154-156] Pressure and Volume Coefficients 137 



2iro- 



where ~Sm 



^^F** (316), 



upon substitution from equation (310). 



Expanding ^ and the cohesion factor as far as the first order of small 

 quantities, we have as the equation giving the pressure, 



m ' 



Nw> / 



1- 



m v - o \ RTJ ' 

 so that 



or, again as far as the first order of small quantities, 



(317), 



where a = N 2 mty, 



agreeing with Van der Waals' equation (281). 



We shall now use this equation to investigate the behaviour of gases 

 when the deviations from Boyle's Law are slight. 



Changes at Constant Volume. 



156. Imagine the volume of a gas satisfying equation (317) to be kept 

 constant, and let us suppose the temperature first to be T and afterwards 2\. 



We have, if p , p l are the corresponding pressures, 



(318), 

 (319). 



By subtraction we get 



(p 1 -p )(v-b) = RN(T 1 -T ) ..................... (320), 



and dividing the members of this equation by the corresponding members of 

 equation (318), 



T -T 



-* 1 * O t'O 



From this it is clear that if T , p refer to a fixed temperature the increase 

 in T is proportional to that in p. Hence a gas kept at constant volume 

 may be regarded as a thermometer giving readings on the kinetic theory 

 scale, the reading being proportional to p. 



