A.— MATHEMATICAL AND PHYSICAL SCTENCES. 

 OSMOTIC^CONSIDERATIONS . 



29 



.2 I 



o 



T, 



n § 



o 



02 



Osmotic 

 Osmotic pressure at 'Y^ir=Vi='p{' —Vi • 

 T, = P,=i),"-i','. 



Heat of dilution at T.2=( '^iTf^' )»,• 



T,= T, 



.'^ 



>.)T,> 



T 



Theemoelectric . 

 Potential difference at T.2 = V.. = V,"— V./. 

 Ti=V,=V,"-V,'. 



7t2=Heat entry at T.,=To-=^ per 



unit charge. 



/V, 



7ri= 



T,=T,^ 



T, ^ 

 unit charge. 



Now although the fact that both cases are sohitions enables oue to 

 write down the general expressions for both, it does not follow that there 

 ia precise numerical correspondence. Nevertheless it is instructive to 

 enquire what is found to be true for ordinary solutions. 



It is found in practice for solutions such as sugar in water that P can, 

 with fair accuracy, be represented by a simple equation such as 



P=«RT/(1— «6). 

 With this equation the 



Heat of dilution=T^J^=P. 



Hence the heat taken in is nearly equal to the external work done. 

 Recent measurements of it have been made by Miss D. Hunter and 

 by Perman and Downes, and deviations from this statement have been 

 determined. 



On the other hand, in the thermoelectric case 



7r = aT(To-T] 

 for many pairs of metals. At temperatures remote from the neutral 

 temperature (To) this is of the same form, but in general since 



n9V 



7r=T' 



aT' 



=a(To-T) or V-V2To=KT„T- 



There seems to be nothing in the osmosis of solutions to indicate what 

 the value of the integration constant V2T(, may be. 



The second property of solutions is that of vapour pressure or, as it 

 is called, thermionic emission. We have two solutions, Zinc + E and 



