Boiling Point at Altitude Calculator
93 °C at two thousand metres and 70 on Everest — the food cooks slower because the water is genuinely cooler.
The formula
log₁₀P = 8.07131 − 1730.63 ÷ (233.426 + T), P in mmHg
Boiling is a condition, not a temperature
A liquid boils when its vapour pressure equals the pressure pressing down on it.
At sea level water reaches 760 mmHg of vapour pressure at 100 °C. Reduce the surrounding pressure and it reaches the new, lower threshold at a lower temperature. Nothing about the water has changed.
Why food takes longer up a mountain
Boiling water at 2,000 metres is genuinely 93 °C rather than 100, and on Everest about 70.
Once water boils it stops getting hotter however much heat you apply, so the food is cooking at a lower temperature. Turning up the flame boils it away faster and cooks nothing quicker. A pressure cooker is the only real answer.
The Antoine equation is empirical
It is a fitted three-parameter curve, not a derivation from first principles.
The constants used here cover roughly 1 to 100 °C for water; outside that range a different set is required, and using these would give a confident wrong answer.
Ideal behaviour is an approximation
The colligative and gas relations here assume dilute solutions and ideal gases, which real systems approach and do not reach.
At high concentration or high pressure the deviations become large, and the corrections are substance-specific. These figures are right where the assumptions hold and approximate where they do not.