THERMODYNAMICS OF CHANGE OF STATE, ETC. 807 



equilibrium with each other at 1 atmosphere, as long as the temperature 

 is 100. If the volume increases, then more steam is formed till at C 

 all is steam with a volume about 1640 c.c. On the other hand, if the 

 volume diminishes more water is formed till at B all is water with a 

 volume about 1'04 c.c. The process is reversible at every point. 



The general course of a substance at the melting-point may also be 

 represented by a curve like ABCD. For ice and water at DC will 

 represent ice. At C the ice begins to melt, having then a volume about 

 1 '09 c.c. At B it is all water having a volume about 1 c.c., and BA 

 represents water. 



If the temperature is not that of the'normal boiling-point or the normal 

 melting-point the curve will have the same general character, but the 

 horizontal portion will be at a different level. For steam and water at 

 99 C., for example, it is at 733*21 mm. instead of 760 mm. For ice 

 and water at 1 C. it is, as we shall see below, raised up to about 134 

 atmospheres. We do not, in ordinary experience, meet with ice and 

 water in equilibrium except at or very near the normal melting-point. 

 The possibility of such equilibrium at other temperatures was indeed first 

 discovered as a result of thermodynamical reasoning by Professor James 

 Thomson (Trans. R.S. Edin., xvi., 1849, p. 575), and was first experi- 

 mentally demonstrated by his brother shortly afterwards (see chap. xii.). 



The following investigation applies to either change of state. Let 

 ABCD, A'B'C'D', Fig. 172, be isothermals at and 6-dO respectively 

 for 1 gramme of the substance. Let B represent volume v l and let C 

 represent volume v z . Let L be the latent heat taken in along BC in 

 changing state. Through B and C draw adiabatics BM, CN, where 

 M and N are on the 6 - dO isothermal. Then BCNMB may be taken 

 as a Carnot cycle, and we have 



- = external work = area MBCN. 

 u 



If the isothermals are sufficiently near to each other, any want of 

 parallelism of BM and CN may be neglected, and the area of MBCN 

 may be taken as 



Hence 



7--* > 



If then v 2 is greater than v v as in the case of steam and water, - 



du 

 is positive, or the boiling-point rises with the pressure. 



If, on the other hand, i> 2 is less than v v as in the case of water and 



fjff\ 



ice, -~ is negative, or the pressure at which equilibrium is possible 



increases with fall of temperature. That is, pressure lowers the melting- 

 point. 



In change from solid to liquid, in which there is an increase of volume, 

 a rise in pressure corresponds to a rise in temperature, or pressure raises 

 the melting-point. 



