AND MODERN PHYSICS. 131 



boat measured as energy contained by a single 

 molecule, and T its temperature, we have 



H = /JT 



From tbis it can bo shown* that if 7 represent the 

 ratio of the specific heat of a gas at constant pressure 

 to the specific heat at constant volume, then 



3 y-1 



For air and some other gases the value of 7 has 

 boon shown to be 1-408. From this it follows that 



The proof is as follows : 



If ff bo the specific heat at constant volume, <r'ut constant pressure, 

 and consider a unit of mass of gus at pressure p and volume v, let the 

 volume increase by an amount dv, while the temperature dr. 

 Thus 0-'dT = *dT -f pdv 



But p v =r j^ 



If enco p being constant, 



, 2 dT 

 pd v rr - 



3 ia 



Therefore 9' =. 9 + J -- 



6 Hi 



Now suppose an amount of heat, d If, is given to a single molecule 

 and that its temperature is T. Its specific heat is <r, and 



dlI=r<rmdT 

 But dlfrr/SdT 

 Therefore ft = 9 m 



Hence -- = ^ 

 in 



Thus *' = 



And <r'/<r y 



2 



Therefore y = i -f " 

 j P 



I 2 



