ISOTHERMAL AND ADIABATIC CHANGES. 289 



T&jdO (where dd is the temperature difference between 

 = K^ Hand BO) 



Then 



This relation only involves the Second Law of Thermodynamics in 

 the assumption of the smallness of HBA, and it was obtained by Laplace 

 before the law was known. 



The ratio is usually denoted by y. 



The Difference between the Two Specific Heats. Taking unit mass of a 

 substance round HBO, and using the value for the heat along BO found 

 on p. 285, we have ^ ^ 



K v d6 + a6e*dv - K p d6 = area of HBO 



avdOdp 

 ~2~ 



= in the limit, 



, -rr " TT vftuiu 



whence Kp - K = - ^ 



Putting dv = avdO we have 



Kp-K. 



Dividing by K p we get at once 





From this we see that y is constant when a?ve e l'K p is constant. 

 The Numerical Value of 7, the Ratio of the Two Specific Heats. The 

 last formula at once gives us y, when the quantities on the right are 

 known. 



Thus let us take : For air at and 760 mm., 

 a =-00367 

 v =773-4 ' 

 6 "l/ 



e a =p = 1 atmosphere = 1013600 dynes per cm 2 

 K, -2389 x 4-19x10* 

 whence y = 1*41 nearly. 

 If we take Swann's value (p. 8G) as 0'2414 we get y = 1'396. 



For water at 30. 



a =-00032 



v =1 



=303 



ft = 1-014 xlOx 22000 



(since the decrease in volume is 1 in 22000 



for 1 atmo.) 

 Kp = 4-2xl0 7 

 whence =1-017 



