Ice waler 



vapoui 



vapour 



THERMODYNAMICS OF CHANGE OF STATE, ETC. 309 



Taking 1 atmosphere as 1014000 dynes/cm., this gives 134 atmo- 

 spheres as the pressure required to produce a lowering of 1 C., or the 

 lowering per atmosphere is -0074 0. 



This result, due to James Thomson, was confirmed by Lord Kelvin 

 (Phil. Mag, [3] xxxvii., 1850, p. 123). He used a strong glass piezometer, 

 in which was a mixture of ice and water. A manometer and a sensitive 

 thermometer enclosed in an outer tube were inserted in the piezometer, 

 and when the pressure was increased a mean lowering of -00735 per 

 atmosphere was obtained. 



Other experiments have already been described in chap. xii. 



The Triple Point and the Difference of Vapour- Pressures of Ice and 

 Water below 0. When ice and water are at the melting-point under 

 the pressure of their vapour alone, that point is above C. by about 

 0'0074, since the vapour-pressure is less than 5 mm. or nearly an atmo- 

 sphere less than 1 atmosphere. At this point it is easily shown that the 

 vapour-pressures of ice and water are exactly equal, by taking the 

 substance through a " one temperature " reversible cycle, or a cycle in 

 which the temperature is throughout the same. Since the cycle is 



reversible, \-fr Qi and if 6 is constant lcZQ = 0, or the total heat 



given is zero. Then the total external work done is zero. Now 

 imagine some such apparatus as that 

 in Fig. 173, where ice and water 

 at this melting-point, + 0-0074 C., 

 are in contact through the pipe re- 

 presented in the lower part of the 

 figure, and let all be maintained at one 

 temperature. Suppose, if possible, 

 that ice-vapour has a greater pressure 

 than water-vapour. Then, in allowing FIG. 173. 



ice -vapour to expand into water- 

 vapour, it will do work. Allow this expansion to take place isothermally 

 and reversibly through an engine in the pipe represented in the upper 

 part of the figure. Then the ice will continually give off vapour which 

 can be passed through the engine, where its pressure is reduced to that 

 of water-vapour. It will then condense on the water surface, and the 

 excess of water can freeze on to the lower surface of the ice. Here 

 is a reversible cycle which can continue endlessly, giving off work 

 through the engine. But this is contrary to the principle that the total 

 work must be zero. Then our supposition is wrong, and the vapour- 

 pressure of the ice cannot be different from that of the water. 



At this point, -0074 0., ice, water, and their vapour are all in 

 equilibrium with each other at the same pressure. The three states or 

 the three " phases" can co-exist without changing from one to another. 

 The point is therefore called the triple point. 



If we use a temperature -pressure diagram, as in Fig. 174, T will 

 represent the triple point, TA the vapour-pressure of water above the 

 temperature of the triple point, TB the vapour-pressure of ice below that 

 temperature, TO the line giving the relation between melting-point and 

 pressure a line going up very nearly vertically, sloping in fact only 

 0074 per atmosphere. 



