Chapter 13, Problem 1E

Interpretation Introduction

(a)

Interpretation:

When increasing the length of the box to 2 L for fixed total energy, the change in the number of accessible microstates and the entropy of the system should be explained.

Concept introduction:

Microstates is a specific microscopic configuration describing how the particles of a system are distributed among the available energy levels.

In a system, the entropy of a system depends on the total number of possible microscopic states by the Boltzmann relation as shown below:

${\text{S = K}}_B\times \text{ ln W}$

Here, ${\text{K}}_B$ is Boltzmann constant, S is entropy and W is number of microstates.

Answer to Problem 1E

Number of microstates and the entropy increases.

Explanation of Solution

Given information:

Number of particles = 5

1D box length = L

When the length of the box is increased to 2 L, the number of the microstates increases for fixed total energy. the energy levels are shifted to lower values and are more closely spaced. Therefore,

more energy levels are accessible

According to the ${\text{S = K}}_B\times \text{ ln W}$ equation, when number of microstates increase, entropy also gets increased.

Interpretation Introduction

(b)

Interpretation:

Whenthe total energy for constant box length is increased, the change in the number of accessible microstates and the entropy of the system should be explained.

Concept introduction:

Microstates is a specific microscopic configuration describing how the particles of a system are distributed among the available energy levels.

In a system, the entropy of a system depends on the total number of possible microscopic states by the Boltzmann relation as shown below:

${\text{S = K}}_B\times \text{ ln W}$

Here, ${\text{K}}_B$ is Boltzmann constant, S is entropy and W is number of microstates.

Answer to Problem 1E

Number of microstates and the entropy increases.

Explanation of Solution

Given information:

Number of particles = 5

1D box length = L

With the increase of total energy, the number of microstates increases because more energy levels are accessible.

According to the ${\text{S = K}}_B\times \text{ ln W}$ equation, when number of microstates increase, entropy also gets increased.