137-141] Deviations from Boyle's Law 121 



Deviations from Daltoris Law. 



140. Equation (285) expresses the general law for the pressure in 

 a mixture of gases. Dalton's law is no longer true, because (i/ a ) & depends 

 not only on the number of molecules of type a which are present, but also 

 on the numbers of molecules of other kinds. 



The correction required, at any rate to a first approximation, can best be 

 seen from an inspection of Van der Waals' equation (280), which, throughout 

 the range for which it is true, namely as far as the first order of small 



quantities, may be written 



ENT /- 



p = -cp 2 + - - 



v \ 



If there are two gases denoted by suffixes a and ft, it will be found that 

 in the simple case in which the molecules are supposed all of the same size, 

 the total pressure is given by 



For Capa+Cppp replaces cp as. the intensity of the force of cohesion, and 

 b a + bp replaces b as four times the sum of the molecular volumes. 



The partial pressures, calculated on the supposition that only one kind of 

 gas is present, are given by 



. m ^ , a 



Pa= C a /) a 2 + - - 1 H -- 



V \ V 



hence, instead of p being equal to the sum of the partial pressures p a , pp, 

 we have 



The correction to be applied to Dalton's law is too complex for further 

 investigation to be profitable. 



Deviations from Boyle's Law and Charles' Law. 



141. It is obvious enough that the laws of Boyle and Charles will 

 require correction. 



If it were not for these corrections all gases would expand in the same 

 proportion under an increase of temperature or a decrease of pressure, so 

 that the scales of all gas thermometers would be the same, and the equation 



pv = RNT ...... '. .......................... (288), 



would identify the Kinetic Theory scale of temperature with that of any gas 

 thermometer. 



