Solitaren: Mean Free Path Vacuum
Measurement, Noise & the Lab arc, page 136 of 193. Back to The Pixelated Physics Universe
Who they are
Solitaren has one line, and says it often: “At 1e-6 mbar, molecules get 66 m alone.”
Solitaren is a character of the Measurement, Noise & the Lab arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Mean free path λ = kBT/(√2 π d² p). For air at room temperature, λ ≈ 6.6 × 10⁻³ cm /(p in mbar), about 66 m at 10⁻⁶ mbar.
$$ \begin{gathered} \lambda = \frac{k_B T}{\sqrt{2}\,\pi d^{2} p} \\ \lambda_{\text{air}} \approx \frac{6.6 \times 10^{-3}\ \text{cm}}{p\,[\text{mbar}]} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $\lambda$ | mean free path | m |
| $k_B$ | Boltzmann constant | J/K |
| $T$ | temperature | K |
| $d$ | molecular diameter | m |
| $p$ | pressure | Pa |
Sources
- K. Jousten (ed.), Handbook of Vacuum Technology (Wiley-VCH, 2016), ch. 3
Crossovers
Solitaren meets Voidcask (Vacuum Flask Insulation). Voidcask's insulating gap works because Solitaren's rule holds: with the pressure low enough, gas molecules cross the gap without colliding, so conduction through the gas almost vanishes.
Solitaren meets Streakwin (Cosmic Ray Muon Flux). Solitaren's mean free path is set by how often gas molecules collide. Streakwin's muons cross the whole atmosphere and reach the ground, helped by time dilation that stretches their short lifetimes.
Wear the lore
Concept keywords: Mean Free Path Vacuum, Solitaren, Measurement, Noise & the Lab, physics lore, Pixelated Physics