Chapter 16, Problem 16.40SP

(a)

Interpretation Introduction

Interpretation:

A disordered crystal of monodeuteriomethane is oriented randomly in one of four possible ways.  Using Boltzmann’s equation the entropy of the disordered state of the crystal has to be calculated for the crystal containing 12 molecules of monodeuteriomethane, $C{H}_{3}D.$

Concept Introduction:

Boltzmann proposed an equation to calculate the entropy of a system in a particular state by relating it to the number of ways that the state can be achieved.  The equation is given as,

$S=k\ln W$

Where,

$\begin{array}{l}S=\text{ Entropy of the state}\\ \ln \text{ W}\text{= natural logarithm of the number of ways the state can be achieved}\text{.}\\ \text{k}\text{= Boltzmann's constant}\end{array}$

(b)

Interpretation Introduction

Interpretation:

A disordered crystal of monodeuteriomethane is oriented randomly in one of four possible ways.  Using Boltzmann’s equation the entropy of the disordered state of the crystal has to be calculated for the crystal containing 120 molecules of monodeuteriomethane, $C{H}_{3}D.$

Concept Introduction:

Boltzmann proposed an equation to calculate the entropy of a system in a particular state by relating it to the number of ways that the state can be achieved.  The equation is given as,

$S=k\ln W$

Where,

$\begin{array}{l}S=\text{ Entropy of the state}\\ \ln \text{ W}\text{= natural logarithm of the number of ways the state can be achieved}\text{.}\\ \text{k}\text{= Boltzmann's constant}\end{array}$

(c)

Interpretation Introduction

Interpretation:

A disordered crystal of monodeuteriomethane is oriented randomly in one of four possible ways.  Using Boltzmann’s equation the entropy of the disordered state of the crystal has to be calculated for the crystal containing 1 mol of molecules of monodeuteriomethane, $C{H}_{3}D.$

Entropy of the crystal has to be described if the $C-D$ bond of each of $C{H}_{3}D$ molecules points in the same direction.

Concept Introduction:

Boltzmann proposed an equation to calculate the entropy of a system in a particular state by relating it to the number of ways that the state can be achieved.  The equation is given as,

$S=k\ln W$

Where,

$\begin{array}{l}S=\text{ Entropy of the state}\\ \ln \text{ W}\text{= natural logarithm of the number of ways the state can be achieved}\text{.}\\ \text{k}\text{= Boltzmann's constant}\end{array}$