[ 357 ] 



XL. The Variation oj the Specific Heat of a Qas with 

 Temperature. By GEORGE W. Todd, J\l.A.(Cantab.), 

 JJ.Sc.(J3ir»i.), Professor of Experimental Physics, Arm- 

 strong College, Neiceastle-on-Tyne* . 



TP^HE criticisms which are frequently brought up against 

 JL the principle of the equipartition of energy among the 

 degrees of freedom of the molecules of a gas are the experi- 

 mental observations (a) that the molecular heat varies with 



the temperature when it should be C = =wi(%R0l= li, 



d<9\2 ) 2 > 



and (I) that the ratio of the specific heats of a gas also 

 varies with the temperature when it should jigree with the 



9 



equation ry=l+ — , n being the number of degrees of 



freedom. It is often argued that since one cannot have a 

 fractional degree of freedom, then if C and y do change 

 with temperature, the changes should take place in steps. 



It will be shown that the criticisms are unjust and that 

 the principle will account for the available experimental 

 facts, as well as does the quantum theory which discards 

 altogether the equipartition principle. 



The Specific Heat at Constant Volume. 



Adopting a method of treatment similar to that used in 

 previous papers t, we will assume that the gas molecules 

 have three degrees of freedom so long as their velocities are 

 below a critical value. Above this critical value we assume 

 that the collisions result in added degrees of freedom (e. q. 

 rotation produced). Let the number of degrees of freedom 

 added be q. 



The number of molecules per c.c. with velocities between 

 c and c + dc is 



m \3/2 - 



4 / m V 



/^\2ne) e ***** 



where the symbols have their usual significance. 



* Communicated by the Author. 



t Todd & Owen, Phil. Mag. vol. xxxvii. p. 224, and vol. xxxviii. 

 p. 600. 



