Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 105

The factor 2appears for the flowrate sincethere are two portalsfrom

regionB.On the otherhand, for anideal gas, andtherefore

We can rewrite(S.4.18.1) as

yielding

For the state ofequilibrium, theenergy in the volume Bis constant.This
meansthat the total rate of energytransfer out ofvolumes I and II should
be equal to therate ofenergytransfer out ofvolumeB:

The average energy per particle is proportional to the temperature, so

(S.4.18.6)becomes

We thenhave

Dividing(S.4.18.8) by (S.4.18.5),we can obtain

and