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## Configurational Entropy

Ludwig Boltzmann killed himself so that we could do thermodynamics by enumerating the states of a system. Learn to count, the most important skill in statistical mechanics.

# Calculating 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.

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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