Chapter 18, Problem 18.101SP

(a)

Interpretation Introduction

Interpretation:

In accordance with the given conditions the residual entropy in the $\text{CO}$ lattice has to be calculated.  The calculated value has to be compared with the observed value.

Concept Introduction:

Entropy is the measure of randomness in the system.  According to the third law of thermodynamics entropy of a perfectly crystalline substance at zero Kelvin is zero.  The substances which are not perfectly crystalline, possess entropy even at zero Kelvin.  The entropy of a substance at zero Kelvin is known as residual entropy.

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 residual entropy in the $\text{CO}$ lattice has to be calculated.  The calculated value has to be compared with the observed value.

Concept Introduction:

Entropy is the measure of randomness in the system.  According to the third law of thermodynamics entropy of a perfectly crystalline substance at zero Kelvin is zero.  The substances which are not perfectly crystalline, possess entropy even at zero Kelvin.  The entropy of a substance at zero Kelvin is known as residual entropy.

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