TEMPERATURE AND THE PROPERTIES OF GASES 51 



vapour state at moderate pressures, again increasing with the 

 temperature very rapidly, and in some cases passing the first 

 maximum at easily attainable temperatures. The molecular 

 heats of gases at constant pressure appear to be given by a 

 formula as follows : 



(14) Cp = &s + zT 



where z is a coefficient which increases with the complexity of 

 the gas. 



In the above no mention has been made about density, as it 

 is always assumed that the density was small. However, in 

 some of the experiments which determined the best values we 

 have, the density was certainly very high, and we may consider 

 shortly the effect of density ; but the measurements are very 

 contradictory, and unfortunately the results which have been 

 deduced as yet from theoretical grounds do not appear to be 

 reconcilable with the best experimental evidence. 



If an easily manageable equation of state were to hand, which 

 were true over a large range, there should be no difficulty in 

 deducing the changes of both Cp and Cv from the well-known 

 relations 



(15) 



8Q_ -&£ 

 dv := 8/» 



Putting these equal to zero respectively should then give the 

 temperatures at which the maximum and minimum values of 

 Cv and Cp occur at various densities (pressures). However, 

 with either (2) or (4) Cv appears as a constant, and with (8) it 

 appears to only show maxima between very narrow limits of 

 density. This subject is now under consideration with improved 

 coefficients. It is known that Cv increases with increase of 

 density with all gases, excepting hydrogen, which have been 

 tried. In the case of hydrogen it decreases, and hence, as the 

 reduced temperature of hydrogen at ordinary experimental 

 temperatures is much higher than that attainable with the other 

 permanent gases which were tried, one is naturally led to the 

 supposition that the maximum value will occur for hydrogen 

 at some lower temperature with moderate pressures. 



The maximum value of Cv appears to increase with the 

 density, so that at very high pressures it is possible that the 



