Chapter 16, Problem 16.44SP

Interpretation Introduction

Interpretation:

The factor by which the entropy of $1000$ molecules increase when moved from $1.00\times {10}^6$ boxes to $1.00\times {10}^7$ boxes has to be calculated.

The factor by which the entropy of $1000$ molecules increase when moved from $1.00\times {10}^{16}$ boxes to $1.00\times {10}^{17}$ boxes has to be calculated.

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,

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