!6 PROPERTIES OF STEAM AND OTHER VAPORS. 



be investigated. The expansion line which an indicator would draw 

 under such conditions is called an adiabatic line. Calculations for 

 adiabatic changes of >u-um can be made by aid of a special function 

 ised for the purpose and called entropy. A discussion of adiabatic 

 ons and of entropy can be found in any text-book on Thermo- 

 dynamics; for example, on pages 17 and }i of the riicnnodynamks of 

 the Steam Engine by the author. It is sufficient for our present purjxjse 

 to consider that entropy can he e.\prc>>cd numerically and that the 

 numerical valiu^ enter into the calculation of certain engineering 

 problems. 



It is customary to represent entropy in general by <f>, but entropy may 

 be represented by in dealing with a liquid like water. 



The second law of thermodynamics enables us to deduce the equation 



in which dQ is an infinitesimal amount of heat added at the absolute 

 temperature T. This equation is the basis of the calculation of 

 entropy. 



Entropy of Vaporization. If a pound of steam at the temperature / 

 (or absolute temperature T) is partially vaporized, the heat expended 

 for that purpose is xr; the temperature being constant the above equation 

 may be directly integrated giving 



xr r 



In Tables I, II, and III values of ^ are given for each degree or each 



pound as the case may be. 



Entropy of the Liquid. The increase of entropy due to heating water 

 from freezing-point to any temperature / may be represented by the 

 equation 



rd JL = w 



J T J T 



Inspection of the table on page 10 shows that the specific heat of water 

 is but little larger than unity; it is convenient to represent it by the 

 expression 



c - i + k; 



