Boiling Point At Altitude Calculator

A liquid boils when its saturated vapour pressure equals the ambient pressure, so the boiling point is not a property of the liquid alone but of the liquid together with the atmosphere above it. This calculation runs in two steps. The barometric formula of the International Standard Atmosphere, P = P0 times (1 - 2.25577e-5 h) raised to the power 5.25588 with h in metres, gives the pressure at altitude from a sea-level value of 101.325 kPa and an assumed temperature lapse rate of 6.5 degrees C per kilometre. The Clausius-Clapeyron equation, ln(P1/P2) = (deltaHvap/R)(1/T2 - 1/T1), then converts that pressure into a boiling temperature using 40,660 J per mole for the enthalpy of vaporization of water and R = 8.314 J per mole-kelvin, with all temperatures expressed in kelvin. Near sea level the result approximates a linear rule of thumb, roughly 1 degree C lost per 285 metres or about 0.5 degrees C per 150 metres, but the relationship steepens with height. Denver at 1,609 metres boils water near 95 degrees C, Mexico City near 93, and the summit of Everest at 8,849 metres near 70, a temperature at which eggs will not hard-cook and pressure cooking becomes the practical answer; a domestic cooker at 15 psi gauge restores boiling to about 121 degrees C. The main approximation is treating the enthalpy of vaporization as constant, when it actually rises from 40.66 kJ per mole at 100 degrees C to roughly 44 kJ per mole near 25 degrees C, so errors grow at extreme altitude. Real weather shifts sea-level pressure by several kPa, and dissolved solutes raise the boiling point through a separate colligative effect.

That boiling temperature tracks pressure was established experimentally long before it was explained. Denis Papin's steam digester of 1679 showed that confining steam raised the temperature of boiling water enough to soften bones, and Daniel Gabriel Fahrenheit observed in the 1720s that the boiling point shifted with the barometer, which is why fixed points on temperature scales were later defined at a specified pressure. Eighteenth and nineteenth-century travellers turned the effect into an instrument: the hypsometer determined altitude from the boiling point of water, a lighter and sturdier alternative to a mercury barometer for surveyors and mountaineers. Henri Victor Regnault's meticulous vapour-pressure measurements, published around 1847, supplied the reference data those methods needed. The theory came from thermodynamics. Emile Clapeyron, in an 1834 memoir reworking Sadi Carnot's reasoning, derived the relation between the slope of a phase boundary, the latent heat and the volume change across it. Rudolf Clausius restated the result on a sound entropy basis around 1850, and integrating it under the assumptions that the vapour behaves ideally, that the liquid volume is negligible and that the latent heat is constant produces the logarithmic form used here. The atmospheric half of the problem was standardized separately: aviation and meteorological bodies agreed on a model atmosphere with a 6.5 degrees C per kilometre lapse rate, adopted internationally by ICAO in 1952 and later republished as the US Standard Atmosphere. Combining the two lets a single altitude figure be turned into a boiling temperature, which is the basis of the published high-altitude cooking adjustments found in recipe books.