eo 
( 781 ) 
Physics. — “On the calculation of the pressure of a gas by the 
aid of the assumption of a canonical ensemble.” By Dr. 
O. Postma. (Communicated by Prof. H. A. Lorentz.) 
(Communicated in the meeting of February 27, 1909). 
To the different existing methods for the derivation of the pressure 
of a gas (or the equation of the isotherm), GisBs has of late added 
another, namely the method by the aid of the theory of a canonical 
ensemble. According to this method we take for the force exerted 
by a system on an external body in the direction of one of the 
f de de 
coordinates a of that body, the value — a the mean are taken 
Ga a 
over a canonical ensemble. Dr. Ornsrrin was the first to apply this 
method *). He shows that 
= J J 
Zeef" Gu 
da da da 
nad ae 
in which w is determined by e 7 = { e Tdà. Suppose the gas 
to be in a cylinder, closed by a piston at a height a, A repre- 
sents the pressure exercised on this piston. The pressure pro 
Si 
cM’. will be represented by p= — and by means of this formula 
Dr. ORNSTEIN arrives at the known result. If, however, we examine 
the method somewhat more closely, we are confronted with different 
difficulties. In the first place it should be borne in mind, that if 
de . 
A= ie is to denote the force exerted on the piston, the coordi- 
a 
nates of the molecules must be thought to be constant in this diffe- 
rentiation °). Apart from the energy of gravity, the ¢ consists of four 
parts: €, =the potential energy of the repulsive forces acting between 
the walls of the vessel and the molecules, ¢, = the potential energy 
of the repulsive forces between the molecules inter se, ¢, = the 
potential energy of the attractive forces, ¢,—= the kinetic energy. 
Only the first is a function of a, and it determines the A, which is 
1) Cf “Toepassing der Statistische Mechanica van GiBBs op molekulair-theoretische 
vraagstukken’”’. Leiden 1908. Further: ‘Calculation of the pressure of a mixture 
of two gases by means of GrpBs’ statistical mechanics,” These Proc. Vol. XVII, 
p. 116, and “Statistical theory of capillarity”, These Proc. Vol. XVII, p. 526. 
2) When we substitute at once V for a, there is some danger to overlook this. 
53 
Proceedings Royal Acad. Amsterdam. Vol. Xl. 
