Classical Mechanics

Configurational Entropy

Configurational entropy (quantitative)

         

A system consists of 4 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 kB. k_B.

We isothermally compress 7 7 mole of O2 O_2 from 6 L 6 \text{ L} to 3 L. 3 \text{ L}. How much does the entropy of the gas change?

Assumptions and Details

  • O2 O_2 is ideal gas
  • NA N_A is Avogadro's number and kBk_B is the Boltzmann constant.

John set up a password which consists of 7 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 77 digits long. Find the increase in entropy concerning John's memory of the password.

4 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 33C. 33 ^\circ \text{C}.
  • The Boltzmann constant is kB k_B

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

Assumptions and Details

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