18 MOLECULAR MOTION AND ITS ENERGY 9 



time, i.e. the pressure of the gas, is increased by an addition 

 of heat. 



Beyond these considerations no further proof is needed 

 of the proposition that the pressure increases as the square 

 of the molecular speed, or, what comes to the same thing, as 

 the energy of the molecular motion. In agreement, there- 

 fore, with the general principles of thermodynamics it 

 follows that the mechanical measure of heat and of tem- 

 perature is the kinetic energy of the molecular motion. 



1O. Mean Value and Components of the Energy 



The closer investigation of the relation between the 

 temperature of a gas and the kinetic energy of its molecules 

 is rendered difficult by the circumstance that the molecules 

 have not all the same speed, and, therefore, not all the same 

 energy. This consideration is really identical with this 

 other, that the energy of each particle changes on collision. 

 If, however, we can say that the resultant action of the 

 / impacts which each particular molecule makes in a fairly 

 long time with its energy ever changing is equal to that 

 which would result if the impacts all occurred with a 

 uniform mean energy, then we must allow that the resultant 

 action of the impacts of all the molecules is the same as if 

 the molecules have all a uniform mean energy of motion. 



We gain a further advantage in our calculation by 

 making use of the proposition that, just like a velocity or a 

 force, kinetic energy may be separated into three components, 

 of which each corresponds to a component of the motion in 

 a given direction. The whole energy is equal to the sum of 

 its components, as is easily seen from the known formula 



0) = 



for a velocity G> in terms of its rectangular components u, v, w ; 

 for this gives/ 

 j/ 



This proposition enables us to substitute a simpler 

 motion for that which really goes on in the gas near the 

 walls of the vessel and produces pressure on it : we divide 



