520 On a Modification of the Plug Exjyeriment. 



thermometer coils in the various places where different tem- 

 peratures are to be expected, and so test the uniformity of 

 temperature throughout the apparatus in some detail ; and 

 such differential measurements, with the platinum coils 

 arranged after the manner of the bolometer, may be given a 

 very high degree of sensitiveness. 



The fundamental equation of the plug experiment, per- 

 formed in the manner outlined above, assumes a particularly 

 simple form : Let v, p^ and e be the specific volume, the 

 pressure, and the specific internal energy of the gas before 

 the passage through the plug ; and let v\ p , and e' be the 

 corresponding values after the 23assage. Let X8/:> be the 

 energy supplied per unit mass of gas to keep the process 

 isothermal when the fall of pressure is hp. For a finite fall 

 of pressure we shall then have 



e^ = e -\-pv —p'v' + 1 \dp^ 

 %) 'p' 



or for an infinitesimal fall of pressure 



Se= —h[pv) -{-\Bp. 



Letting 6 represent the absolute temperature, and 77 the 

 entropy of unit mass, we have, for any reversible change of 

 state, 



Be=68r]—2?Bv. 



The passage through the plug is not reversible, but since e 

 and 7] are functions only of the coordinates which define the 

 instantaneous state of the system, the changes of entropy and 

 energy 0/ the mass of gas are the same as if the process had 

 been reversible, and we may apply the formulae for reversible 

 processes to the case in hand. Equating the two values of 

 he, we have 



h{pv) —\Bp — — OBt] -hpSv, 

 whence 



— dS?'/ = vBp — \Bp, 

 or 



But we have the familiar thermodynamic relation 

 whence, by comparison with the last equation, we obtain 



(li)."-'- 



