EQUILIBKIUM OF HETEROGENEOUS SUBSTANCES. 181 



represents the excess of the heat evolved over the work done by 

 external forces when a mass of the gas is compressed at constant 

 temperature until a unit of NO 2 has been converted into N 2 O 4 . 

 This quantity will be constant if .6 = 0, i.e., if the specific heats at 

 constant volume of NO 2 and N 2 O 4 are the same. This assumption 

 would be more simple from a theoretical stand-point and perhaps 

 safer than the assumption that & = Q. If B = 0, H = a 2 . If we wish 

 to embody this assumption in the equation between D, p, and t, we 

 may substitute 



for the second member of equation (336). The relative densities 

 calculated by the equation thus modified from the temperatures and 

 pressures of the experiments under discussion will not differ from 

 those calculated from the unmodified equation by more than '002 in 

 any case, or by more than '001 in the first series of experiments. 



It is to be noticed that if we admit the validity of the volumetrical 

 relation expressed by equation (333), which is evidently equivalent to 

 an equation between p, t, v, and ra (this letter denoting the quantity 

 of the gas without reference to its molecular condition), or if we admit 

 the validity of the equation only between certain limits of temperature 

 and for densities less than a certain limit of density, and also admit 

 that between the given limits of temperature the specific heat of the 

 gas at constant volume may be regarded as a constant quantity when 

 the gas is sufficiently rarefied to be regarded as consisting wholly of 

 NO 2 , or, to speak without reference to the molecular state of the gas, 

 when it is rarefied until its relative density D approximates to its 

 limiting value D v we must also admit the validity (within the same 

 limits of temperature and density) of all the calorimetrical relations 

 which belong to ideal gas-mixtures with convertible components. The 

 premises are evidently equivalent to this, that we may imagine an 

 ideal gas with convertible components such that between certain 

 limits of temperature and above a certain limit of density the relation 

 between p, t, and v shall be the same for a unit of this ideal gas as for 

 a unit of peroxide of nitrogen, and for a very great value of v (within 

 the given limits of temperature) the thermal capacity at constant 

 volume of the ideal and actual gases shall be the same. Let us regard 

 t and v as independent variables ; we may let these letters and p refer 

 alike to the ideal and real gases, but we must distinguish the entropy 

 r\ of the ideal gas from the entropy r\ of the real gas. Now by (88) 



dv 

 therefore ******* 



dv dt ~dt dv~dt dt ~~ dt 2 ' 



(338) 



