2-4 PROCEEDINGS OF THE AMERICAN ACADEMY. 



where f j and ( ] represent the change of internal energy 



and volume respectively, with a change of temperature at constant pres- 

 sure, P. 



\<l 1 J ,. \</ l J,. \ dv J T \t( J J ,. 

 ** \dTj f \dv) T \dT); 



mi 



from (^7), 



= c P -P\ 



drj P ~ '' \d /•),: 



1 -TV 



We have found for a gas or a liquid, = ... Substituting in (88), 



°' = c '-{T ! t)A P + £)- (30) 



Since (7-,,,) is the measure of thermal expansion, equation (39) 



contains only quantities capable of experimental determination, and we 

 are able to calculate c v from the experimentally found value of Cp. The 

 calculation is further simplified by the fact that in thFcase of most va- 

 pors ., is negligible compared with P } and in liquids Pis negligible 



compared with ■=. For close approximations, therefore, we may write 

 for liquids, 



c ' = e *-v\dTj; (4 °") 



and for vapors, 



c v = c P -P^)=c r -P, (40 ft) 



that is, the equation for the specific heats of perfect gases applies to 



