402,403] Specific Heats 333 



As a conspicuous instance of a gas in which these laws are not satisfied 

 we may take chlorine, of which the boiling point at normal pressure is 

 33'4 C. According to Stas's determination of the atomic weight of chlorine 

 its density relatively to that of air would be 2-4501 at all temperatures 

 if Avogadro's Law were satisfied. The observed densities are as follows : 



Temp. C. Density 



20 2-4807 



50 2-4783 



100 2-4685 



150 2-4609 



200 2-4502 



On inspection of these figures, we see that the deviation at 150 C. is 

 about 100 times as great as that at 200 C. This rapid diminution as the 

 temperature increases, suggests that aggregation plays the preponderating 

 part in the production of these deviations. 



Calorimetry. 

 403. The total translational energy per unit volume is 



We must also regard each compound molecule as possessing internal 

 energy of amount [|m.F 2 + 2"^]. This is negative, the explanation of course 

 being that it is referred to the energy of two molecules at rest and clear 

 of each other's sphere of influence as zero. Let us write / 2 , 7 3 , ... for 

 the average internal energy of double molecules, triple molecules, etc., 

 so that the total internal energy of the clusters of molecules, referred to the 

 standard already explained, is 



- (r 2 / 2 + V S I 3 + ) 



The general equation of calorimetry is now 



d<& = d [3RT ( Vl + i/ a + . . .) v - (vJ 2 + 1/3/3 + . . .) v] +pdv. 

 At constant volume, this becomes 



d = vd [3RT( Vl + v 2 +...)- (i/a/a + 1/3/3 + ...)] 

 and since the value of d<& is JpvC^dfS 1 , we have by comparison, 



If there were no aggregation, the value of G v would be 

 ' 



so that by subtraction, 

 ' 



"3/3 



