630 SUPPLEMENTARY. 



The expression in the parenthesis should also be an exact 

 differential, from which it follows that 



~oa a <)/ 



(4) ^~T = ^' 



OL T ox 



This equation (4) may also be considered as the translation 

 of Carnot's principle. 



Comparing equations (3) and (4), we deduce 



An analogous equation would be obtained for any other 

 independent variable. If A is the whole differential coefficient 

 of the calorific energy absorbed for any transformation of the 

 body at a constant temperature, which corresponds to the latent 

 heat relative to this transformation, and if B is the corresponding 

 differential coefficient of the external work, we shall have 



(6) A--T*. 



^T 



647. We may deduce the following conclusions from this 

 equation (6) : 



Whenever the external work takes place in a direction such 



that the rate of change is negative, the value of A is positive. In 



other words, whenever the deformation produced by the external 

 work is such that a deformation of the same kind could be 

 produced by a cooling of the body, this work is accompanied by 

 a disengagement of heat, and therefore by a rise of temperature. 



The reverse is the case if the rate of change were positive. Hence 



it is that a gas becomes heated when it is compressed, and cooled 

 when it expands. 



As solids expand as a general rule when the temperature rises, 

 we see that the uniform compression of a solid will also produce 

 a rise of temperature. 



It is otherwise with bodies whose expansion is abnormal, such 

 as water at a temperature below 4, and iodide of silver at ordinary 

 temperatures. The compression of these bodies would produce a 

 lowering of temperature. 



