What if you boiled water on a high mountain?

Put a pot of water on the stove. It gets hotter and hotter. Then it bubbles and boils!

What if you did this on top of a high mountain? Would the water boil in the same way?

Many people learn that water boils at 100 °C (212 °F). But cooks who live in the mountains know something surprising: their water boils before it gets that hot, and food like pasta, beans and eggs takes longer to cook.

Why would a mountain change the way water boils? In this lab you can carry a pot of water up through a model of the atmosphere, from the seaside to 5 kilometers up and beyond, and read off the temperature at which it boils.

The 'normal boiling point' of water, 100 °C, is defined at a pressure of 1 atmosphere (101.3 kPa). OpenStax's chemistry text defines a liquid's boiling point more generally as the temperature at which its vapor pressure equals the pressure of the gas above it, which for an open pot is the atmosphere.

So the boiling point depends on where you are. This lab couples the International Standard Atmosphere to a Clausius–Clapeyron estimate of water's boiling point. How far does the boiling point fall at 5 km, and how well does the model agree with measurements from mountain towns?

At the seaside, there is lots of air pressing down on everything.

There, water boils at 100 degrees. That is very hot!

Start at sea level. The model's air presses down with a pressure of 101.3 kilopascals, the weight of all the air above. Here, water boils at 100 °C.

Once water is boiling, it stops getting hotter. OpenStax's chemistry book explains that if you turn the burner up, boiling water does not get any hotter; it just bubbles more strongly. So the boiling point is the hottest that water in an open pot can get, and that is the temperature your food cooks at.

At sea level the ISA gives 101.325 kPa and the model's boiling point is 100.0 °C, the normal boiling point by definition.

OpenStax notes that a heating curve has plateaus at phase changes: once a pot of water reaches its boiling point, its temperature stays constant while it boils, and extra heat from the burner only makes the boiling more vigorous. For anything cooked in boiling water, the boiling point therefore sets the cooking temperature, wherever the pot happens to be.

Now Olly carries the pot up, up, up a high mountain.

The air up there is thin. The water boils before it gets so hot! It boils at about 83 degrees.

Slide the height to 5 kilometers. The air pressure has fallen to 54.0 kilopascals, about half of sea level, and the model says water boils at only about 83 °C.

Try other heights. In Denver, 1.6 kilometers up, the model's water boils at about 94.6 °C. Find the height where it first boils below 90 °C: about 3 kilometers. At Mount Everest's height, 8.8 kilometers up, the model's water boils at only about 70 °C.

At 5 km the ISA pressure is 54.0 kPa (53 percent of sea level) and the model's boiling point is 82.9 °C. Denver (1.6 km): 83.5 kPa, 94.6 °C. The boiling point first drops below 90 °C at 3.0 km (89.8 °C), and at Everest's 8.8 km it is 69.6 °C at 31.7 kPa.

Near the ground the model's boiling point falls by about 3.4 °C per kilometer. Compare New Mexico State University's rule of thumb: a drop of about 1 °F for every 500 feet, which works out at roughly 3.6 °C per kilometer.

Air pushes down on the water in the pot. To boil, the water has to push back.

High up, the air pushes less. So the water can boil when it is not so hot.

Air has weight, and UCAR explains that gravity pulls it down toward Earth. At the bottom of the atmosphere there is the most air pressing down, so the pressure is highest. Higher up, there is less air above you, so the pressure is lower.

To boil, water has to make bubbles of steam that push back against the air. Hotter water pushes harder. OpenStax explains that water boils when its push, called vapor pressure, matches the air's pressure. On a mountain the air pushes less, so the water does not need to be as hot to boil.

A liquid boils when its equilibrium vapor pressure equals the external pressure (OpenStax). Vapor pressure rises steeply with temperature, so lower external pressure is matched at a lower temperature. The Clausius–Clapeyron relation, ln(p₂/p₁) = (ΔH_vap/R)(1/T₁ − 1/T₂), turns that into a number.

The model's limits: it uses the standard atmosphere, an average day with no weather; it treats the latent heat as constant at 40.66 kJ/mol, a simplification that its documentation compares with steam tables (within about 1 °C over this range); and it describes pure water in an open pot; a sealed lid, as in a pressure cooker, would change the result.

In mountain towns, cooks need more time to boil eggs and cook beans.

Some cooks use a pressure cooker. It traps steam inside, so the water gets hotter and food cooks faster.

This really happens. New Mexico State University says water boils at about 202 °F (94 °C) at 5,000 feet, about 1.5 kilometers up. The model gives about 94.9 °C at 1.5 kilometers: very close!

Because boiling water is cooler up there, food cooked in it takes longer. NMSU says a soft-boiled egg that takes 3 minutes at sea level may take 5 to 6 minutes at high elevations. Oven roasting is different: an oven's temperature does not depend on the air pressure. Many mountain cooks use pressure cookers, which build up pressure inside a sealed pot so the water boils at a higher temperature.

NMSU Extension's high-altitude guide gives rolling-boil temperatures of 212 °F at sea level, 208 °F at 2,000 ft, 202 °F at 5,000 ft and 198 °F at 7,500 ft (100, 97.8, 94.4 and 92.2 °C). The model gives 98.0, 94.9 and 92.2 °C at 0.6, 1.5 and 2.3 km. OpenStax's worked example for Leadville, Colorado (10,200 ft) uses a typical pressure of 68 kPa and a boiling point of about 90 °C; the model gives 69.2 kPa and 89.5 °C at 3.1 km.

NMSU notes that moist-heat cooking takes longer at altitude (simmered or braised meat may need about 25 percent more time at 5,000 ft), that oven temperatures are unaffected, and that a pressure cooker can cut preparation time by 25 to 35 percent, because the temperature of boiling water rises as pressure builds inside the sealed vessel.