Summitbrew: Boiling Point at Altitude
Thermodynamics & Statistical Physics arc, page 55 of 193. Back to The Pixelated Physics Universe
Who they are
Summitbrew has one line, and says it often: “At 4200 m, my coffee never gets hot enough.”
Summitbrew is a character of the Thermodynamics & Statistical Physics arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Boiling point drops with pressure; at ~4200 m (≈ 61 kPa) water boils near 86–87 °C.
$$ \begin{gathered} \frac{dp}{dT} = \frac{L}{T\,\Delta v} \approx \frac{L\,p}{R_w T^{2}} \\ p \approx 61\ \text{kPa} \;\Rightarrow\; T_{\text{sat}} \approx 86\ ^\circ\text{C} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $p$ | saturation pressure | Pa |
| $T$ | temperature | K |
| $L$ | latent heat of vaporisation | J/kg |
| $\Delta v$ | specific-volume change | m^3/kg |
| $R_w$ | specific gas constant of water vapour | J/(kg·K) |
| $T_{\text{sat}}$ | boiling (saturation) temperature | K |
Sources
- IAPWS-IF97 saturation tables
- Clausius–Clapeyron
Crossovers
Summitbrew meets Vaporelle (Latent Heat of Vaporization). Vaporelle pays 2257 kJ/kg to boil water away. Summitbrew boils at a lower temperature on the mountain because the pressure is lower. The latent heat barely changes, but the boiling point does.
Summitbrew meets Drycrest (Precipitable Water Vapour). Drycrest chooses mountain sites for their dry air. Summitbrew lives up there too, where water boils near 86–87 °C.
Summitbrew meets Puckwarden (Darcy's Law Espresso). Summitbrew's water boils cooler at altitude. Puckwarden doesn't wait for boiling: she pushes water at about 9 bar through the puck, and Darcy's law says the flow scales with the pressure drop divided by viscosity and bed length.
Wear the lore
Concept keywords: Boiling Point at Altitude, Summitbrew, Thermodynamics & Statistical Physics, physics lore, Pixelated Physics