82 On the Isothennals of Isopentane. 



There is one of the isothermals in the set determined by 

 our formula which is of peculiar interest. The biggest value 

 of t occurs when v is indefinitely large, its value being then 



^-, Let us call this quantity t for shortness, and let us see 



lie 



what form the isothermal for this particular temperature takes. 



We shall easily obtain 



]' : 



Rr„ 



+ 



ig 



tfip + k-Z-Mv + k) 



so that the pressure for a long range of volume is practically 

 given by Boyle's law ; and when an increase does occur, it 

 varies as the fifth power of the density. In the case of 

 isopentane this is merely a deduction from theory, since the 

 temperature required is 567° C. ; much too high to allow of 

 any experiments being carried out for verification. Indeed, 

 for most other substances, the temperature of minimum 

 deviation from Boyle's law, being much higher than the 

 critical temperature, is much too high to allow of any 

 experiments being performed there. An exception may be 

 made, however, in the case of nitrogen, which has a very low 

 critical temperature. The following are the values of pv at 

 16° C. for nitrogen under different pressures determined by 

 M. Amagat (" Memoires sur l'elasticite et la dilatabilite des 

 Fluides jusq'aux tres-hautes Pressions/' Ann, Chim. Phys. 

 6th series, vol. xxix. p. 107). 



Pressure in 





Pressure in 





metres of 



pv. 



metres of 



pv. 



mercury. 





mercury. 





•76 



10000 



45 



•9895 



20 



•9930 



50 



•9897 



25 



•9919 



55 



•9902 



30 



•9908 



60 



•9908 



35 



•9899 



65 



•9913 



40 



•9896 







From this table it is evident that at 16° C. for nitrogen we 

 are only a short way off the temperature of minimum 

 deviation from Boyle's law. At temperatures higher than 

 the temperature of minimum deviation the gas would have 

 pv increasing with pressure from the first, and this is what 

 happens with hydrogen at ordinary temperatures. 



