The Adiabatic Condensation of Ether Vapour 



97 



Somewhere between 120° and 194°, the specific heat becomes zero 

 and changes sign and the temperature-entropy diagram must show the 

 lines of constant x leaning over toward the left as the temperature is 

 raised, probably somewhat as shown in the diagram of Fig. 3. 



Fig. 3. 



Strictly speaking, as was shown by Raveau, whether condensation or 

 evaporation occurs when a saturated fluid is expanded adiabatically, 

 depends on the algebraic sign of the expression 



xh + (l-x)c 

 where h is the specific heat of the saturated vapour. This may be shown 

 easily as follows. If we take the result given by Mathais already 

 referred to viz., that the temperature falls upon adiabatic increase in 

 volume, we may use the expression for the heat absorbed by a saturated 

 liquid and vapour 



dQ = Ldx [hx (1-x)] dT 

 where L is the heat of vaporization. For an adiabatic expansion this is 

 zero and 



dx L 



dPr'^hx (1-x) c 



If h be positive, dx is positive, or the mixture becomes dryer when 

 expanded. If on the other hand h be negative the expression hx + (1 — x)c 

 may be negative and then dx is negative and the mixture becomes wetter 

 upon expansion. If x is near unity, a negative value of h always means 

 condensation with expansion, but if x is small, hx (1 — x)c may be positive 

 even when h is negative, and then evaporation results. Thus if water 

 vapour contains too much liquid it will not condense. This is shown also 

 by the manner in which the isentropic cuts the lines of constant x for 

 X <0.5. This is, however, not a very practical point as the condition of 

 the vapour must be very near the state, x= 1. 



The condensation of ether vapour near the critical temperature may 

 then be taken as a proof that the specific heat of the vapour is negative, 

 as demanded by the investigations of Raveau. 



—7 



