552 The Specific Heat of Carbon Dioxide and Steam. 



has shown, will be very rapid if the duration of collision is 

 comparable with the periods of vibration of the molecule. 

 In the case of carbon dioxide and steam at high temperatures 

 (1000° C. and over*) the duration of collisions between mole- 

 cules is probably short in comparison with the periods of 

 their low frequency vibrations, and the vibratory energy of 

 the molecules will therefore tend to take up during collisions 

 a value such that the energy in each of the vibratory degrees 

 of freedomj equals that in each of the rotational and trans- 

 lational degrees. During collisions therefore the vibratory 

 energy of the molecules will tend to take up a value which 

 is proportional to the absolute temperature ; but, as we have 

 seen, during the free-path there may be considerable depar- 

 ture from this value if the energy density in the aether is 

 above or below a certain value and the time of description 

 of free-path is not very short. It is clear therefore that the 

 value of the vibratory energy of the molecules averaged over 

 a time which is greater than that of the description of free- 

 path may depart considerably from a value proportional to 

 the absolute temperature of the gas. The extent of this 

 departure will depend for any given gas at any given tem- 

 perature upon the energy density in the aether (which, in 

 view of the high transparency of a gas to its own radiation, 

 is dependent in a very large measure upon its volume) and 

 also upon the time of description of free-path (which, of 

 course, depends upon the density of the gas). 



3. The specific heat of a gas is dependent upon the trans- 

 lational, rotational, and vibratory energies of its constituent 

 molecules. In a gas in thermal and chemical equilibrium 

 the translational energy and the rotational energy are 

 proportional to the absolute temperature of the gas ; but, 

 as we have seen, the vibratory energy may depend upon 

 volume and density as well as temperature. The specific 

 heat would therefore appear to depend upon volume and 

 density as well as temperature. At any particular tem- 

 perature the greater the volume of the gas the greater its 

 specific heat, and the greater the density the less its specific 

 heat. 



4. It is clear from the theory suggested in § 2 that the 

 vibratory energy of the molecules during the free-path will 

 vary to a considerable extent only when the gas radiates 



* See Phil. Mac-. Jan. 1920, p. 93. 



t Or, rather, those vibratory degrees of freedom which share in the 

 heat motion of the gas. In the case of steam and carbon dioxide at tem- 

 peratures of 1000® C. and over these degrees of freedom are those which 

 correspond to radiation of 2'8 n and longer. 



