Chapter 5, Problem 5.18CP

Interpretation Introduction

Interpretation: The change in entropy observed on mixing equal volumes of $\text{Ar}$ gas in two different valves is to be stated. Whether the value of $\Delta S$ remains same if one of the volumes possesses $\text{Ar}$ and another one possesses $\text{Ne}$ or not is to be stated.

Concept introduction: Mixing of two distinct gases generally cause a rise in system’s entropy. The corresponding reason is the higher microstates available for the gases in mixed system as compared to unmixed system. However, if the gases being mixed are same, then no entropy change is observed. The entropy change encountered on mixing two distinct gases is calculated by the formula shown.

  $\Delta S=-2.303R\left(n_{\text{A}}\log x_{\text{A}}+n_{\text{B}}\log x_{\text{B}}\right)$