598 Prof. R. C. Tolnian on the Relativity Theory : 



For the total energy of N such particles we obtain 



and introducing relation (17) which defines k, we have 



E = 3?*RT. 



It is instructive to compare this with the ordinary expres- 

 sion of Newtonian mechanics 



E=|nRT, . . . . (20) 



which undoubtedly holds when the masses are so large and 

 the velocities so small that no appreciable deviations from 

 the laws of Newtonian mechanics are to be expected. We 

 see that for particles of very small mass the average kinetic 

 energy at any temperature is twice as large as that for large 

 particles at the same temperature. It is also interesting to 

 note that in accordance with equation (20) a mol of par- 

 ticles, which had zero mass at the absolute zero, would have 



. 3 x 8-31 x 10 7 x 300 _,_ 1A „ 

 a mass or ^rni = ' "^' x -^ grams at room 



temperature (300° absolute). This suggests a field of 

 fascinating if perhaps profitless speculation. 



The Approximate Partition of Energy for Particles of 

 any Desired Mass. 



For particles of any desired mass we may obtain an 

 approximate idea of the relation between energy and tempe- 

 rature by expanding the expression for kinetic energy into a 

 series. For the average kinetic energy of a particle we have 



K 



-b&s-l 



Expanding into a series we obtain for the total kinetic 

 energy of N particles 



~ AT /1_ 3_ 15- 105- \ 



where v 2 , ?> 4 , &c. are the average values of v 2 , r 4 , &c. for the 

 individual particles. 



To determine approximately how the value of K varies 



