Chapter 18, Problem 13QP

Interpretation Introduction

Interpretation:

The change in entropy of the system in the given isothermal expansion and compressionis to be calculated.

Concept introduction:

Entropy is the direct measurement of randomness or disorderness. Entropy is an extensive property. It is a state function.

Entropy of a system is a measure of how spread out or how dispersed the system’s energy is. Change in entropy of a system is the difference between the entropy of the final state and the entropy of the initial state.

Mathematically, the change in entropy of a system is represented as $\Delta S_{system}=\Delta S_{final}-\Delta S_{initial}$

The above expression is reduced to:

$\Delta S_{system}=n\text{R}\ln \frac{\left(V_{final}\right)}{\left(V_{initial}\right)}$

Here, $n$ is the number of moles, $\text{R}$ is the universal gas constant, $V_{final}$ is the final volume, and $V_{initial}$ is the initial volume of the system.

The entropy of the system and the entropy of the surroundings make up the entropy of the universe.