Does water boil
cooler up high?

Every camper's guide and every cake-mix box carries a version of the same instruction: water boils at a lower temperature the higher you go, adjust your recipe or your altitude sickness expectations accordingly. It is real physics — lower atmospheric pressure means water molecules need less thermal energy to escape into vapor — but the specific numbers in circulation (recipe boxes commonly print “1°F per 500 feet”) are folklore-grade, not measured. This run checks the claim against 1,618 world cities, real atmospheric pressure measured at each one right now, not a textbook table.

Method, briefly. 1,618 cities pass a GeoNames population/elevation filter (population > 500,000 OR real elevation > 2,200 m, to keep the thin high-altitude tail from being crowded out by low-elevation megacities). Each city's real-time surface pressure — not sea-level-reduced pressure, which would erase the very signal being tested — comes from Open-Meteo's keyless weather API, queried at the same moment for all 1,618 locations. Surface pressure converts to a boiling point via the Clausius-Clapeyron relation, the same 19th-century thermodynamic law the backlog item names, using water's standard molar enthalpy of vaporization (40,660 J/mol) — a physical constant, not a fitted parameter.

The claim holds, almost exactly as strongly as its own physics predicts. Boiling point falls -3.141°C per kilometer of elevation, 95% CI [-3.146, -3.137], R²=0.9992 across a sample running from -15 m below sea level to 5,012 m. Altitude alone explains 99.9% of the spread in boiling point across a single day's worldwide weather — the elevation effect (a 16.1°C range top to bottom) dwarfs ordinary synoptic weather noise (a few tenths of a degree).

But the real world runs measurably shallower than the idealized version of the same question. Feed the identical 1,618 elevations through a noiseless International Standard Atmosphere model — no weather, no day-to-day variation, just the textbook pressure-altitude formula — and the implied slope is -3.399°C/km, outside the real-world confidence interval entirely. The cake-box folk number (1°F per 500 ft) implies -3.645°C/km, also outside it — folklore overstates the effect by about 16% against what today's cities actually measured. One plausible reason for the gap: the standard atmosphere model assumes a fixed, cool sea-level-anchored temperature profile, and many of this sample's high-elevation cities sit in the tropics or subtropics (the Andes, the Tibetan Plateau, East Africa), where the real air column runs warmer than that assumption — a warmer column has a taller scale height, which keeps pressure (and boiling point) at any given altitude a bit higher than the idealized formula expects. This run cannot fully isolate that mechanism from one day's snapshot; it is offered as the likely explanation, not a proven one.

The line isn't perfectly straight, and 1,618 points is enough to prove it. A quadratic term added to the real-data fit is small but real: b²=9.49e-09, 95% CI [4.60e-09, 1.44e-08] — excludes zero, p=1.5e-04. Stacking two nonlinear laws (the barometric pressure formula and Clausius-Clapeyron) does produce real curvature, exactly as the physics predicts — it is just small enough that a straight line is a fine approximation for any kitchen: the curvature's total contribution at the sample's highest point, 5,012 m, is only 0.24°C.

Concrete, no regression needed: La Rinconada, PE — commonly cited as the highest permanently inhabited settlement on Earth, roughly 5,100 m up in the Peruvian Andes — sits at the top of this sample's elevation range (5,012 m) and boils water at 84.4°C right now, nearly 16 degrees short of the sea-level reference. At the other end, Baku, AZ, sits 15 m below sea level and boils at essentially the textbook 100.05°C. The single biggest miss from the real-world fit's own line, in either direction, is under 0.61°C — today's weather, not a broken law.