# Andrews Fig 2-A James Thomson Isothermal B Isothermals of Co

## equation, water, values, steam, air, liquid, vapour, molecules, pressures and method

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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.

## Modified Joule-Thomson Equation.

The modification (6) of Rankine's equation which was adopted by Joule and Thom son to represent the deviations of gases from the ideal state, proved more convenient in practice than that of van der Waals, because it gave V directly in terms of P and T, instead of giving P as a cubic function of V, and also gave a much better account of the properties of CO2 at moderate pressures. In applying the same equation to steam and other gases and vapours (Proc. R.S. June 1900, Phil. Mag. Jan. 1903) it was put in the more general form, in which b is the covolume as in van der Waals's equation, and c represents the reduction of volume due to coaggregation or pair ing of molecules. To a first approximation, c is a function of the temperature only, as in the original Joule-Thomson equation (6), but it may vary with temperature in different ways for molecules of different types. Thus in the case of steam, in order to satisfy the adiabatic equation, P/T13/3 = constant, cP/T must be constant along any adiabatic, in which case c must vary as The value of c was determined by the throttling method on this as sumption, and found to be 26.3 c.c./gm. at 'co° C. The equation in this simple form gave very convenient expressions for the total heat H, and the entropy cl) of the dry vapour. (See THERMO DYNAMICS.) When taken in conjunction with equation (16) for the liquid, it appeared that the effect of coaggregation on the sat uration pressures could be represented by simply adding the term a(c—b)p/RT to Rankine's theoretical equation (4) for an ideal vapour, which was about 1.5% in error at ioo° C without this addition, though agreeing closely with observation at low pres sures. The addition of the term required by (i8) to represent the coaggregation, brought the values of p into good agreement with Regnault's cbservations up to 200° C. Beyond this point the values of p given by the modified equation (4) began to deviate gradually from observation, until they were about 15% too small at 365° C according to the observations of Cailletet and Colar deau. It was evident that the first approximation, represented by c, though very good at moderate pressures, or at high superheats, would necessarily fail at high pressures near saturation, because it took no account of the higher degrees of coaggregation due to the combination of the complex molecules with each other. This effect could most easily be represented by employing, in place of c for the coaggregation, a series of the form, etc. . . . )=c/(i—Z) (i8) representing a geometrical progression with first term c and corn mon ratio Z, where Z = kcP/T, being proportional to the mass of the coaggregated molecules present in the vapour. It was found however that, in order to represent the values of p satisfactorily at pressures up to zoo lb., the second term Z in this series must be absent, and that the common ratio should be instead of Z, giving the sum of the series in the form c/(i —Z'). This was con firmed by the observations on the values of V up to the critical point described in the preceding section. Unfortunately the value FIG. 6 of Z thus found would not necessarily give correct values of H, unless the adiabatic equation, which required an expression of this type for the coaggregation, remained true up to the critical point. No values of H were at that time available beyond C, and the series suggested by the observations of V was quite incon sistent with the orthodox theory of the critical state, which could not be questioned without the most conclusive experimental evi dence. The only practicable method of verifying the adiabatic at such high pressures would be to measure the values of H and h, in addition to those of V and v, which would be a very laborious and expensive undertaking.

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.

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