Statistical Mechanics · Problem 1.1

Elements of Ensemble Theory — R. K. Pathria

Physics — Statistical Mechanics · gaussian-distribution-thermal-contact

Problem

(a) Show that, for two large systems in thermal contact, the number

\Omega^{(0)}(E^{(0)}, E_1)

of Sec. 1.2 can be expressed as a Gaussian in the variable

E_1

. Determine the root-mean-square deviation of

E_1

from the mean value

\bar{E}_1

in terms of other quantities pertaining to the problem. (b) Make an explicit evaluation of the root-mean-square deviation of

E_1

in the special case when the systems

A_1

and

A_2

are ideal classical gases.