S10 



HEAT. 



The three included regions may then be marked vapour, water, ice 

 respectively. If we have all three states or phases present, T is the only 

 point of equilibrium, and the system is said to be non-variant. 



If, however, we have two phases only, say water and vapour, we may 

 have equilibrium anywhere along TA. We can vary the temperature, 

 but given any one value of the temperature the pressure is fixed. The 

 system is therefore said to be monovariant. 



If we have only one phase present, as water, we can vary both tem- 

 perature and pressure so long as they give a point within the region 

 OTA, and the system is said to be divariant. 



When Regnault made his celebrated researches on the vapour- 

 pressure of ice and water, he supposed that the line AT was continuous 



Lc. 



vapour 



temperature 



FIG. 174. 



through T. But Kirchhoff (Pogg. Ann., ciii. p. 206) showed that the slope 

 of AT continued was different from that of TB, a conclusion which 

 follows at once from the latent heat equation. Putting that equation in 

 the form 



dp _ L 



dB~ '0(v 2 -v a ) 



p may represent the saturation pressure of the vapour of either ice or 

 of water, while v 2 v^ is the change in volume from the denser to the 

 rarer state. Let o> represent the pressure of water- vapour, &/ that of ice- 

 vapour. Let L be the latent heat from water to steam at 0, L' the 

 latent heat of fusion of ice. Then the latent heat from ice to steam is 

 L + L'. We may evidently neglect v v the volume in the denser state, 



since it is exceedingly small compared with v 2> and if we put = tr, the 



*2 



vapour density 



