737 
Physics. — “Some remarks on the theory of monatomic gases”. 
By H. A. Lorenz. 
(Communicated in the meeting of September 26, 1914.) 
§ 1. Several physicists have recently applied the theory of quanta 
to gaseous bodies, especially to monatomic gases. The common object 
of their considerations, much though they differ from each other, 
may be said to have been the determination of the entropy S of a 
gas as a function of the volume v and the energy /. 
If this function is known, the temperature 7’ and the pressure p 
may likewise be expressed in terms of # and v by means of the 
thermodynamic relations | 
osn 1 0S p 
Dre SP My TTT" 
Further the relation between p, v, and 7), ie. the equation of state 
ean be found and also that between v, 7), and /, from which we 
can derive the specifie heats. 
In the case of an ideal monatomic gas classical thermodynamics 
lead to the formula 
3 
S= kN (logv + log E) Ha, EE U DI 
in which N denotes the number of molecules, 4 PLANck’s well known 
coefficient and « an undeterminate constant. In the way just men- 
tioned we infer from this 
3 
Pe ENT, BANT ene ee ® 
Now, the new theories differ from classical thermodynamics in so 
far as they assign to the entropy a completely definite value without 
an undeterminate constant. As to the way in which v and Moccur 
in the formula, this may either remain as it is in (1) or the form 
of the connexion may be a more complicated one. In the first case 
the only change is, that a, which has been called by Nernst “the 
chemical constant” of the gas, takes a definite value, the equations 
(2) remaining unmodified. In the seeond case these latter equations 
have to be changed. 
In the theories in question the entropy is always determined by 
means of BontzmMann’s formula 
S= * lag W, 
where W is the “probability” of the state considered. Generally 
speaking there can be no donbt about the validity of this relation 
47 
Proceedings Royal Acad. Amsterdam. Vol. XIX 
