in relation to Pressure, Volume, and Temperature. 407 



Now, if we imagine the substance making the transition 

 from a to e along the path represented by the curve abode, 

 and returning from e to a along the path represented by the 

 straight line e a, we have a reversible cyclical process. Hence, 

 for the positive or negative quantity of heat communicated 

 from without to the changing substance in the course of this 

 process, an element of which may be called dQ, the well-known 

 equation 



Jf=o 



must hold good. And since in the present case the tempera- 

 ture T is constant, and the lines which graphically represent 

 the cyclical process are only isothermal lines for one and the 

 same temperature, the equation simplifies itself into 



jdQ = 0. 



Therefore the positive and negative quantities of heat commu- 

 nicated to the substance eliminate one another. 



It hence follows, further, that the positive and negative 

 parts of the external work done during the cyclical process 

 must also counterbalance one another. The excesses of the 

 positive work over the negative belonging to the two sections 

 of the cyclical process are represented by the areas occurring 

 in the figure : the area cdec above the straight line represents 

 a positive, and the area abca beneath the same line a nega- 

 tive excess. Consequently these two areas must, in order to 

 give for the value of the total work, be equal the one to the 

 other. Hereby, when the theoretical pressure-curve corre- 

 sponding to the homogeneous state is given, the position of 

 the horizontal straight line answering to the actual processes 

 of vaporization and condensation is also determined. 



The foregoing condition can be expressed as a proposition 

 thus: — The pressure of the saturated vapour is so great that the 

 external ivork performed at the vaporization is equal to that 

 which would be performed if, the increase of volume being the 

 same, the substance remained homogeneous. This can also be put 

 still more briefly thus: — The pressure of the saturated vapour 

 is equal to the mean pressure of the substance remaining homo- 

 geneous while receiving an increase of volume corresponding to 

 complete vaporization. 



The curve drawn between a and e by J. Thomson for the 

 temperature 13 0, 1 does not correspond to this condition; for 

 the areas of the figures abca and cdec formed by it and the 

 horizontal straight line are visibly unequal. Now, in order 

 to see what is the form taken when equation (7) is employed 



