Chapter 11, Problem 11.35P

Interpretation Introduction

Interpretation:

Equation $11.12$ for $\Delta S^{id}$ is to be developed by the appropriate application of equations $5.36\text{ and }5.37$ to a mixing process.

Concept Introduction:

Equation $5.36$ to calculate number of different ways in which microscopic particles can be distributed among the ‘states’ accessible to them is:

   $\Omega =\frac{N!}{N_1!N_2!N_3!\dots }$ .....(1)

Here, $N$ is total number of particles, $N_1$ is the number of particles in state 1, and so on.

Relationship between entropy $\left(S\right)$ and $\Omega$ is given by equation $5.37$ as:

   $S=k\ln \Omega$ .....(2)

Here, $k$ is Boltzmann constant and is defined as:

   $k=\frac{R}{N_{\text{A}}}$ .....(3)

Here, $R$ is universal gas constant and $N_{\text{A}}$ is the Avogadro’s number.