M. Achille Cazin on Internal Work in Gases. 



275 



effected, there must have been a variation of the virtual energy 

 equivalent to this work and of contrary sign. Let us examine 

 whether there is external work. 



The motion of the plane A to the position C represents a 

 work p ] v l ; that of the plane D passing in the same time to B 

 represents a work p'v', taken with the opposite sign to that of 

 the preceding. The work p ] v l is expended ; the work p'v 1 is, on 

 the contrary, produced ; finally our gas has flowed out, produ- 

 cing the work p'v 1 — p x v v if the value of this expression is posi- 

 tive ; if it is negative, the gas has, on the contrary, expended 

 this quantity of work. Without foreseeing the sign of this 

 quantity, we shall only say that 



1 



%Jv lPl 



d~E=p'v'—p l v l . 



As to the variation of the virtual energy, we shall have the 

 same expression as in the preceding section, so that the equation 

 of the problem is 



K(T'-T,) +AJ* " T '(T J| -pyv+A(pV-j, lVl )=0, 



(8) 



from which we can deduce T ; when we have the function (2). 

 The second term of equation (8) represents internal work esti- 

 mated in calories. 1 am now going to apply this equation to 

 carbonic acid. 



By combining equations (8) and (6) we obtain 



KCT'-TO+A^pzIi +3av (^- -—)] =0, 

 whence may be deduced 



\ t'=|'-n+\/(J-n) 2 + n', 



N ^ SAapj p lTp .... (9) 



2T> 1 (KT + A Po v }' 



N ,_ 3A«p t)gT u 

 ^(KTo + Ajvo)' 



formulae analogous to formulae (7). 



When T' is calculated,, its value and that of v' may be intro- 

 duced into formula (6) and thus p' may be deduced ; we shall 

 then obtain the quantity joV—p^,. 



Numerical application.— By employing the same data as in 



