188 K. Clausius on the Application of the 



I have already in my former paper of 1850, on the motive 

 power of heat, developed the equations which represent the two 

 principal theorems of the mechanical theory of heat in their ap- 

 plications to vapors at a maximum density, and have applied 

 them to deduce various conclusions. 



As I have however introduced in my last memoir "on a 

 change in the form of the second principal theorem of the me- 

 chanical theory of heat," a somewhat different mode of repre- 

 senting the whole subject, I consider it, as already mentioned, 

 more advantageous for the sake of greater simplicity and breadth 

 of view, to suppose only this last memoir as known. I will 

 therefore again deduce in a different way the equations referred 

 to from the results obtained in it. 



In this memoir it was assumed, in order to apply the general 

 equations first established to a somewhat more special case, that 

 the only foreign force acting upon the variable body which de- 

 serves consideration in determining the external work, was an 

 external pressure, the force of which was equal at all points of 

 the surface, and whose direction was every where perpendicular 

 to it, and that further this pressure always changed only so 

 slowly, and consequently was at every instant only so little dif- 

 ferent from the expansive force of the body acting opposite to it, 

 that in calculation the two might be considered as equal. If 

 then we denote by p the pressure, by v the volume, and by Tthe 

 absolute temperature of the body, which last we will introduce 

 into the formulas instead of the temperature as estimated from 

 the freezing point, because they take a simpler form in this way, 

 the equations deduced for this case are as follows, 



These equations are now to be applied to the still more special 

 case of vapors at a maximum density. 



11. Let the given mass of the substance whose vapor is to be 

 considered be If, and let this be contained in a completely closed 

 extensible vessel, the part m in a state of vapor, and the re- 

 maining part, M—m, in a fluid state. This mixed mass is now 

 to form the variable body to which the previous equations are 

 to be applied. 



If the temperature T of the mass and its volume v — that is 

 to say, the content of the vessel — are given, then the condition 

 of the mass, so far as it here comes under consideration, is thereby 

 completely determined. Since namely, the vapor by supposition 

 always remains in contact with the liquid, and consequently at 

 a maximum density, its condition, as well as that of the liquid, 



(IV) 



(HI) 



