244 J. W. Gihbs — EquUihrium of Heterogeneous Substances. 



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



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



temperatnre until a unit of NO 3 has been converted into NgO^. 



This quantity will be constant if J3 =zO, i. e., if the specific heats at 



constant volume of NO^ and N2O4 ^i"e the same. This assumption 



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



safer than the assumption that B' = 0. li B =1 0, B' = a^. If we 



wish to embody this assumption in the equation between Z>, p^ and t, 



we may substitute 



2977 4 

 6.5228 + log, „ {t, + 273) ^ j^i^^ 



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 diflTer 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, y, and ni (this letter denoting the quan- 

 tity 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 con- 

 sisting wholly of NO2, — or, to speak without reference to the m.olecu- 

 lar state of the gas, when it is rarefied until its relative density D 

 approximates to its limiting value Z>,, — 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 ^reat value of (witliin 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 ?/' of the ideal gas from the 

 entropy tf of the real gas. Now by (88) 



