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XLVIII. On the Velocity of Atomic Motion. 

 By Dr. Alexander Naumann*. 



I HAVE shown in a previous communication f that the 

 three component parts into which, with reference to their 

 different functions, the specific heat of perfect gases under con- 

 stant pressure may be resolved, namely the heat of expansion, 

 the heat of molecular motion, and the heat of atomic motion, are 

 to each other in the constant ratio 2 : 3 : n, where n denotes the 

 number of atoms contained in one molecule. But since the heat 

 of expansion is expended in the performance of external work, 

 the total thermal content of a gas is represented by the vis viva 

 of the progressive motion of the molecules together with the vis 

 viva of the motion of the atoms inside the molecules. 



Now the absolute zero for perfect gases is fixed at — 273° C, 

 or more exactly at — 274°'6 C.J, upon the assumption that the 

 quantity of heat taken up by a gas is constant for equal incre- 

 ments of temperature. Hence it follows that the quantity of 

 heat contained in a gas must be proportional to the absolute 

 temperature, and that the vis viva of the progressive motion of 

 the molecules is to the vis viva of the motions of the atoms 

 inside the molecules in the same ratio as the heat of molecular 

 motion to the heat of atomic motion — that is to say, in the 

 ratio 3 : n. 



Let us. first take the case of gases for which the relations that 

 we have to investigate assume the simplest form. These are the 

 simple gases containing in one molecule two similar atoms, 

 as oxygen, nitrogen, hydrogen, for which the ratio above-men- 

 tioned = 3:2, and the velocities of the two atoms (the nature of 

 whose motion we shall have to consider more particularly here- 

 after) must be supposed equal. 



Now let u be the mean velocity (expressed in metres per second) 

 of the progressive motion of the molecules, and v the velocity of 

 the two atoms. Then, since the sum of the masses of the two 

 equal atoms is the same thing as the mass of the molecule, the 

 two vir^es vivce bear to each other the same relation as the squares 

 of the velocities, and therefore 



v 2 2 /2 



- 2 = o> whence v = u\/ _ =08165w. 



u 6 V 3 



* Translated from Ann. der Chem. und Pkarm. vol. cxlii. p. 284 (June 

 1867). 



f Ibid. p. 265. Phil. Mag. S. 4. vol. xxxiv. p. 205. 

 X Ad. Dronke, Pogg. Ann. vol. cxix. p. 392 (1863). 



