206 Mr. J. C. Maxwell on the Dynamical Theory of Gases. 

 or 



2 



dp 



3/3 §r 



3S B<? 



(106) 



or 



(107) 



3/3 p ' ' • ' ' ' ' * 



which gives the relation between the density and the tempera- 

 ture in a gas expanding without exchange of heat with other 

 bodies. We also find 



p p 6 



_ 2 + 3/3 ^p 



- 3/3 p' • \ '• : 



which gives the relation between the pressure and the density. 



(108) 



Specific Heat of Unit of Mass of Constant Volume. 

 The total energy of agitation of unit of mass is /3V 2 =E, or 



If, now/ additional energy in the form of heat be communicated 

 to it without changing its density, 



(109) 



3/? "dp 3/3 p 50 



(110) 



Hence the specific heat of unit of mass of constant volume is in 

 dynamical measure 



dE _ 3/3 p 



"dd 2 p6 ' 



(111) 



Specific Heat of Unit of Mass at Constant Pressure. 



By the addition of the heat ^E the temperature was raised 

 ~dd and, the pressure "dp. Now 5 let the gas expand without 

 communication of heat till the pressure sinks to its former value, 

 and let the final temperature be 6 + "d'0. The temperature will 

 thus sink by a quantity "d@ — "ft'O, such that 



36>-a' _ 2 -d P __ 2 aa 



2 + 3/3 0' 

 whence 



e 



2 + 3/3 p 



3/3 °b0 



2 + 3/3 ' 



(112) 



