MECHANICAL EQUIVALENT OF PRESSURE MARGULES 503 



(a.) Isothermal change of pressure 



Let R = gas constant, T = absolute temperature and in the 

 equation for elastic gases, 



p = R T [i 



let T be constant and use the relation 



I ll d k = \ /x dk 

 then it follows that 



A = RT jdk a log ( ?.\ = Cdkp\og(P\ . . (la) 



(b.) Adiabatic change of pressure 



For this case we have 



Pt _ / / l t V 



Po V /<o 



where y is the ratio of the specific heat of a gas under constant 

 pressure to that under constant volume, whence 



*-7hS('-*$ 



dk 



under the condition that the mass of air within the volume k 

 remains unchanged, this becomes 



A = —j J (P - p )dk (16) 



Relatively small changes of pressure 



The expressions (la) and lb) seem to imply that the elementary 

 volumes for which pressure and density are above the average value, 

 give a positive addition to the integral, but that those for which 

 these are below the average give negative contributions. But this 

 is not correct. 



If we put 



ix =/x (1 + a) and p = p (1 + e) 



