46 IDEAL AND ACTUAL GASES 105 



and especially the circumstance that the coefficient which 

 determines the increase of pressure with temperature is 

 not identical with that on which the increment of volume 

 depends. 



The value of the former coefficient, which for distinction 

 from the other the expansion-coefficient proper may be 

 termed the pressure-coefficient, is the more easily obtained. 

 The increase which the pressure of a gas undergoes when 

 the temperature is raised from to $ while the volume 

 remains unchanged is found by comparison of the formula 



(p + av~ 2 )(v - b) = E(l + a$) 

 for the latter temperature with that referring to 0, 

 (p Q + av~^(v- b) =JB, 



when we give to v the same value in both. By subtraction 

 we get 



(p- P< )(v-b) = 

 or 



P Po= (Po + aw 



whence we obtain for the pressure-coefficient the corrected 

 formula 



. 



This teaches that gases in which cohesion really exists 

 have a greater pressure-coefficient a p than the ideal gases 

 for which its value is a. Since this behaviour agrees with 

 experience, the formula can be used to deduce the value 

 of the constant a, which measures the strength of the 

 cohesion, from the observations. 



The same agreement between theory and observation 

 is also shown when we calculate from the theoretical 

 formulae the value of the expansion-coefficient proper, i.e. 

 that coefficient which determines the increment of volume. 

 Since p is now to be taken as constant and v as variable, 

 the formulae 



(p + av~*)(v - b) = E(l + aty, 

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



