266 PRINCIPLES OF THE MECHANICAL THEOEY OF HEAT. 



Fig. 11. 





The quantity of lieat r, which must "be supplied to the unit weight of water at 

 fj in order to convert it into saturated vapor at t°, is known, indeed, by Regnault's 

 experiments, but this quantity of heat divides into two parts; one part Apu 

 serves to execute the external work j);f ; it is the other part p which is expended 

 in overcoming the cohesion of the particles of water, and therefore in the per- 

 formance of an internal work. Whence r=p + Kp u. Neither p, nor Ap u, nor 

 the proportion of these two magnitudes is directly given ; in order to determine 

 them, we must first seek in some way to eliminate p, as it were, that is to say, 

 we must propose some operation with the vapor by which a definite external work 

 is performed, while the internal work performed shall, at the end of the operation, 

 be nothino-. A process of this sort is denoted by the name of a circle-p)rocess, 

 (Kreisprocess.) 



Let us suppose the volume iv of the unit weight of water at t°, to be repre- 

 sented by the abscissa O A, (Fig. 11,) the pres- 

 sure p>, which is exerted thereon, by the ordinate 

 A a. Let heat now be conveyed to the water 

 in such wise that the vapor which is formed may 

 maintain the constant temperature t. In virtue 

 of this the pressure p also remains constant. 

 The supply of heat is to be continued until all 

 the water is converted into vapor. The volume 

 w will now have been changed into B=v, 

 and will thus be increased by A B=« ; and 

 ^ ^ EC since the pressure p) has in the meantime re- 



mained unchanged, the external work thus perfomied and represented by the 

 rectangle A a 6 B is equal to jjt(. The quantity of heat supplied during this 

 formation of vapor is r. 



To this vapor we now allow, without supplying or withdrawing heat, a 

 further small expansion from B to C, till the temperature be sunk 1° 

 and the corresponding tension by <p. The work d thereby performed is repre- 

 sented by the quadrangle B C c 6 ; and we will denote by q the coiTcsponding 

 heat which is disengaged from the vapor. In the fourth column of the table 

 here given will be found the amount of diminution of tension <P, when the vapor, 

 which is saturated for any one of the temperatures given in the first column of 

 that table, is cooled 1°. The numbers of the table ranged under ^ are found 

 in the following manner : 



If we subtract anj^ of the values of p contained in the third column from the 

 following one, we shall learn how much the tension of the saturated vapor is 

 increased by an elevation of temperature of 5°. How much it is diminished by 

 a lowering of temperature of 5°, we learn by subtracting from the same value of 

 23 the preceding one. If we now take the mean of these two diflFercnces, and of 

 this mean the fifth part, we shall learn (without sensible eiTor) how much the 

 tension of the vapor of water is changed by an elevation or lowering of temper- 

 ature by 1°. Thus, for example, for 150° C. the first difference is 6897.7; the 

 second difference, 6195.4; the mean of the two is 65i6.5 ; and the fifth part 

 thereof, 1309.3, the number which stands under <l> in the horizontal row of 150° 0. 

 Let the vapor, Avhich now has the temperature t—1 and the tension p^=p— ^, 

 be compressed by the volume ii, (C D, Fig. 11,) while the heat is continuously 

 withdrawn from it in such manner that the temperature shall always remain 

 t—1 and the tension^ — ^. 



The quantity of heat r' becoming free during this compression, and withdrawn 

 from the vapor, consists of two parts, namely : of the quantity of heat Ap'tt, 

 Avhich coiTcsponds to the labor p)'u expended for the compression, and repre- 

 sented by the rectangle QJ) do, and the quantity of heat p which becomes free 

 by the condensation of a corresponding quantity of vapor. 



Let the compression now be finally continued from O D to A, without the 

 addition or abstraction of heat; the temperature will thereby be raised to t°, the 



