ISOTHERMAL AND ADIABATIC CHANGES. 301 



fjf) 

 Though was obtained with finite differences of pressure, it is evident 



Ct-lr 



that, since it is independent of the pressure, we may use it in equation (1), 

 where the difference of pressure is supposed to be very small. We obtain 



(2) 

 W 



- 



a aVII02 



We may at once obtain from (2) the absolute temperature at C., 

 assuming that the degrees have the same value as those of the air scale 

 about that temperature. Thus, for air, since at 0. 6 = 6, 



-2389 x 4-18 x!0 7 x -275 



-00367 x 773 x 1013600 

 95 



or 



Or the absolute temperature does not differ from the air temperature by 

 as much as 1 CJ. 



We refer the reader to Thomson's article on " Heat," Ency. rit., 

 9th ed., 60-2, for the mode of comparing the absolute with the gas scale 

 not assuming that the degrees have the same length about C., but 

 taking the interval from to 100 0. as the same on both. 



It will be observed that equation (2) implies that a, the coefficient of 

 expansion, is not strictly independent of the density of the gas, for the 

 second term on the right is not constant, but when A is positive it 

 increases as V decreases or as the density increases. 



Then - must decrease and a increase with the density for gases such 

 a 



as air and carbon dioxide. For hydrogen, on the contrary, a decreases as 

 the density increases. 



Starting from equation (2) Thomson (loc. cit. 63) has calculated the 

 expansion of air and other gases at different temperatures and obtains 

 results agreeing very closely with those found experimentally by 

 Regnault.* 



The change in internal energy of a gas on expansion has been brought 

 into greater prominence by the " regenerative " method of liquefying 

 gases, in which a gas is forced from a pipe, where it is under great pressure, 

 out through a fine nozzle into the air, the process corresponding very 

 nearly to that of the " porous plug" experiment. At low temperatures 



* Maxwell (Heat, 5th ed., p. 214) gives an equation obtained by integrating 

 equation (1), which is equivalent to 



In the integration it is virtually assumed that a is constant, an assumption which is 



shown to be unjustifiable by the consideration that, if a were constant, dO would be 



p 

 proportional not to P -p but to log . The proper treatment of the equation after 



P 

 its reduction to the form (2) will be found in the Article " Heat," Ency. Brit. loc. cit. 



