^ 



14 M. R. Clausius on the Moving Force of Heat, 



For this purpose let it be as- Fig. 4. 



sumed, as before, that the de- 

 scribed alterations are infinitely 

 small, and under this view let 

 the process be represented by 

 the annexed figure, in which the 

 curves ad and be shown in fig. 3 

 have passed into straight lines. 

 With regard to the content of 

 the quadrilateral abed, it may be - 

 again regarded as a parallelogram, 

 the area of which is expressed by the product ef. bk. Now if, 

 when the temperature is /, the pressure of the vapour at its 

 maximum tension be equal to p, and the difierence of tempera- 

 ture /— T be expressed by dt, we have 



bk^^dt) 

 at 



ef is the increase of volume caused by the passing of a certain 

 quantity of fluid represented by dm into a state of vapour. Let 

 the volume of the unit of steam at its maximum density for the 

 temperature t be called s, and the volume of the same quantity 

 of fluid at the temperature t be called a ; then is 



ef^{s—(T)dm\ 



and hence the content of the rectangle, or 



The work produced 



(s— o") -jidm dt. 



(5.) 



To express the amount of heat, we will introduce the following 

 notation : — Let the quantity of heat rendered latent by the pas- 

 sage of a unit weight of fluid at the temperature /, and under a 

 corresponding pressure into a state of vapour, be called r, and 

 the specific heat of the fluid c; both of these quantities, as 



dp 



Finally, 



also the foregoing s, a, and -^, being functions of t. 



let the quantity of heat which must be communicated to a unit 

 weight of vapour of water to raise it from the temperature t to 

 t + dt, — the vapour being preserved by pressure at the maximum 

 density due to the latter temperature without precipitation, — be 

 called hdt, where h likewise represents a function of t. We shall 

 refer the question as to whether its value is positive or negative 

 to future consideration. 



If we name the mass of fluid originally present in the vessel 

 fi, and the mass of the vapour m ; further, the mass evaporated 

 during the expansion from oe to of, dm, and the mass precipi- 

 tated by the compression from off to oh, d'm, we obtain in the 



