Chapter 14, Problem 14.7QP

 (a)

Interpretation Introduction

Interpretation:

In accordance with the given conditions the number of possible arrangements and the entropy for the given set up has to be calculated.

Concept Introduction:

A thermodynamic system can have degenerate and non degenerate energy levels.  There can be different possible arrangements of the particles in the various energy levels.  These possible arrangements are defined as thermodynamic probability $\text{(W)}$ or microstates.  The thermodynamic probability can be calculated using the following formula.

${\text{W = g}}^{\text{N}}$

Where

$\text{'N'}$’ is the total number of particles

$\text{'g'}$ is the degeneracy of the energy level

The entropy and thermodynamic probability is related by Boltzmann equation.  As the number of possible arrangements increases the entropy also increases.

$\text{S = klnW}$

Where,

$\text{S}$ is the entropy

$\text{k}$ is the Boltzmann constant $\text{k =1}{\text{.38×10}}^{\text{-23}}{\text{JK}}^{\text{-1}}$

$\text{W}$ is the thermodynamic probability

(b)

Interpretation Introduction

Interpretation:

In accordance with the given conditions the number of possible arrangements and the entropy for the given set up has to be calculated.

Concept Introduction:

A thermodynamic system can have degenerate and non degenerate energy levels.  There can be different possible arrangements of the particles in the various energy levels.  These possible arrangements are defined as thermodynamic probability $\text{(W)}$ or microstates.  The thermodynamic probability can be calculated using the following formula.

${\text{W = g}}^{\text{N}}$

Where

$\text{'N'}$’ is the total number of particles

$\text{'g'}$ is the degeneracy of the energy level

The entropy and thermodynamic probability is related by Boltzmann equation.  As the number of possible arrangements increases the entropy also increases.

$\text{S = klnW}$

Where,

$\text{S}$ is the entropy

$\text{k}$ is the Boltzmann constant $\text{k =1}{\text{.38×10}}^{\text{-23}}{\text{JK}}^{\text{-1}}$

$\text{W}$ is the thermodynamic probability

(c)

Interpretation Introduction

Interpretation:

In accordance with the given conditions the number of possible arrangements and the entropy for the given set up has to be calculated.

Concept Introduction:

A thermodynamic system can have degenerate and non degenerate energy levels.  There can be different possible arrangements of the particles in the various energy levels.  These possible arrangements are defined as thermodynamic probability $\text{(W)}$ or microstates.  The thermodynamic probability can be calculated using the following formula.

${\text{W = g}}^{\text{N}}$

Where

$\text{'N'}$’ is the total number of particles

$\text{'g'}$ is the degeneracy of the energy level

The entropy and thermodynamic probability is related by Boltzmann equation.  As the number of possible arrangements increases the entropy also increases.

$\text{S = klnW}$

Where,

$\text{S}$ is the entropy

$\text{k}$ is the Boltzmann constant $\text{k =1}{\text{.38×10}}^{\text{-23}}{\text{JK}}^{\text{-1}}$

$\text{W}$ is the thermodynamic probability