Lesson Plan

• Describe the relationship between the macroscopic ideal‑gas law (pV = nRT) and its microscopic form (pV = NkT).
• Derive the expression k = R / N_A from the two forms of the ideal‑gas law.
• Apply the Boltzmann constant to calculate average kinetic energy and root‑mean‑square speed of gas molecules.

• Projector and screen
• Whiteboard and markers
• Printed worksheet with derivation steps and practice problems
• Scientific calculators
• Handout of constants (R, N_A, k)
• Interactive gas‑particle simulation (e.g., PhET)

Begin with a quick question: “What does temperature tell us about the motion of individual molecules?” Students recall the ideal‑gas law and Avogadro’s number. Explain that today they will link these macroscopic ideas to a single‑particle constant and will be able to use it in calculations.

1. Do‑now (5'): Quick revision checklist – students write pV = nRT and pV = NkT and list values of R, N_A, k.
2. Mini‑lecture (10'): Derive k = R / N_A by substituting n = N/N_A into the ideal‑gas law and comparing with pV = NkT.
3. Guided example (10'): Calculate the average kinetic energy ⟨E_kin⟩ = 3/2 kT for a given temperature.
4. Interactive simulation (10'): Students explore a gas‑particle model to see how temperature affects rms speed, then compute v_rms = √(3kT/m).
5. Formative check (5'): Exit‑ticket – write the derived formula for k and one real‑world application.

Summarise how the Boltzmann constant bridges macroscopic gas behaviour and microscopic particle energy. Collect exit‑tickets as a quick retrieval check. For homework, assign the worksheet’s additional problems on kinetic energy and rms speed calculations.