States, and the Thermodynamic State-Equation. 159 



the tables (giving logs of </> l5 <£ 2 by Waals' and Berth elot's 

 equations). Then the corresponding quantity by Clausius' 

 equation is : <£ + \(<f> — 1). 



Fig. 2. 



iog, n Q 



The curves showing logarithms of <f> l9 </> 2 , ir, in terms 

 of log(l-M) give a clear idea of the relations of these 

 quantities inter se, and their rates of change with respect to 

 one another. The very rapid decrease of pressure in 

 comparison to temperature is especially striking, and also 

 the shape of the curves near the critical point. The rates 

 of change of v x and v 2 with respect to p and T there become 

 equal and opposite, approaching the limit co (see the 

 expansions). It is also interesting that dlp/dlT becomes 

 very nearly constant as the critical point is approached ; in 

 the expansion there is no term involving t. 



With regard to the relation of dlp/dlT and Mr/RT; all 

 three equations lead, in the limit, at low reduced temperatures, 

 to the equality 



dip _ Mr 



^"RT* 



This is connected, through the latent heat equation, with the 

 fact that all three equations lead at low temperatures to the 

 limit 



p(v 1 -V 2 )=pV 1 = jj.T, 



a form which at once suggests the Ideal Gas Equation. 



