30 WILSON 



ART. C 



for smaller values of v. For large values of t the isothermals in 

 the py-diagram are concave upwards throughout their course 

 from V = CO to y = 6 where they become infinite ; for small values 

 of t the concavity changes and indeed the curves have a maximum 

 and minimum. An isothermal of this type may have some degree 

 of realization; for the phenomena of the super-cooled vapor in 

 which condensation does not start and of super-heated liquid in 

 which vaporization does not start are known, and indicate that 

 under suitable conditions the isothermals of the vapor state may 

 cross the critical line as the volume is reduced and the isothermal 

 of the liquid state may also cross that line when the volume in- 

 creases. The part of the isothermal of van der Waals which 

 lies between the minimum and maximum and for which dp/dv is 

 positive cannot be expected to be realized, as a positive value of 

 dp/dv represents a mechanically unstable condition. If none- 

 theless one writes d^ = — rjdt -\- vdp and integrates along an iso- 

 thermal one has f " — f' = J'vdp and as for coexistent states 

 f " — f ' = 0, one must have for such states J'vdp = 0. This 

 means that from any van der Waals isothermal the line p = 

 p' = p", which is the physical isothermal corresponding to 

 coexistent states for the same temperature, must cut off equal 

 areas, one below the line and the other above it. 



If the series of isothermals be drawn there are three interest- 

 ing loci, the critical locus which gives the limiting conditions of 

 coexistence of vapor and liquid phases, the locus of maxima and 

 minima, and the locus of the point at which the rising (unrealiz- 

 able) part of the isothermal cuts the hne p = p' = p". 



Lecture XXI. The word "unstable" is used in thermo- 

 dynamics in not quite the same sense as in mechanics. If we 

 have a supersaturated solution crystalhzation may not start; 

 the substance may be stable within limits to certain variations, 

 but will start to crystallize rapidly if a minute crystal be intro- 

 duced, i.e., the solution may be unstable to the introduction of 

 the crystal phase. So in superheated water, there may be 

 stability with respect to various processes, but not with respect 

 to the introduction of a bubble of steam. 



Entropy has been defined for a body considered homogeneous ; 

 the restriction may be removed. There would be no difficulty 



