136 Physical Properties [CH. vi 



If v is the volume per unit mass of gas, so that vp = \, we have, as far 

 as squares of p, 



_rt_ __ ^L. wn 



p RT P RTv t )m 







P 



pm 



Hence J[T = ~ V log 



(314). 



Now we have seen ( 135) that so long as p is approximately constant 

 throughout the gas, ty may be regarded as constant in equation (312). This 



p<fr 



requires that e RT shall be approximately equal to unity throughout the gas, 

 and therefore that p shall be small. If this condition is satisfied, we may 

 neglect terms beyond b : p 2 in equation (313). Hence from equation (314) we 

 may for sufficiently small values of p suppose the equation of the isothermal 

 to be 



v log - = constant . . . . .(315). 



pmv 



The quantity on the left-hand is the function tabulated by Dieterici in 

 the last column of the table on the last page. Inspection shews that 

 although the function is by no means constant for all values of v, yet it is 

 approximately constant for all values of v which are greater than the critical 

 volume. If Boyle's law were satisfied the entry in the third column would 

 vanish throughout. It does not vanish, and our investigations on the devia- 

 tions from Boyle's law have shewn that it ought approximately to vary 

 as Ijv. The confirmation of our theory, then, lies in. the fact that the 

 variations of the entry in the last column are small compared with those 

 of v. 



VAN DER WAALS' EQUATION. 



155. As far as the first order of small quantities we have from equa- 

 tion (304), 



Nm 



