on the Physical Properties of Gases. 415 



19. In considering the effect of dissociation on the specific 

 heats of gases, we may not treat them as a mixture of two whose 

 proportions remain constant ; for in raising the temperature, 

 not only is work done in increasing the kinetic energy of 

 translation and internal motion, but also in destroying a cer- 

 tain proportion of molecules. Let, as before, x be the number 

 of molecules, 2y the number of atoms present when the tem- 

 perature is 6. Let X 1? A 2 be the ratios of the whole energy to 

 that of translation in molecules and free atoms respectively. 

 Then we have, if Q is the quantity of energy present in unit 

 of volume, and I the potential energy of combination of a 

 single molecule, 



Q =\2mv\ . Xyx + \mv\ . 2\ 2 y + Le 



= {\ i x + 2\ 2 y)\6 + Ix. 



Let a quantity oQ of heat be applied, the volume being 

 constant. Then 



8Q=|(x 1 g+2\ 2 ^)^ + (M + 2X 2 ^ + I^j^ 



=cd6, 



where c is the specific heat at constant volume. Also 



And 



old ^ old ~ u * 



= {(-X 1 + 2^| + X 1 . + 2A 2y -i|jx; 



and if c r is the specific heat at constant pressure, 

 dv 



Nowp=5(l + ?>A 



If Y be the volume occupied by the gas and W the number 

 of atoms in it, 



W 

 1 Y 



Hence 



P Y=\j\(l + Qd; 





