physics / Matter & Energy / free

Statistical Mechanics

Connect the motion of tiny particles to the behavior of matter you can feel.

Follow the mechanism1 / 3

Temperature raises particle energy. Heating the gas raises the average kinetic energy, so the rms speed grows as √T.

microstates behind a temperatureS = kᵦ ln Ω

The dots are not a molecular simulation: their jitter just scales with v_rms = √(3kᵦT/m), shown for helium. ΔS uses a monatomic ideal gas at fixed volume, ΔS = (3/2)kᵦ ln(T/10 K) per atom. A macroscopic variable compresses information about a huge number of microscopic arrangements.

temperature55 K
rms speed (He)585 m/s
ΔS per atom vs 10 K2.56 kᵦ

A macrostate can be realized by many microstates. The overwhelmingly numerous arrangements are why equilibrium is the most likely large-scale observation.

04 / PRACTICE

Make the idea yours.

0 / 3 checked

Use the model, then answer without looking back. Each check isolates one decision a learner should be able to make after this lesson.

CHECK 1 / 3

What does a microstate specify?