126 Physical Properties [OH. vi 



The result of this elimination can be expressed in the form 



(300). 



This is the general relation between pressure and volume. Using the 

 value of Vb given by equation (293), the relation can be written in the form 



/ 



p = RT( ve-'-W 

 \ 



This again can be written 



p = RTe-** v 



\ 



The bracket on the right-hand side may be regarded as the product of v 

 and of a function expanded in powers of 



If we introduce <r c denned by 



o- c = - e -iM< .............................. (301), 



the bracket becomes 



and is now identical with the vj, of equation (293), except that <r c replaces <r. 

 Hence we can suppose the pressure given by 



(302), 



where v b is calculated upon the supposition that the diameters of the spheres 

 are cr c instead of a. 



If we write 2h = - from equation (265), and p b = mv b , this assumes the 



form 



. 

 P= P*e* f ........................... (303), 



IIV 



in which p b is now given by 



*~P*^V+ ........................... (304). 



ISOTHERMALS. 



144. The relation between p, T and p implied in equation (303) is best 

 exhibited by drawing " isothermals " or graphs shewing the relation between 

 p and p when T is kept constant. Following the usual practice we shall 

 assume that we are dealing with a unit mass of gas and therefore replace p 

 by I/v. We now attempt to draw isothermals shewing the relation between 

 p and v for constant values of T. 



