40 K. D. Kraevitch on an Approximate Law of the 



for abnormally high pressures, or when the coefficient of expan- 

 sion of the liquid becomes great. On the liquid attaining the 

 temperature t + dt under the pressure p + dp, let us convert it 

 into saturated vapour at the same temperature and pressure. 

 If p denote the internal (potential) latent heat of vaporization 

 for the temperature t, we find that the internal energy of the 

 liquid increases by p + dp on its conversion into vapour at a 

 temperature t + dt. Thus, if a kilogramme of a substance in 

 a liquid state, having a temperature t and subjected to a pres- 

 sure p, be converted into saturated vapour at a temperature 

 t + dt and under a pressure p + dp, then the energy of the 

 substance increases by 



cdt + p + dp. 



(b) Let us bring the given liquid, which is under a pressure 

 p and at a temperature t, wholly into the state of saturated 

 vapour at the same pressure and temperature. The internal 

 energy of the substance is increased by p. Let us heat the 

 vapour by dt without altering the volume v. By this means 

 the internal energy is further increased by hit, where k is a 

 quantity equal to the specific heat of the vapour at constant 

 volume. The vapour will now be in a superheated state. Let 

 us increase the pressure p, under which it occurs, by dp 

 without changing its temperature t + dt ; the vapour then 

 passes into a state of saturation. Moreover, if it follows the 

 laws of Boyle and Gay-Lussac, the internal energy of the 

 vapour will not change on compression. If, on the contrary, 

 it does not follow these laws y then the internal energy will 

 decrease by some quantity S, because as a rule the internal 

 energy of substances is decreased by contraction. Hence, 

 in order to convert a kilogramme of a liquid at t and p into 

 vapour at t + dt and p + dp, it is necessary (not counting 

 external action) to augment the internal energy of the liquid by 



p + kdt — S. 



And as both expressions represent one and the same thing, 

 therefore 



cdt + p + dp = p + kdt — S, 

 whence 



dp=-~(c — k)dt—&*. 



If it be allowed that a saturated vapour is, at a certain 

 pressure, subject to the laws of Boyle and Gay-Lussac, 

 then S = 0, because the energy of a perfect gas is not 

 dependent upon the pressure. This is the fundamental pro- 

 position of the present paper ; and it is not an arbitrary one, 

 * Gorny Journal, 1869, vol. ii. p. 389. 



