292 HEAT. 



This assumes that the pressure changes are exceedingly small, which is 

 obviously not exact. 



Taking p , P, and p as the initial, atmospheric, and final pressures, 

 and V , V, and V as the corresponding volumes, the first change being 

 adiabatic, we have (p. 295) 



j, V/ = PV (1) 



The second change being isothermal, 



P.V.-PV (2) 



Then 4g 



-() y from (2) 



lo gf? 

 whence y = 



This gives y = 1'348 in the above example. 



The method, as originally devised, has a serious fault in the assump- 

 tion that the newly introduced air will have the same temperature the 

 moment after introduction as the air already in the receiver, and that 

 all will cool down equally. This fault was avoided in a modification 

 due to Gay Lussac and Welter, in which, to begin with, A contained 

 air at a pressure p higher than the atmospheric pressure P. On turning 

 the tap the pressure fell to P, while the air which had previously occu- 

 pied a part V of the volume expanded to fill the whole volume V. 



Finally the pressure rose to p. 



Then 



and p ~V =pV 



whence as above y = 



log% 



p 



In one of the experiments (Baynes's Thermodynamics, p. 136), the pressures 

 on an arbitrary scale were 



P= 1-0096, Po = 1-0314,^= 1-0155. 

 whence y = 1-3745. 



There are still sources of error in the method. The change of 

 volume is not accurately adiabatic, for momentum is produced in the 

 issuing gas, and if the tap is turned off at the first moment of equalisa- 

 tion of pressure with that of the atmosphere, the air being still in 

 motion, its kinetic energy will be gradually converted to heat, and so the 

 entropy will be increased. If, however, the tap be left on for a longer 

 time the outrush will cease and be followed by an inrush, and there will 



