Classical Mechanics

# Configurational entropy (quantitative)

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.

John set up a password which consists of $7$ digits for his new cell phone last night. Upon waking, he finds that he has forgotten his password and only remembers that it was $7$ digits long. Find the increase in entropy concerning John's memory of the password.

$4$ 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.
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