108 Physical Properties [CH. vi 



where the notation is the same as in 73. This leads to the relation 



p = 2m a u 2 v a , 



a 



or by equation (161), 



*-?a 



This again can be written 



where v is simply the numbei*of molecules of all kinds, per unit volume of 

 the gas. 



This calculation shews that the pressure may be regarded as the sum of 

 a number of contributions, one from each constituent gas. This is confirmed 

 by Dalton's Law : 



The pressure exerted by a mixture of gases is equal to the sum of the 

 pressures exerted separately by its several components. 



TEMPERATURE. 



- 



Definition. 



124. The question which naturally presents itself at this stage is the 

 relation of the pressure and density to the temperature. Before this can be 

 discussed we must decide what is to be the Kinetic Theory interpretation of 

 temperature. We have supposed that when the energy of internal motion 

 of a gas is increased, its temperature is raised, but nothing has so far been 

 said as to the quantitative relation between the energy and the temperature. 

 The question of this relationship is complicated by the fact that there are a 

 great number of different scales of temperature outside the Kinetic Theory : 

 the scale of the mercury thermometer, those of the various possible gas 

 thermometers, and the absolute thermodynamical scale may be mentioned 

 as instances, and they all lead to essentially different definitions of tempera- 

 ture. It is true that in practice these scales are except for additive and 

 multiplicative constants in substantial agreement, but this does not help 

 in the least in a theoretical discussion. The simplest plan seems to be to 

 introduce a new and independent Kinetic Theory scale. The selection of this 

 scale is in a sense arbitrary ; but if the hypotheses of the Kinetic Theory 

 are true, it will be possible so to choose it that it will agree very approxi- 

 mately with all the existent scales. We shall define temperature on the 

 Kinetic Theory scale as follows : 



In the normal state of a gas, by equation (161), 

 _ _ __ 1 



raw 2 = mv* = mw" = ~r 

 ZA 



