• Pixel-art Solitaren, the Mean-Free-Path Hermit, on a black mug with the slogan "AT 1E-6 MBAR, MOLECULES GET 66 M ALONE."

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Solitaren, the Mean-Free-Path Hermit Mug

\[\lambda = \frac{k_B T}{\sqrt{2}\,\pi d^{2} p}\]
$21.99 USD
$21.99 USD
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Size

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.

The joke: High vacuum means molecules hit the chamber wall before each other. The slogan on the mug reads AT 1E-6 MBAR, MOLECULES GET 66 M ALONE.

Source: K. Jousten (ed.), Handbook of Vacuum Technology (Wiley-VCH, 2016), ch. 3.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingBy destination

Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Mean free path λ = k_BT/(√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.

The joke: High vacuum means molecules hit the chamber wall before each other. The slogan on the mug reads AT 1E-6 MBAR, MOLECULES GET 66 M ALONE.

Source: K. Jousten (ed.), Handbook of Vacuum Technology (Wiley-VCH, 2016), ch. 3.

Equations

\[\lambda = \frac{k_B T}{\sqrt{2}\,\pi d^{2} p}\]
\[\lambda_{\text{air}} \approx \frac{6.6 \times 10^{-3}\ \text{cm}}{p\,[\text{mbar}]}\]
SymbolMeaningUnit
\(\lambda\) mean free path \(\mathrm{m}\)
\(k_B\) Boltzmann constant \(\mathrm{J/K}\)
\(T\) temperature \(\mathrm{K}\)
\(d\) molecular diameter \(\mathrm{m}\)
\(p\) pressure \(\mathrm{Pa}\)

Sources

  1. K. Jousten (ed.), Handbook of Vacuum Technology (Wiley-VCH, 2016), ch. 3

Field notes

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