I 



16 PRESSURE OF GASES 31 



On an ordinary scale of temperature wherein a is the co- 

 efficient of expansion [see note 6, p. 28] we have 



p = Po (l + oS), and K = K (l + 



The latter formula, which is the mathematical expression 

 for the proposition named several times already [ 9, 14], 

 that the energy of the molecular motion is the mechanical 

 measure of the temperature, shows that the kinetic energy 

 increases by the same amount for every degree of tern- 

 perature. 



17. Dalton's Law for the Pressure of Mixed 



Gases 



From this relation between the pressure and the kinetic 

 energy of molecular motion a very important conclusion 

 may be drawn if we extend our consideration to a gaseous 

 medium containing molecules of different kinds, that is, to 

 a gaseous mixture. 



For such a mixture the calculation of the pressure 

 exerted would be carried out in exactly the same way as 

 was done in 11 in the special case of a simple gas. The 

 pressure on a surface is, in the more general case of a 

 mixture of gases, also measured by the sum of the impulses 

 of the molecules on a unit of area in a unit of time ; its 

 value is therefore represented by the total energy given 

 up to the surface by all the different kinds of molecules 

 present. 



The formula for the value of the pressure exerted by 

 a mixture of different gases therefore takes the slightly 

 modified shape 



p = (#, + K, + ...), 



where the magnitudes denoted by K are the values of the 

 kinetic energy per unit volume of the molecular motions in 

 the single components of the mixture, and are given by 



p p 2 , . , . being the densities of these components, and G I} 

 2 , . . . the mean speeds of their molecules. 



