FUNDAMENTAL EQUATIONS OF IDEAL GASES 339 



The complete concept, therefore, of the perfect gas, accepted 

 by Clausius and here taken by Gibbs, is defined by the first 

 three equations of this section. For convenience of reference 

 they will be designated as follows : 



pv = at, (II) 



de = c dt, (III) 



€ = ct + E. (IV) 



It is noted that the heat capacity employed is that at constant 

 volume rather than that at constant pressure. There is wisdom 

 in the choice, for the former is the simpler quantity, and while 

 it must usually be derived from measurements at constant 

 pressure in default of direct measurements at constant volume, 

 nevertheless this reduction may be carried out once for all as a 

 special operation in preparing heat capacity data for use in the 

 applications of thermodynamics where gases are involved. 

 It is, moreover, not difficult to show that many applications of 

 thermodynamics involving liquids and solids proceed very 

 advantageously where the constant-volume heat capacity is 

 employed. 



2. Mixtures of Ideal Gases. The question of greatest impor- 

 tance in all detailed applications of thermodynamics is that of 

 determining the laws to be employed in representing the physical 

 behavior of mixtures of gases. Until the various aspects of 

 this problem are resolved no real progress with applications of 

 the general theory becomes possible, and it is for this reason 

 that Gibbs took the greatest care to investigate all ramifica- 

 tions of this far from simple matter. It also seems evident 

 from the statements and form of this section that Gibbs was 

 seeking for a principle which would carry further than the 

 popularly phrased statement of Dalton's law or rule for mixtures 

 of gases. Indeed he found a statement of Dalton's law ("Gibbs- 

 Dalton law") which he showed to be "consistent and possible" 

 for mixtures of gases which are not ideal.* 



S. Ideal Gas Concept as Related to the Behavior of Actual 

 Gases under Diminishing Pressure. Because (II), (III), (IV) 



A test of this law has recently been made. See reference (6). 



