Chapter 17, Problem 17.5P

Interpretation Introduction

Interpretation:

Boltzmann’s equation is used to determine the number of ways in which a molecule can be arranged in containers in an energy level.

Concept introduction:

Boltzmann’s equation

$W={(g_J)}^{N_J}$
$g_J$ = degeneracy or number of different containers.

$N_J$ = number of molecules
Therefore, entropy S can be expressed as

$S=k_B\ln W$

Where k = Boltzmann constant = 1.3807 x 10 -23 joule s per kelvin (J. K -1)

Given:

The distribution of ideal gas molecules among three bulbs (A, B, and C) having equal volume.
Use Boltzmann’s equation.
The given states are-

1. 10 molecules in bulb A
2. 10 molecules randomly distributed among bulbs A, B, and C.

To determine:

To determine the number of ways (W) that the state can be achieved and the entropy of the state.