Variation in the Pressure of Saturated Vapours. 41 



but is, on the contrary, proved by calculations and theoretical 

 considerations given below. Under such a state of the vapour 

 we obtain from the preceding equation, 



d p = — {c — k)dt (1) 



If v denote the specific volume of the vapour in a state of 

 saturation, and if it be supposed that the vapour at this volume 

 and corresponding pressure p and temperature t has the pro- 

 perties of a perfect gas, i. e. is subject to the laws of Boyle 

 and Gay-Lussac, we shall have 



where T=273-f t and D is, as is known, a special quantity 

 for every substance when the latter occurs in the state of a 

 perfect gas. The amount of heat required by the vapour in 

 this state for the completion of external work in raising its 

 temperature by 1° is equal to AD, where A denotes the 

 thermal equivalent of work. Moreover, if c 1 be the specific 

 heat of the vapour at constant pressure, we have 



£ = d-AD ( c ) 



If r denote the latent heat of vaporization and iv the specific 

 volume of the liquid, then, as is known, 



p = r—Ap(v—iv). 



Under small pressures w is exceedingly small compared 

 with v ; therefore it may be said without any perceptible error 

 that 



p(v—w) =DT, 

 and consequently 



p = r-AJ)T, 



dp = dr—ADdt. ..,...(/>) 

 The equations (1), (c), and (/?) lead to the following, 

 dr — ADdt = — (c — c x + KD)dt y 

 whence it follows that 



dr=—(c—c 1 )dt (2) 



* This equation is not exact. D. T. Mendeleeff showed that near a 

 certain pressure, proper to every gas, the latter is subject to Boyle's 

 law; beyond this pressure pv varies with^j. The pressure at which pv is 

 constant should fall with a rise of temperature. Let us imagine a satu- 

 rated vapour and allow it to expand freely at a constant temperature • 

 then, according to Mendeleeffs law, the vapour will attain such a state of 

 rarefaction that it will fully satisfy the equation pv = a constant, and 

 will therefore possess the properties of a perfect gas. It is possible to 

 imagine such an instance, that a vapour will follow Boyle's law even 

 in a state of saturation. Thus the proposition, that a vapour in a 

 state of saturation follows Boyle's and Gay-Lussac's laws near a certain 

 temperature, is in harmony with other well-known phenomena. 



