﻿788 Prof. A. W. Porter and Mr. R. E. Gibbs on tlie 



Case (I). 



At the end of the change of temperature, let the mass of 

 solution be (M + mj gm., where 



M = mass of water, 

 m=mass of salt in solution. 



Since the solution is in equilibrium with the salt, it will be 

 saturated, and as it is in equilibrium with ice, it will be at the 

 freezing-point ; hence the final temperature must be the 

 cryohydric. 



In determining the connexion between M and m at the 

 end of the change, the external work done can be neglected 

 owing to the very small change of volume at the moderate 

 pressure of one atmosphere obtaining during the experiment. 

 In these circumstances the heat change in a cycle can be taken 

 as zero with sufficient approximation ; or, in other words, the 

 particular path of transformation is immaterial so far as heat 

 changes are concerned. Representing the cryohydric 

 temperature by — t° C, the heat equation will be 



r(Isi + Ss s ) = ML W + mL s , 



where si and s s are the specific heats of the ice and salt 



respectively, and where 



L w is the latent heat of fusion of ice at — t° C, and 

 L s is the latent heat of solution of salt at — t° C. 



In writing this equation, all the salt and ice has been assumed 

 to cool down initially to - t° C. and the transformation to 

 take place then at this low temperature. 



Nothing would be gained by aiming at meticulous accuracy 

 in regard to numerical values. The general trend of results 

 can be illustrated by using constant and approximate values 

 for which the calculations can be made easily. As the 

 solubility of salt varies very little with temperature, one can 

 assume mjM. to have a constant value -J-. Assuming also the 

 following approximate values, 



-t=-21°-6 0. j Si = % s 8 = -2, 

 L w --70, L s =6 (at -t°C.)*, 



one obtains 



-i l °\2 + 0} 



* In calculating L w at — r the formula ^7^ = 1 — si has been ern- 

 ployed. It would even he erroneous to employ the more usual equation 



^=^ — ^- =1 - si, because this gives strictly the latent heat under 

 ol I 



equilibrium conditions, i. e. under a pressure corresponding to a melting- 

 point of — r, whereas the pressure is approximately atmospheric 

 throughout. 



