quartz-glass, which showed that the meniscus vanished at C, and that the densities did not become equal at this point, as commonly assumed, but were 0.438 gm./c.c. for the liquid and
0.264 gm./c.c. for the vapour. Moreover, the difference of density could be traced nearly up to 38o° C, with suitable illumination, under favourable conditions, and the coefficients of expansion remained finite. These phenomena could not be reconciled with van der Waals's theory, but could be represented satisfactorily by the modified equation (17) with the series c/( — V) in place of c. Many other stable liquids showed similar effects when carefully purified, but the equilibrium under these critical conditions might be completely upset by small traces of air or other impurities. In order to complete the proof, it was necessary to measure the total heats of both water and steam in the critical region. This had not previously been attempted, owing to grave experimental difficulties, but was successfully accomplished by the jacketed condenser method as described in the article CALORIMETRY. H-P Diagram for Steam.—The application of the method described above proved to be less troublesome than in the case of water, because no air cushion was required to protect the gauge from vibration, since the steam itself acted as a perfect cushion, and the gauge readings were always steady. It was most important however to keep a continuous check on the purity of the water, and especially on the absence of air, which appeared to have a profound effect on the attainment of true equilibrium between the complex molecules at high pressures near the critical point. The apparatus required for eliminating air was very simple and effective. The water for supplying the pump was passed through two boilers in series, which were kept boiling with a free escape of steam. Before reaching the first boiler the water was heated nearly to the boiling point by passing, through a regener ator. Most of the air was carried off with the steam from the first boiler, the remainder, to a very small fraction, was eliminated by the second. The air-free water then returned through the re generator, and was further cooled to atmospheric temperature before being delivered to the pump. With ordinary distilled water, which may contain from a tenth to a twentieth of its volume of air at atmospheric pressure (about I part in i0,000 by weight) an almost continuous stream of bubbles could be observed issuing with the condensate through the glass inspection tube attached to the outlet ‘of the condenser. It was impossible under these con ditions to obtain consistent values of H owing to accidental fluc tuations in the air content of the water. With the air-free ap paratus in action, not a single bubble could be seen in the course of an hour's run, and the observations near saturation became incredibly more consistent. The elimination of air appeared to be just as important as in the case of the observations on the satura tion volumes in the quartz tubes by the static method. It was also important to keep the fluid in the superheater at a steady tempera ture for a sufficient time to permit the attainment of true equi librium before passing into the high-pressure pocket where its initial temperature and pressure were measured. It was then throttled to atmospheric pressure before entering the condenser, where' its total heat was measured by observing the rise of tem perature of a steady stream of cooling water, and deducing the increase of total heat as explained in the article CALORIMETRY. The results thus obtained on the basis of the above are ex hibited in the annexed figure 3, in which the observed values of the total heats are plotted against the pressure, and the tempera tures are indicated by isothermal lines. The observations of H and h confirmed those of the saturation volumes by showing that the saturation lines for water and steam could be traced beyond C and appeared to meet in a sharp cusp tangential to the isothermal of 380.5° C, which made an abrupt bend at this point, and became parallel to the lower isothermals of water, showing that all the active molecules of steam were condensed. Taking V —b from the modified equation (i7), the observed values of H for dry steam were found to agree with the fundamental relation, H—B= (i3/3)aP(V—b)-FabP, (19) as required by the equation for the adiabatic. (See THERMO DYNAMICS.) The observations of h for the liquid verified equation (I I), which explains the peculiar form of the water saturation line, since it requires that the active molecules of steam in the liquid must be condensed with increase of pressure at the same rate per unit volume as in the vapour.