THERMODYNAMICS. 



281 



8 



passes along BH, the two meeting at the common temperature H. For 

 this secures that the entropy remains constant. The heat converted is 

 given by the area AHB. In other words, if HCM is the horizontal line 

 from one curve to the other, bisected in by AB, ON is the common 

 temperature and 



HAG + BOM is the heat converted. 



The Possible Efficiency of a Steam-Engine. We shall conclude 

 this account of reversible engines, and of the idea of entropy arising 

 therefrom, by a calculation of the possible efficiency of a steam-engine 

 supposing that there is no waste of heat and no friction. 



Let us for definiteness take an engine in which the boiler is at 

 140 C., say 413 absolute, and the condenser at 30 0., say 303 

 absolute. We shall suppose that the steam is admitted into the cylinder 

 at the temperature and pressure of the boiler till the moment of cut off, 

 that then there is adiabatic expansion till the temperature is reduced to 

 that of the condenser, and that 

 then the contents of the cylinder, 

 which will be partly saturated 

 steam at that temperature and 

 partly water, are let into the 

 condenser and there condensed 

 to water. We shall further 

 suppose, in order that we may 

 take the working substance 

 round a cycle, that the con- 

 denser water feeds the boiler. 



The path may be simply 

 represented on an entropy tem- 

 perature diagram, Fig. 162. 

 Using absolute or work-scale 

 temperatures, A represents the 

 water returned to the boiler from the condenser at 303, AB the water 

 as it rises in temperature to 413, BC the conversion into steam at 413, 

 CD the adiabatic expansion till the temperature is 303 again. In this 

 expansion water will at once be formed, and the result will be a mixture 

 of saturated steam and water, the proportion of water gradually increas- 

 ing as the temperature falls.* When 303 is reached, the further 

 condensation into water is represented by DKA. 



The heat given during the cycle is represented by the area LABCNL, 

 and that transformed by ABCDA. 



FlG. 162. Entropy Temperature Diagiam 

 for Steam-Engine. 



Then the efficiency = 



ABCDA ABK + BCDK 



LABCNL ABML + BCNM' 



In calculating the value of this, we shall make very slight error in 



* The reader may calculate the proportion of water at 303 very nearly one-fifth 

 by assuming that the entropy is the same at the beginning and at the end. We 

 may refer to Perry's Steam-Engine, 200, for the mode of calculating the entropy of 

 wafer and of steam, or to p. 320 of the same work for tables giving the entropy at 

 different temperatures. 



