94 Transactions of the Royal Canadian Institute 



expansion was announced simultaneously by Clausius' and Rankine^ 

 and was shown later experimentally by Hirn^. 



This phenomenon was shown by Clausius to be a necessary conse- 

 quence of the fact that the specific heat of water vapour is negative. 

 It is shown in the larger treatises on Thermodynamics that where the 

 specific heat of a saturated vapour is negative, adiabatic expansion causes 

 condensation if there is not too much liquid present, while, if the specific 

 heat is positive, expansion always causes evaporation of the liquid. 

 That the specific heats of the vapours of many common liquids are nega- 

 tive is shown by figure 1, which was plotted from the data given by 

 Duhem*. While there seems to be considerable diversity in the varia- 

 tions in the specific heat, Duhem has shown that there are only two 

 classes of substances, those for which the specific heat of the saturated 

 vapour is always negative and those for which the specific heat is negative 

 for very low and very high temperatures becoming zero for two inter- 

 mediate temperatures between which it is positive. Raveau^ showed 

 that the specific heat of a saturated vapour becomes negatively infinite 

 at the critical temperature, while that of the liquid becomes positively 

 infinite at the same temperture. So, it would appear that while the 

 specific heat of ether vapour is positive throughout the region in which 

 it has been studied, it must become negative as the temperature is raised 

 to a point near the critical temperature. If this is so, adiabatic ex- 

 pansion should produce condensation of the vapour as it does with water 

 and most other liquids^. 



This phenomenon of condensation has been observed repeatedly 

 with a very simple apparatus. This apparatus resembles the classical 

 apparatus of Andrews and was built for lecture demonstration of the 

 phenomena exhibited by a liquid and its vapour near the critical point. 

 A thick walled glass tube of a few mm. bore and about 30 cm. long was 



iClausius Pogg. Ann. LXXIX, 368, and 500, 1850. 



2Rankine, Trans. Roy. Soc. Edin. XX, I, 157, 1850. 



^Hirn, Bull, de la Soc. Industrielle de Mulhouse No. 183. 



^Duhem, Traite Elementaire de Mecanique Chimique, vol. II, p. 213. 

 Raveau, Jour, de Physique 3. I, 461, 1892. 



^Mathias (Annales de la Faculte des Sciences de Toulouse T, 10, 1896) has shown 

 that sulphurous acid behaves according to theory. He measured the specific heats of 

 both liquid and vapour from 0° to 155° C, or just below the critical temperature and 

 found the specific heat of the liquid is always positive and increases slowly until at about 

 130° when it grows larger rapidly and becomes very large. The specific heat of the 

 vapour is negative at 0°, increases to zero at about 98°, remains positive for a short 

 interval, reaches a second point of inversion at 116° and then changes sign becoming 

 very large negatively at 155°. In all probability the same general trend would be obser- 

 ved for other liquids, though many would never be positive and have no points of inver- 

 sion. 



