120 GENERAL PRINCIPLES OF THERMO-CHEMISTRY. 



Theorem IV. Formation of alcohols. The heat liberated 

 when an alcohol is formed by the union of water and of a 

 hydrocarbon is the difference between the quantities of heat liberated 

 ivhen the alcohol and the hydrocarbon form one and the same 

 combination with an acid such as sulphuric acid. 



The formation and the decomposition of conjugate bodies 

 (ethers, amides, etc.) give rise to various other theorems, analogous 

 to those relative to the salts, but which are omitted in order not 

 to unduly extend this summary. 



4. Theorems relative to the Variation of the Heat of 

 Combination with the Temperature. 



In general, the quantity of heat liberated in a chemical 

 reaction is not a constant quantity ; it varies with the changes 

 of state, as has been said above; but it also varies with the 

 temperature, even when each one of the reacting substances 

 preserves the same physical state during the interval considered. 

 This variation is calculated in the following manner for any 

 reaction whatever, according to the second principle. 



The reaction may be determined at an initial temperature, t, 

 and the heat liberated, Qt, may be measured. 



The component bodies may also be raised separately from the 

 temperature t to the temperature T : which absorbs a quantity 

 of heat, U, depending on the changes of state and of the specific 

 heats, then the reaction is determined, which liberates Q; 

 lastly, the products are brought by a simple lowering of tempera- 

 ture from T to t, which liberates a quantity of heat, V, also 

 depending on the changes of state and of the specific heats. The 

 initial and final states being the same in both processes the 

 quantities of heat liberated are equal, that is to say : 



Theorem I. The difference between the quantities of heat liber- 

 ated by the same reaction, at two distinct temperatures, is equal to the 

 difference between the quantities of heat absorbed by the components 

 and by their products, during the interval of the two temperatures. 



QT = Q* + U - V. 

 U V represents the variation in the heat of combustion. 



Theorem II. If, during the interval T t, none of the original 

 or final bodies undergoes change of state, this expression reduces 

 itself to the sum of the mean specific heats of the first bodies 

 during this interval, minus the sum of the mean specific heats of 

 the second bodies, multiplied by the interval of the temperatures. 

 U - V = (Sc - SoO (T - t). 



The heat of combination will go on increasing or diminishing 

 with the temperature, and may even change in sign, according 

 as the first sum is greater than the second, or vice versa. 



Theorem III. Gaseous combinations formed without condensa- 

 tion. In order that the heat liberated may be independent of the 

 temperature, the two above sums must be equal. Now this 



