290 Variation of the Dissociation Coefficient with Temperature. 



cyclic process is 



W + JH, 



while the external work performed is 



dT dl > 



and by the second law of thermodynamics this last is equal to 

 the fraction dT/T of the heat absorbed. Hence 



^T=^(W + JH) (9) 



In equation (7) for W, C t and C 2 are constant, so that the 

 only variables are T and K. The differential in T, however, 



w ... 



produces -™- dT, which goes out with the similar expression 

 on the right-hand side of (9). We therefore have 



JR_dW dK 

 T " dK "dT 9 



or, after a little algebraical simplification, 



JH_2RT dKf 1 1 y 



Substituting now the expression (8) for H, we obtain 

 Q{(VX+4C 2 -^K)C 1 -(^K + 4C 1 -^K)C 2 } 

 _4RT 2 dK cr f 1 1 ) 



or, on simplification, 



n _RT 2 dK 



^~ K "dT' 

 which may be written 



^(logK) _ _Q_ 

 dT ~~ BT 2 ' 



the expression already obtained by van 't Hoff. 



