156 Intelligence and Miscellaneous Articles. 



2. Let us seek as well the condition for there being no heat con- 

 sumed in internal work when the body is heated under constant 

 volume, which is sensibly the case for permanent gases. 



The quantity of heat necessary for raising the temperature by cZT 

 is then KdT ; in this case dL = 0, 



dT+2T-^ =0. 



^ 



This relation is equivalent to the following — 

 Ti*= constant. 



By substituting for i and T the values deduced from the prece- 

 ding relations we find for the condition 



a— constant. 



Therefore, that there may be no heat consumed in internal work 

 when a body is heated under constant volume, the amplitude of the 

 oscillations must remain the same ; on the contrary, there is expen- 

 diture of heat in internal work when the amplitude of the oscilla- 

 tions increases. 



3. When the body undergoes transformation with the tempera- 

 ture constant, as in changes of state, the quantity of heat necessary 

 for effecting the transformation is 



Q=2MKT £— ==2MKTlog(i\ 



designating by i and i the durations of an oscillation before and 

 after the transformation, and by log the Napierian logarithm. 



The temperature being the same, if a Q and a denote the corre- 

 sponding durations of an oscillation, 



But, besides, f and / denoting the mean values of the molecular 

 forces before and after the transformation, the temperature remain- 

 ing the same, 



and consequently 



Q==2MKTlog0>\ 



This relation shows the connexion existing between the heat ne- 

 cessary for determining a change of state, such as fusion or vapori- 

 zation, and the variation of the molecular actions in consequence 

 of the change of state. When the molecular actions diminish (which 

 is the ordinary case), the transformation demands an expenditure 

 of heat (heat of fusion or vaporization); while the body evolves 

 heat when the change of state is accompanied by augmentation of 

 the molecular forces. — Comptes Rendus de VAcademie des Sciences, 

 vol. lxxx. pp. 40-44. 



