18 PROCEEDINGS OF THE AMERICAN ACADEMY, 



show that the value of c„ in a gas does change considerably through wide 

 limits of volume. He has been the first to succeed in measuring directly 

 the specific heat of gases at constant volume. The values were deter- 

 mined by means of his differential steam calorimeter, a method which 

 seems to give very accurate and consistent results. The results showed 

 that the specific heat at constant volume could be expressed in the 

 following formulae, 



For Air, c„ = .17151 + .02788 p, 

 ForCOa, c„=.1650 + .2125 p + .3400 p^ 



where p is the density in grams per cubic centimeter. According to 

 these formulae the specific heat at constant volume at atmospheric pres- 

 sure differs from that at infinite volume by only two hundredths of one 

 per cent in the case of air, and by three tenths of one per cent in the case 

 of carbon dioxide. Between the specific heats of the gases at atmos- 

 pheric pressure and in a highly compressed or liquid condition the 

 change is much greater. For example, the value given by the formula 

 for f„ in the case of carbon dioxide is about twice as great at the critical 

 volume and about three and one half times as great in the liquid at 0° C. 

 as the value for the gas at ordinary pressure. Further evidence of the 

 change of c„ between the liquid and gaseous condition will be given later. 



In these variations in the specific heat we find the probable cause of 

 many of the deviations from the equation of van der Waals that have been 

 noticed. It may be found necessary, therefore, in order to obtain a more 

 exact equation of condition, to return to the more general equation (8), 



V J 'v-T do 



do dv 



7 ^t* 



in which the value of —^ contains not only the function for volume 



dv ■^ 



correction, but also a term depending upon the value chosen for the lower 

 limit of integration, 7{) . If we write 



^^-p^Fiv), then ^-F{v)T=—^-—T-r{o)T, 

 dv V V —f{v) 



where y(y) denotes the same function of v that has been used in equations 



(27) and (28), namely, the quantity h in the van der Waals formula, and 



dc^, 

 F' (o), another function of v. Now — — ^' is practically independent of 



the temperature and the equation may be written 



