338 KEYES 



ART. J 



where v is the volume of a "gram molecule" and would have 

 referred in the first half of the last century, to the absolute tem- 

 perature as measured by a mercury thermometer. The upper 

 limit of pressures was low and the precision of measurement, 

 moreover, hardly sufficient to make evident the limits of vahdity 

 of the relation (I) for describing the behavior of actual gases. 

 The extraordinarily ingenious and precise measurements of Reg- 

 nault were the first which showed the degree of inexactness 

 which must be accepted. Thus for the gases air, nitrogen, 

 carbon dioxide and hydrogen, compressed to a twentieth of the 

 volume at zero degrees and one atmosphere, the following 

 pressures were found : 



Air N2 CO2 H2 



Vn 



Pressure at — atm 19.72 19.79 16.71 20.27 



Percent deviation from 

 Equation (I) -1.4 -1.1 -16.45 +1.4 



At one-fifth of the volume, however, the magnitudes of the 

 deviations reduce to —0.4, —0.3, —3.4 and +0.24 percent, 

 respectively. Thus with respect to pressures at constant tem- 

 perature Regnault's classical investigations, of which the fore- 

 going is but a fragment, make it clear that equation (I) is to be 

 regarded strictly as the expression of a limiting law to which 

 actual gases may be expected to conform as the pressure is 

 indefinitely reduced. The gas-thermometric investigations of 

 Regnault^ and subsequently others'^ showed that the volume- 

 temperature coefficient at constant pressure, and similarly the 

 pressure-temperature coefficient at constant volume, tend to 

 an identical constant with diminishing pressure, thereby estab- 

 lishing the universality of the temperature scale definable by 

 equation (I) for p -^ 0. In addition, researches of Joule and 

 later of Joule and Thomson proved that the internal energy of 

 a gas at very low pressures is a temperature function only. 

 The investigations of the heat capacities of gases had, moreover, 

 shown in many cases, particularly for the gases whose critical 

 temperatures were low, that the temperature coefficients were 

 very small indeed. 



