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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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