M. Achille Cazin on Internal Work in Gases. 285 



ft^V^Fj - T 'V^-ptV,-^ * * ' ( J 



*\V 9 -xJ To V,+a? T'(V 1+ #) 2 V ' 



After the moment we are now considering, there is exchange 

 of heat between the gases m } and m 2 : the first receives heat, 

 the second loses it ; and the piston falls back a little. When the 

 exchange is accomplished, there is a definitive state of equili- 

 brium ; the two masses m l and m 2 are at the same temperature 

 6 ) the specific volumes are equal, 



m i m 2 ' 



and, lastly, the common pressure is p. 

 From the last equality is deduced 



g.V.-m.V, (32) 



Equation (19) alone is sufficient to calculate 0. As to p, its 

 value is deduced from relation (2). 

 For carbonic acid we shall have 

 K + mJKltf-TJ 



^ Lt.V, ^(V. + yJ^T.V^ 0(V 2 -y)J 

 an equation which, if combined with (22), gives 



^=2- N+ \/(-§ I - N ) 2 + N '' 



(23) 



N= Aw;KV,+m;y,) 



KT.VjV.K+mJ ' 

 N ,_ 2Aap » » 

 K(V 1 + V,)' 

 and, from (6), the final pressure will be 



^~ T V 1+ V a " 0(V 1 + V 2 )* ' * ' ^ 



It may be remarked that by making m 2 = 0, m x — l in these 

 two formula, we recur to the equations (6) and (7) of § I. For 

 V, becomes the specific volume v lt and Vj + V 2 is the final spe- 

 cific volume v', 



I shall give some numerical examples of equations (23) and 

 (24) by taking, as in the preceding examples, the data which 

 relate to my experiments. 



