Physic Labs

Thermal physics

Structure of matter and kinetic theory

Watch the random thermal motion of gas molecules in a closed vessel and how wall collisions produce pressure. Check qualitatively that mean kinetic energy tracks temperature, ⟨Etrans⟩=32kBT\langle E_{\text{trans}}\rangle = \frac{3}{2}k_B T, and pV=NkBTpV = Nk_BT.

High school

Equipment

  • Virtual closed vessel holding randomly moving molecule dots
  • Temperature slider controlling the molecules' characteristic speed
  • Slider for the number of molecules N in the vessel
  • Vessel walls and a collision/pressure readout

Procedure

  1. Observe thermal motion

    Run the simulation at moderate temperature and follow a single molecule: its path is jagged, redirecting at each collision with another molecule or the wall. Every wall hit transfers momentum — averaged, these impulses produce pressure.

  2. Raise the temperature

    Drag the temperature slider up and observe: molecules move faster, and wall collisions become more frequent and harder. Since the characteristic speed scales as T\sqrt{T}, mean kinetic energy is proportional to T — consistent with ⟨Etrans⟩=32kBT\langle E_{\text{trans}}\rangle = \frac{3}{2}k_BT.

  3. Change the molecule count

    Hold T fixed and increase N: the density of wall impacts rises proportionally, so pressure grows as pV=NkBTpV = Nk_BT. Predict the pressure when N doubles at fixed V, T, then compare with the picture.

Simulation

Experiment history

In 1738, Daniel Bernoulli in Hydrodynamica already derived gas pressure from collisions of moving particles — an idea soon forgotten. In the nineteenth century, John Herapath (1820), John James Waterston (1845, rejected for publication), and August Krönig (1856) rebuilt the kinetic model. Rudolf Clausius gave a rigorous model in 1857 with the mean free path; James Clerk Maxwell (1859–1860) found the statistical velocity distribution, which Ludwig Boltzmann generalized into his kinetic equation (1872). Brownian motion, observed by Robert Brown (1827) and measured quantitatively by Jean Perrin (1908), finally proved molecules physically real.

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