THERMODYNAMICS OF CHANGE OF STATE, ETC. 329 



by the adiabatic BC, the temperature falling to 6 - dd. Then let the 

 piston be pushed back at 6 - d6 along CD, and finally back along the 

 adinbatic DA to its initial position. 



Then the work done is ABCD = AEFB, 



and by the second law this is 



or 



-$ 



dp 



dO 



dv = 



H 



Now, if the dilution is sufficiently great, further dilution neither gives 

 out nor absorbs heat. Whatever in the action of 

 solution does produce heat changes, is all finished by 

 the time the solution is sufficiently diluted. We may 

 picture the action perhaps as a separation of the salt 

 molecules, and as a surrounding of each salt molecule 

 by solvent molecules. When this is once done, it does 

 not matter how many more solvent molecules we add, 

 for we shall not alter the condition of the salt mole- 

 cules. Hence H is, as with a gas isothermally expand- 

 ing, equivalent to the external work done, and is if 

 no such work is done. 



We put 

 whence 



II 



pdv, 



dp _p 

 dO~~B 



only 



gas 

 insolulioi 

 Os m 

 Press 

 P 



liquid 

 only 



tp.m 



pe.rm-.lo 

 qas only 



or p = cd. 



When the dilution has not proceeded so far that no A r \permito 



heat is evolved or absorbed on further dilution, we 

 cannot assume that H =pdv, and we cannot draw the 

 conclusion that p = c6. 



Having thus shown that osmotic pressure follows FIG. 187. 



one of the gas laws, Van t'Hoff then showed that 

 when the solute is a gas, it follows from Henry's law that the 

 osmotic pressure is actually equal to the pressure the dissolved gas 

 would exert if it occupied the same volume in the absence of the 

 solvent. Henry's law states that a liquid at a given temperature 

 always dissolves the same multiple of its own volume of a given 

 gas whatever the pressure of the gas. Or, put in another way if a 

 space contains a liquid and a gas, the liquid dissolving some of the gas, 

 say n volumes at a given pressure, then if the volume and pressure 

 be varied the relation between them will be given by Boyle's law, on the 

 supposition that the one volume of the liquid counts for n volumes. To 

 apply Henry's law to osmotic pressure, imagine a cylinder containing a 

 quantity of liquid with gas dissolved in it (Fig. 187). Let A represent 

 a movable piston permeable to the liquid only. Let B represent a fixed 



