282 M. Achille Cazin on Internal Work in Gases, 



For carbonic acid in particular, formula (6) must be used, and 

 equation (16) will become 



T, Aap v 2 _ Ap<p pVz Aap v 2 

 L T 2 + K^ " KTo^ + K^Tf * " * ; 



Whence T 2 may be deduced by tentative methods. 

 The internal work effected will be 



2 Wo(t^-tI;)- 



If there were no external work (as in § I.) between the same 

 volumes, initial and final, we should evidently have a final tem- 

 perature T' > T 2 ; and we have seen in this section that the in- 

 ternal work was 



Mc^} 



Hence it would be greater than the preceding. 



According to this, the internal work would not be a function 

 of the volume alone, and there would be internal work expended 

 during the cooling at constant volume, which ought to reduce 

 the gas from the condition v 2 T' to v 2 T 2 . In other terms, the mo- 

 lecular forces ought to create heat during the cooling. 



Conversely, during the heating at constant volume there would 

 be internal work produced. 



It is probable that the apparent specific heat at constant vo- 

 lume decreases when the temperature rises. Let C v be that spe- 

 cific heat ; C« the specific heat at constant pressure (determined 



C 

 by M. Regnault), then ^ ==7. 



The quantity C p increases considerably with the temperature; 

 hence it seems probable that 7 increases rather rapidly with the 

 temperature. 



It is for experiment to confirm these previsions. By the 

 method described by me in these Annates in 1862, 7 might be 

 investigated up to 100°. The apparatus described in the first 

 part of this memoir would be very suitable. I hope to be able 

 to make some trials in this direction. 



The calculations indicated in this section would be of no utility 

 at the present time, because I know of no experiments on the 

 expansion and compression of carbonic acid. I content my- 

 self at the present moment with indicating them, reserving the 

 application of them for a special study, and remark that my 

 method permits us to find the relation which exists between the 

 pressure and the volume of a gas which is compressed or expanded 

 under the conditions stated in the enunciation of the problem. 



