Classical Mechanics
# Configurational Entropy

A system consists of $4$ coins. Each coin has a 50-50 probability to show heads or tails. Find the entropy of the case where all coins show heads.

The Boltzmann constant is $k_B.$

We isothermally compress $7$ mole of $O_2$ from $6 \text{ L}$ to $3 \text{ L}.$ How much does the entropy of the gas change?

**Assumptions and Details**

- $O_2$ is ideal gas
- $N_A$ is Avogadro's number and $k_B$ is the Boltzmann constant.

$4$ particles are in a room which is divided into two equal parts. If we consider the macrostate of the even split, what is its entropy?

**Assumptions and Details**

- The room temperature is $33 ^\circ \text{C}.$
- The Boltzmann constant is $k_B$

A $6 \text{ L}$ container is separated by a partition into two equal halves. Each half contains $8 \text{ mole}$ of either $\text{He}$ or $\text{Xe}$. What is the change in entropy of the total system after the partition is removed?

**Assumptions and Details**

- $\text{He}$, and $\text{Xe}$ are ideal gases.
- $N_A$ is Avogadro's number.