68 Mr. J. Kam on Molecular Attraction and 



We may call v the " specific density" of a gas in respect 

 of a perfect gas at the same volume, temperature, and 

 pressure II. It is always < 1, and in respect of II it 

 compensates the effect of (3, viz. 



n = ^ = ^ (5) 



If, however, the volume of the actual gas is given in 

 respect of i'o=l, 0° C. and 760 mm., and such is naturally 

 the case, then the pressure is 



_U.T_v + h R.T 



n i- t ,-^-^ — r* • • • • (6) 



and we consider either /3 or b as a constant, but the other as 

 a variable. 



We can, e.g., consider 6t c as the theoretical co-volume 

 for the critical state. Then |3 Tc and v e have the values of the 

 experiment. At any other state the relative values are 

 the same. 



At small densities the values of b and /3 are practically 

 the same. For large pressures they differ considerably. 

 Another characteristic of b is, by definition, that its value 

 is inversely proportional to the temperature T, — which, as 

 was pointed out previously, is not the case for ft. This 

 characteristic will presently prove most useful. 



It will be seen that for a definite temperature T we can 

 express v in &t or /3 T , viz. 



v = n .b T = n .v^./St = (n+l)/3 T ; ... (7) 



hence (vide equation 6), 



R.T __ B.T_ (n+l)&t R.T _ v + b T R.T 



v—/3t w./3t n . by ' n . by v v ' ^ ' 



The total pressure II of equation (8) is equal to the 

 pressure p from the exterior plus the effect of the cohesive 

 forces pi. We make 



n = p+2 Pi , (9) 



for the following reason. 



A molecule travelling towards the surface conquers the 

 attraction p lm The normal component of its impact is 

 diminished by p l5 but its temperature is not affected, as 

 the gas is in thermic equilibrium with its surroundings. 

 After the impact it at once proceeds with the velocity 

 corresponding to its temperature, and on impinging towards 

 the interior its impact is supported by the molecular 



