Chapter 18, Problem 13PS

Interpretation Introduction

Interpretation:

The change in entropy of the system in going from $5$ accessible microstates to $30$ accessible microstates should be calcualted.

Concept introduction:

Entropy$\text{S}$: it is used to describe the disorder. It is the amount of arrangements possible in a system at a particular state. ${\text{ΔS}}_{\text{univ}}={\text{ΔS}}_{\text{sys}}+{\text{ΔS}}_{\text{surr}}$

The entropy of a system $\text{S}$ is directly proportional to the number of accessible microstates, represented by the symbol $\text{W}$. The relationship can be expressed by the Boltzmann equation,

  $\text{S = k lnW}$

Here, $\text{k}$ is Boltzmann constant whose value is equal to $\text{1}{\text{.381×10}}^{-\text{23}}\text{ J/K}$

The change in entropy can be represented as,

  $\Delta S=\text{k }\ln \left(W_{\text{final}}-W_{\text{initial}}\right)$