281 M. Acliille Cazin on Internal Work in Gases. 



in the latter the mixture of the masses m Xi m 2 commences at the 

 same time as the efflux. 



The gas m l produces external work which is entirely consumed 

 by the gas ?n 2 ; so that, if the virtual energy of m l has diminished 

 by a quantity equivalent to this work, the virtual energy of m% 

 has increased by the same quantity. The sum of these two 

 energies has remained constant. 



Denote the specific volume of the gas by v, the increase of 

 virtual energy in the unit of weight by AU; we shall have, for 

 the algebraical increase of the energy of the gas m v 



« 1 AU.=« 1 K(!F-T l ) + mi AJ VT '(T^ - P )dv, 

 then, for the gas m 2 , 



m 2 AU 4 =m S! K(T''-T 1 ) + m 2 Ar" T "(Tj i - iJ )& J 



and finally 



H^AUa + maAUarsO (19) 



After having calculated the integrals by means of the rela- 

 tion (2), 



!>=#>, T), 

 and put 



V, , Y x + x V 2 „ V 2 -* 



1 m, m 1 * m 2 m 2 



we shall have the first equation, between x, T', T". 



If the relation between p and v, which expresses the law of the 

 compression of the gas m 2 , be known (§ III.), we shall have 



y = f(/> 2 ,^'0 = <MTV'), .... (20) 

 which is the second equation, between x and T". 

 Finally, we have similarly 



*(/>*."* f")=<KT',A (21) 



the third equation, between x and T', which^ united to the pre- 

 ceding ones, will enable us to determine the unknowns of the 

 problem. 



For carbonic acid, if for (2) formula (6) be taken, and for (20) 

 the approximative formula 



equations (19), (20), and (21) will become 

 w 1 K(T'-T 1 ) + w 2 K(T"-T 1 ) 



1 ° ° LV 1 T 1 (V, + X)V + ? 2 T, (V 2 -*) T"J ' K ) 



