30 MOLECULAE MOTION AND ITS ENERGY 16 



16. Pressure and Energy 

 The formula found for the pressure of a gas, 



brings this magnitude into very close relation with another, 

 namely, the kinetic energy of the molecular motions. Since 

 the density p measures the mass of gas contained in the unit 

 of volume, the magnitude 



K = 



is nothing else than the amount of kinetic energy possessed 

 by the molecules in unit volume. 



The simple relation deduced from these two formulae, 

 viz. 



enables us to express the molecular energy by a magnitude 

 which is directly amenable to observation. The pressure 

 and kinetic energy of a gas stand to each other in an in- 

 variable relation which is independent of the temperature. 



This simple relation is nothing else than an expression 

 of the thought which underlies our theory. Both mag- 

 nitudes, pressure and energy, have their origin in the 

 molecular motion ; they are even completely alike in their 

 nature. Their difference consists only in the difference of 

 the units in which their values are expressed. For the 

 pressure which the walls of a gas-holder support forms 

 also a measure of the kinetic energy of the contained gas. 



Both magnitudes change proportionally to the absolute 

 temperature, and we have 



P = *B, and K = #, 



VJ ^0 



where p Q , K Q are the values of the pressure and kinetic 

 energy per unit volume at the temperature of the freezing- 

 point of water, which on the [Centigrade] scale of absolute 

 temperature is 



= 272-5. 



