DIEMER : THERMAL DIAGRAMS. 229 



or RTv^~^ — joivi" = 0. Differentiating, we have : 



{n—l)RTv--Hv = — Rv^-HT, or dv = nv--^dT 



{n — l)RTv''-^ 

 vdT dv _ 1 dT ,,,v 



[u — l)T ' °^- V ~ n — 1 T ^^^' 



dv 



Substituting this vahie of -^ in equation (8), we have: 



dT lncy — c^^ \n ^1 



\ = c 



dT , 



T n-1 j ^^1 ^ T ' 



integrating between limits T\ and Ti for which the entropies are <^i 

 and ^2, we have : 



«^i-<^2 = c. ! :i!%e4^ (12) 



Equation (12) gives a means for determining the linear length of 

 the entrojiy factor. The temperatures T\ and T2 are disclosed by 

 the pv conditions shown by the indicator card. The exponent n is 

 found by taking any two points on the curve, such as pxvx and pivi. 



Since we have »it'i° =^ »2r2^ we have, also, i ^* i = i — i or, taking 



their logarithms, log p2 — log pi = ii{ log Vi — log V2 ) . Hence, 



l"g p2 — lod pi log p\ — Inn p^ 



n = 7 -. ~, or, 71 = -^^-^ , ^ 



log I'l — lay V2 (eg V2 — log vi 



For accurate work, a number of points should be taken, the method 



of least squares being used if the requirements of the calculation 



demand it. 



In the case of vapors such as steam, ether, alcohol, etc., the general 

 case is that in which a part x of original liquid has been converted into 

 vapor, the portion i — x remaining liquid. If a unit weight be con- 

 sidered as raised from the freezing-point to a temperature Ti and the 

 part X is evaporated at that temperature, the increase in entropy takes 

 place in two stages, that of the liquid part and that of the vapor part. 



If the heat contained in the liquid part be denoted by q, then the 

 entropy of the liquid. 



dn 

 T 



rr C^ dT 1 T 



Owing to the differing of the specific heat at different temperatures, 

 this value for entropy of the liquid should be built up of small values 

 corresponding to small increments of temperature, using the value of 

 the specific heat corresponding to the temperature range taken. 



In order to determine the entrojDy of the vapor portion, if r repre- 

 sents the latent heat of vaporization at the temperature at which 



