392 



NA TURE 



[Mar. 19, 1874 



TNE CASEOUS, LI(2UID, AND SOLID STATES 

 OF WATER-SUBSTANCE* 



IN two communicatiors made by me lo the British Association 

 at its meetings at Edinburgli in 1S71, and at Brighton in 1S72, 

 and printed as abstracts in the Transactions of the Sections for 

 those years, considerations wtie adduced on relations between 

 the gaseous, the liquid, and the soHd states of matter. The new 

 subject of the present paper constitutes a furtlier development of 

 some of those previous considerations, and a brief sketch of these 

 is necessary here as an iDtroduction for rendering intelligible 

 what is to follow. 



Taking into consideration any substance which we can have 

 in the three states, gaseous, liquid, and solid, we may observe 

 that when any two of these states are present in contact together, 

 the pressure and temperature are dependent each on the other, 

 so that when one is given the other is fixed. Then if we denote 

 o-eometrically all possible points of temperature and pressure 

 jointly by points spread continuously in a plane surface, each 

 point in the plane being referred to two axes of rectangular co- 

 ordinates, so that one of its ordinates shall represent the tempe- 

 rature and the other the pressure denoted by that point, we may 

 notice that there will be tliree curves, one expressing the relation 

 between temperature and pressure for gas with liquid, another 

 expressing that for gas with solid, and another expressing that 

 for liquid with solid. These three curves, it appears, must all 

 meet or cross each other in one point of pressure and temperature 

 jointly, which may be called the triple-point. The triple-point, 

 considered in respect to its temperature, is in fact what would 

 often be called the freezing point in -'acuo ; that is, the freezing 

 temperature of water in contact with no gas except its own 

 aqueous vapour or steam ; and the pressure at the triple point is 

 just the pressure of that aqueous gas or steam. 



The curve between gas and liquid, which may be called the 

 boiUn«-line, will be a separatmg boundary between the regions of 

 the plane corresponding to the ordinary liquid and those corre- 

 sponding to the ordinary gaseous state. But by consideration of 

 Dr. Andrews's experimental results ("Phil. Trans.," 1S69) 

 we may see that this separating boundary comes to an end at a 

 point of temperature and pressure wliich, in conformity witli 

 his language, may be called the a-ilual point of pressure and 

 temperature jointly ; and we may see that, from any liquid state 

 to any gaseous state, the transition may be gradually effected by 

 an infinite variety of courses passing round the extreme end of 

 the boiling-line. 



The accompanying figure serves to illustrate these considera- 

 tions in reference to transitions between the three states, the 

 gaseous, the liquid, and the solid. The figure is intended only 

 as a sketch to illustrate principles, and is not drawn according 

 to measurements for any ]iarticular substance, though the main 

 features of the curves shown in it are meant to relate in a 

 general way to the substance of water, steam, and ice. A X 

 and A Y are the axes of coordinates for the temperatures and 

 pressures respectively ; A, the origin, being taken as the zero 

 for pressures and as the zero for temperatures on the Centigrade 

 scale. The curve L represents the bciling-linL- terminating in 

 the critical point K. The line T M represents the line between 

 liquid and solid. It is drawn showing in an exaggerated degree 

 the lowering of the freezing temperature of water by pressure ; 

 the exaggeration being necessary to allow small changes of 

 temperature to be perceptible in the diagram. The line T N 

 represents the line between tlie gaseous and the solid states of 

 water-substance. The line L T N appears to have been gener- 

 ally (in the discussion of experimental results on the pressure of 

 aqueous vapour above and below the freezing-point) regarded as 

 one continuous curve ; but it was part of my object in the two 

 British- Association papers referred to, to show that it ought to 

 be considered as two distinct curves (L T P and N T Q) crossing 

 each other in the triple-point T. 



In the second of the two British-Association papers already 

 referred to (the one read at the Brighton meeting, 1872), I gave 

 demonstrations showing that these two curves L T and N T 

 should meet, as shown in the accompanying figure, with a re- 

 entrant angle at T, not with a salient angle such as is exempli- 

 fied in the vertex of a pointed arch ; and offered in conclusion 

 the suggestion that the reasoning which had been adduced 



• " A Quantitative Investigation of cerlain ReKitions between the Gaseous, 

 the Liquid, and the Solid .States of Water-Substance." By Prof. James 

 Thomson, LL.D., lately of Queen's College, Belfast, now of the University 

 of Glasgow. Communicated to the Royal Society by Sir William Thomson, 

 LL.D., F.R.S. Abridged for Nature by the Author. 



might be followed up by a quantitative calculation founded on 

 experimental data, by which calculation the difference of the 

 pressures of steam with water, and steam willi ice for any given 

 temjieratiire very near the triple point, may be found with a very 

 close approximation to the truth. 



In the month of October 1872 I explained to my brother. Sir 

 William Thomson, the nature of that contemplated quantitative 

 calculation : I mentioned to him the method which I had pre- 

 pared for carrying out the intended investigation, and inquired 

 of him for some of the experimental data, or data already 

 deduced by theory from experiments, which I was seeking to 

 obtain. On his attention being thus turned to the nutter, he 

 noticed that the desired quantitative relation could be obtained 

 very directly and easily from a simple formula which he had 

 given in his paper on the Dynamical Theory of Heat, "Transac- 

 tions of the Royal Society of Edinburgh," March 17, 1S51, § 21 

 (3), to express the second law of thermodynamics for a body of 

 uniform temperature throughout, exposed to pressure equal in 

 all directions. 



That formula is 



;l--^ 



dp 



in which p denotes the amount of the pressure, and ... 



rate o( increase per unit increase of temperature, the volume 

 being kept constant ; C denotes Carnot's function ; and M 

 denotes the rate of absorption at which lieat must be supplied to 



the subsUance per unit augmentation of volume, to let it expand 

 without varjing in temperature. The body may be either 

 homogeneous throughout, as a continuous solid, or liquid, or 

 gas ; or it may be heterogeneous, as a mass of water and aqueous 

 vapour (i.e. steam), or ice and water, or ice and aqueous vapour 

 {i.e. steam). 



Now apply that formula, 1st, to steam with wa'er, and 2nd, 

 to steam with ice, the temperature of the hetcrogenenus body in 

 each case being that of the triple-point, or we may (or tlie pre- 

 sent purpose say 0° C, which is almost exactly the same. It 

 is to be observed that while in the genetal application of the 

 formula the rate of increase of the pressure with increase of tem- 

 perature, 'luhen the volume is kept constant, has been denoted by 



-f', yet in each of the two particular case? r.ow brought under 



consideration it is a matter of indifference whether the volume 

 be kept constant or not ; because the pressure of steam in con- 

 tact either with water or with ice, for any given temperature, is 

 independent of the volume of the whole heterogeneous body ; so 

 that the chanije of pressure for change of temperature is inde- 

 pendent of whether there be change of voluire or not. As C is 

 a function of tlie temperature "which has the same value for all 

 substances at the same temperature, it has the same value for 

 the two cases now under consideration. Hence, retaining for 

 the first case (that, namely, of steam with water) the same nota- 

 tion as before, but modifying it by the use of an accent where 

 distinction is necessary in the second ease (that of steam with 



ice), and thus using y to denote the rate of increase of the 

 pressure per unit increase of temperature for steam with wate 



