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Microstate Visualizer

Run the microstate explorer fullscreen
Edit the MicroSim in the p5.js editor

About This MicroSim

Blue and orange particles bounce inside a container split into left/right halves. You can adjust the particle count, randomize distributions, remove the wall, and highlight any macrostate. A bar chart shows the binomial distribution of microstates (W) for each macrostate, along with ln(W) and S = k_B ln(W).

How to Use

  1. Move the N slider to set the number of particles.
  2. Press Randomize Distribution to redistribute particles between halves at random.
  3. Toggle Remove Wall to let particles mix freely (wall returns when pressed again).
  4. Use the Highlight macrostate dropdown to emphasize a particular left:right ratio in the bar chart.
  5. Read the live W, ln(W), and S values beneath the chart.

Classroom Ideas

  • Probability storytelling: Students narrate what happens to W as N increases and explain why the peak moves toward N/2.
  • Entropy discussion: Use the bar chart to connect S = k_B ln(W) with macroscopic spontaneity.
  • Data recording: Learners set N to different values and record W for the 50:50 distribution, then calculate S manually to verify the display.

Lesson Plan

Grade Level

Grades 11–12 (AP Chemistry Unit 7) and introductory statistical thermodynamics

Duration

10–12 minutes as a guided exploration or homework companion

Prerequisites

  • Definition of microstates vs. macrostates
  • Boltzmann equation S = k_B ln(W)

Activities

  1. Demo (3 min): Instructor shows how W skyrockets near N/2 as N increases.
  2. Guided slider practice (6 min): Students try N = 6, 10, 14 and compare W(0:N), W(N/2:N/2).
  3. Reflection (3 min): Learners explain why ΔS > 0 when the wall is removed.

Assessment

  • Exit ticket: “Why does the 50:50 macrostate dominate for large N?”
  • Homework extension: Students capture a screenshot with N = 12 and calculate S from W and k_B.

References

  1. Atkins & de Paula, Physical Chemistry, 11th ed., Oxford University Press, 2017 — Microstates and entropy.
  2. Baierlein, Thermal Physics, Cambridge University Press, 1999 — Boltzmann statistics and combinatorics.