Chapter 10, Problem 10.73PAE

Interpretation Introduction

Interpretation:

Reason to why playing cards on a table and leaves lying in the yard are not a good analogy for the entropy of a system containing only ${\text{H}}_2\text{O}$ molecules or only ${\text{O}}_2$ molecules should be explained.

Concept Introduction:

Entropy is defined as the measure of randomness or disorder in a system.

Entropy of a system is defined statistically on a microscopic level. In statistical mechanics the number of microstates or energy states that is the number of ways in which these microscopic particles acquire same energy is determined.

The number of microstates for a particular energy is denoted as Omega (O). And the entropy is then related to number of microstates by the equation:

$S=k_{\text{B}}\ln \Omega$

Where, $k_{\text{B}}$ is Boltzmann’s constant.

More random arrangements of particles of a system would increase the number microstates possible for the system. And so entropy of any system increases if it moves towards more random distribution of particles constituting the system.