340 KEPOKTS ON THE STATE OF SCIENCE. 



On the Cause of the Variation of Specific Heat, 



6. It appears from theory that the energy of translation and 

 rotation of the molecules of an ideal gas should vary in direct pro- 

 portion to the product pv. The internal energy of vibration of the 

 molecules, however, which is related to the absorption or emission of 

 radiation must vary by the Stokes-KirchhofF law in relation to the full 

 radiation of a black body at the same temperature. According to 

 Planck's formula, which has been verified over a very wide range, the 

 energy of full radiation corresponding to wave-length L in full radiation, 

 varies with the temperature according to the expression 



E=CL-=(e'--L^-l)-' 



the value of the constant c is 14,700 if L is measured in microns, ix, or 

 millionths of a meter. The energy of vibration of a molecule which 

 is in equilibrium with full radiation at any temperature will depend on 

 the extent to which its free periods of vibration respond, as indicated 

 qualitatively by its absorption spectrum. Those periods which respond 

 ■very strongly may produce an appreciable effect on the specific heat. 



It happens, for instance, that CO.j has a very marked absorption 

 band at 15//, nearly, which can be detected even when the gas is present 

 in small quantities in the atmosphei'e. So far as this particular mode 

 of vibration is concerned, the specific heat would inciease most rapidly 

 at ordinary temperatures, which is actually observ'ed to be the case 

 with CO2. According to Planck's formula, the effect of any mode of 

 vibration would be a maximum when 6 is intiiiite, and would then 

 contribute the term C 'cL' to the mean specific heat ; but for L=15/t 

 the effect would have already reached within about 10 per cent, of the 

 possible maximum at 2000°. According to Wion's original formula 



which holds very well for short wave-lengths and low temperatures, 

 but appears to fail when L^ is large, the energy E would reach a tin'te 

 lim't CL~"' when is infinite, and the specific heat for L=15/j would 

 reach a maximum when ^=500°. This does not appear to agree so well 

 with the changes of specific heat actually observed. 



In the case of steam it appears that there are no equally well- 

 marked absorption bands corresponding to strong natural periods of 

 vibration, in the range of the heat spectrum available for investigation. 

 The very high dielectric constant of water for short electric waves has 

 been taken to indicate that there is a period of marked resonance very 

 low'down in the spectrum in the unexplored field between the shortest 

 electric waves and the longest heat waves hitherto obtainable. This 

 might account for the relatively high value of the specific heat of water 

 and steam at ordinary temperatures. It must be remembered, how- 

 ever, that the absorption spectrum is very complicated and difficult to 

 investigate 'beyond the limits of photography. Moreover, it is very 

 difficult to deduce, except in a qualitative manner, the relative intensities 

 of the energy corresponding to each absorption band. An absorption 

 band may appear strongly marked in a thick layer of absorbent, which 

 really corresponds to a very small amount of energy. For this reason 



