THERMODYNAMICS OF CHANGE OF STATE, ETC. 313 



of the body in the second state, always just on the point of changing 

 into the first state. That given along C'B' is 



and that given along B'B is + 0^0, where Cj is the specific heat of the 

 body in the first state, always just on the point of changing into the 

 second. Thus the total heat is the sum of these, 



or T7r + 1 -0 a ki0. 



\dO l V 



But this is equal to the area BCO'B', which is practically equal to the 

 rectangle with base BO and height dd. Now BC x BM = total heat along 





 Then the area 



. 



6 



Equating the two values of the heat given we have 



<L n n L 



W +QI G * r 



In the case of water and steam at 100 0., 



_^= -0'695 from Regnault's equation (p. 180), 



C 1= l L = 537 = 373 

 whence C 2 = -1-135, 



or the specific heat of steam when kept saturated is negative. 



This means that if we have a quantity of saturated steam at 100, i.e. 

 atapressureof 760 mm., and we increase 

 the pressure adiabatically to 787 mm., 

 which is the saturation pressure at 

 101, the work done will raise the tem- 

 perature above 101, and heat must be 

 abstracted to keep it down to that 



TTjr 1 1 77 



temperature. Or if we decrease the 



pressure adiabatically to 733 mm., the 



saturation pressure corresponding to 99, the temperature will fall below 



99, and heat must be given to restore it to that point. 



In this latter case of adiabatic expansion, if dust nuclei are present, 

 condensation will occur, for as the temperature is reduced the pressure 

 will always be above the saturation pressure. For example, when the 

 temperature has reached 99 the pressure will not yet have fallen to 733 

 mm., and the excess of vapour will condense on the dust nuclei. This 

 agrees with the common observation that the adiabatic expansion of 

 saturated water vapour produces cloud. Let A'B', AB, A"B" (Fig. 177) 

 represent the three isothermals at 101, 100, and 99 on an indicator 

 diagram, and let MBN be the adiabatic through B ; then the above result 

 implies that BM cuts the upper isothermal in the vapour part to the 



