138 HEAT. 



a single gas and keep its density constant while altering its temperature, 

 we have the relation between the pressures at t" and at 0. 



V 2 v 



But ^s=- if p is constant. 



2 



Therefore, V, 2 = V 2 (l +at) or V, 2 



where 6 is the temperature on the gas scale. Hence the energy of trans- 



"\T2 



lation of the molecules in a c.c., P ',is proportional to the gas temperature. 



a 



Energy of Translation and Internal Energy. If our investi- 

 gation applies to real gases it is e"asy to show that the energy of trans- 

 lation is not for most gases the only energy possessed by the molecules. 

 When a gas is heated we must suppose that in general some of the 

 energy goes to increase molecular potential or molecular vibrational 

 energy. For the energy of translation of 1 c.c. at 0. is 



and if the volume is constant the increase in translational energy, fcr a 

 rise of 1 is 



where a is the coefficient of pressure increase. 



The total increase of energy is K e , the work measure of the specific 

 heat at constant volume. 



The difference of the specific heats at constant pressure and constant 

 volume is given by K p - K^ = op , the work done in expansion. 



Putting =? = y , we have (y - 1 )K e = ap 



& 



TT increase in translational energy _ 3op _ 3(y - 1)K B 3/ _ , . 



increase in total energy ~ 2 K ~ 2K B ~ 2 



This is unity, or the total energy given is converted wholly into transla- 

 tional energy when and only when 



r -l = _ ory = - = l-66 



This is the value of y found by experiment for mercury vapour, argon, 

 and helium. For these gases, then, we must suppose the collisions 

 to be of such kind that the internal conditions of the molecules 

 are not appreciably affected by the collisions ; in fact, that there is no 

 interchange between the energy of translation and the energy of position 

 or vibration of the constituent parts of a molecule. 



