408 Mr. R. E. Baynes on Saturation Specific Heats, <5'c, 



The thermal capacities of a fluid with van der Waals' 

 characteristic 



(p+av- 2 )(v-b) =Bt 

 being defined by 



*dH = kdt -f Idv = Kdt + hdp, 

 their values are 



k = it, I = -5* , K = it + 



6' l-2a(>-&) 2 /R^ 3 ' 



T v— b 



~ ~l-2a(v^by/WtiV 



where fe is in the general case a function of t. 



Their further calculation is simplified by using the charac- 

 teristic in its e reduced 3 form 



(7r + 3v- 2 )(3v-l) = 8r, 



in which the units employed are the critical values P, V, T 

 of the pressure, volume, and temperature respectively, in 

 terms of which we have 



a = 3PV 2 , b = JV, R = 8PY/3T ; 



and if, to simplify our calculations, we introduce * a new 

 variable /jl defined by 



/*= + V / {(3*-l) 2 -W}, 



which will be real in all the cases we need consider, and for 

 shortness of expression put 



A==3v-1, B=i(3*-l-f0, G— i(3v^l+/x), 



F = i(3-3v-/.), a = i(3-3v+/*), 

 we have 



7T = BC/v 3 , t = ADE/8^% 



//P = DE/v 3 , (K-fc)/R = DE/FG, L/Y = - ADE/3FG. 



To determine the variations of the thermal capacities we 

 may plot their values for given values of t against the values 

 of 7r or v. We easily see that the /7r, Jjtt, Lv curves may 

 present singularities while the Jv curves do not ; that the 

 value of K— it, which is positive except when v lies between 

 1 + \yb and 1 — jam, i. e. except when v lies between the largest 

 pair of the roots of the equation 4ti> 3 = (3v — l) 2 which are 



* This variable was also employed by Hitter, Wien. Sitz.-Ber. July 

 L902. 



