392 BABCOCK. 



VII. The Satukation Specific Heat of the Liquid Cg^, and the 

 Saturation Specific Heat of the Vapor c^^, in Terms of c„i2- 



1, Derivation of Equations. 



Let the total mass of substance in the hquid container be M, and 

 since this is constant 



bM = Q (21) 



Let Ml and Mi be the masses of the vapor and Hquid phases respec- 

 tively. These are variables and functions of the temperature but 

 related by the equation 



Ml + Ml = M (22) 



Let V = the volume of the container, a constant, 



and call J'/M = v. 

 Let Vi = the specific volume of the saturated vapor, and 



V2 = the specific volume of the saturated liquid. 

 Then 



ViMx + 1)2^2 =V=Mv (23) 



If bd = the temperature change of the substance due to the heat BQ 



added to that substance, and 



L = the total heat of vaporization of the liquid phase, then 



bQ = CsJh bd + Cs.Mi bd + LbMi (24) 



By means of (21), (22) and (23), M^, 31 1, and bMi, are eliminated 

 from (24). Rearranging terms after this elimination, 



1 bQ _ vi — V V — vi 



M bd Vi — Vo Vi — ih 



T. (\_v-vAbvi_/v_-^\/2bjA) ^25) 



^1 — "^2 ( \ ^1 — ^2/ bd \Vi — V'lj \ bd ^ 



1 bO 



By Equation 1 c^,, ^ JiYd ^^^ 



and a general thermodynamic relation ^^ gives 



c., = c, - (f - §) (26) 



15 Reference 3, p. 4. 



