536 



SMITHSONIAN MISCELLANEOUS COLLECTIONS 



VOL. 51 



(see fig. 1 a). Let the cold air be in the left hand chamber 1 but 

 the warm air in the right hand 2 ; each mass of air to be at rest and 

 in either stable or neutral equilibrium; the whole mass of air in the 

 enclosure above these two chambers takes no part in the follow- 

 ing processes, we can replace it by a movable heavy piston. What 

 amount of kinetic energy becomes available when we remove the 

 screen and let the masses 1 and 2 move adiabatically? 



If in the initial stage the entropy of a kilogram of the highest 

 layer of the mass (1) is smaller than that of the lowest layer of mass 

 (2), then in the final stage the whole cold mass of air will spread 

 out below or at (1'), and the warm mass will be spread out above 

 or at (2') as shown in fig. 16. 



hi 



Ph 



hi 



B 



* 01 Poi 



P02 * 



fig. ia, 



A 



C 



D 



\k> 



K 



B 



P.' 



T 



D 



FIG. lb. 



If the equilibrium was stable on both sides of the screen then 

 in every part the serial order of the strata is retained after the 

 overturning. 



If the equilibrium in (1) and (2) was neutral in the initial stage 

 then it will remain so in the final stage (i') and (2'). 



Let T be the absolute temperature of an elementary mass 

 dm in the initial stage: T' that of the same mass in the final stage; 

 C p the specific heat of air under constant pressure; C v that for con- 

 stant volume, C p — C v = R, then we find 



dP =R j {V- T) dm dl = C v j (V - T)dm 



whence the available kinetic energy of the system is 



-d(p + 1) = Cpj (T - rod 1 



m 



