206 Dr. A. Naumann on the Specific Heat of Gases 



thermal unit as appears from the mean value (0*23773) of the 

 specific heat of the three permanent gases (oxygen, nitrogen, and 

 hydrogen) and the ratio (1*41) of the specific heat under con- 

 stant pressure to the specific heat at constant volume, as deduced 

 from the velocity of sound * and other observations f. If 7' 

 denote the specific heat of equal volumes of perfect gases under 

 constant pressure, and 7 the specific heat at constant volume 

 (which latter is connected with molecular and atomic motions), 

 the heat of expansion, namely «/— 7, under equal pressure is a 

 constant for all gases. 



We will now in the first place show that the heat of molecular 

 motion m bears a constant relation to the heat of expansion y' — 7, 

 and is consequently also a constant for equal pressure. Accord- 

 ing to Clausiusf, if K denote the vis viva of the progressive 

 motion of the molecules, and H the total vis viva of the gas, 



K_ |( 7 '-7) 

 H~ 7 



Consequently, if W represent the thermal equivalent of the 

 unit of work, KW is the quantity of heat which produces the 

 progressive motion of the molecules, and HW is the total quan- 

 tity of heat in the gas, and 



KW_ |(V-7) 

 HW" 7 



But since this relation is independent of the temperature, (if 

 Kj and Hj represent the values corresponding to 1° C, and K 

 and H those corresponding to 0° C.) we have the equation 



whence 



K 1 W_K W_|(V-7) 

 H^^HoW*" y : 



K 1 W-K W _ §(y- 7 ) 

 H^V-HoW" 7 



But I^W— H W is the specific heat at constant volume =7; 

 and K X W — K W is the portion of this heat employed in produ- 

 cing the progressive motion of the molecules =m. Hence we 

 have 



™ = W-v) , 



7 7 



* Ad. Dronke, Pogg. Ann. vol. cxix. p. 393 (1863). 

 t Ann. der Chem. und Pharm. vol. cxviii. p. 113. 

 % Pogg. Ann. vol. c. p. 379 (1857). 



