How long does it take to boil an egg on Mt Everest?
Suppose we're on top of Mt. Everest. A 50 mph (80 km/h) gale blasts the mountaintop this fine June day. We've pitched a tent, got the stove going and put a pot of water on to boil. Gradually the tent warms above freezing. Finally, the water's boiling, and I drop an egg in. How long does it take for it to boil? About 20 minutes for a soft-boiled egg.
How did I arrive at the answer? First, I looked up the temperature at which water boils at Mt. Everest's altitude: 29,035 feet (8850 m). At that altitude, water boils at 156° F (69° C). The Mt. Everest boiling water is much cooler than boiling water at sea level (212° F, 100° C) because the mountaintop air pressure is only about a third of that at sea level.
By the way, if you don't have tables handy, a good rule of thumb is that the temperature of boiling water decreases by 3.33° C for each kilometer of altitude. Or, in English units: 1.83° F for each 1000 feet of altitude. Knowing this, "people who live in Denver or who backpack in mountains now have an easy way for determining the boiling point at their elevation," says meteorologist Craig Bohren, author of What Light through Yonder Window Breaks?
Furthermore, I assumed that the initial temperature of the egg is as cold as if I had removed it from a refrigerator: 4° C. Then, I turned to Google to find the soft-boil temperature. According to the FDA code, an egg is safe for immediate consumption if I raise the egg's temperature to about 63° C for 15 seconds. This was reassuring since the temperature (69° C) at which water boils on top of Mt. Everest is greater than the necessary cooking temperature (63° C). Therefore, I can actually soft boil the egg.
Now, how long must I cook it? Bohren came up with 24 minutes, based on chemical-reaction speeds. The rate of chemical reactions doubles with every increase in temperature of 10° C — another useful rule of thumb. Boiling an egg involves chemical reactions as the egg protein cooks.
Thus, for every drop in temperature of 10° C, the speed halves and the time it takes doubles. The boiling temperature (69° C) on Mt. Everest is about 30° C lower than at sea level (100° C). Therefore, the time doubles (for the first 10° C), doubles again (four times, for the second 10° C) and doubles again (eight times, for the last 10° increment). Thus the time for boiling increases by a factor of eight.
A soft-boiled egg takes about 3 minutes to cook at sea level. Thus, Bohren predicts the soft-boiled egg will take about 24 minutes on top of Mt. Everest.
Finally, I estimated 17 minutes based on a heat-transfer formula derived by physicist Charles D.H. Williams of Exeter University in England.
But is either estimate right? Like any good scientist, I checked the predictions with an experiment. First pressing a helper into service, I gathered my apparatus: a pot for boiling water, a candy thermometer, a plastic stirring spoon, ice cubes and a couple of 57-g eggs.
We cooled the initially boiling water (93° C temperature, at my altitude) to the temperature at which water boils on Mt. Everest (69° C), put the egg in the hot water, maintained the 69° C temperature for 17 minutes and stirred the water continually to simulate the mixing associated with boiling.
When the timer dinged, we removed the egg from the hot water, and plunged it into ice water to stop the egg cooking. Then we sampled the egg. Good, but the white part of the egg was a tad runny. We repeated the experiment on a second egg, increasing the time to 20 minutes. The results: a perfect soft-boiled egg.
Both Bohren's and William's predictions are consistent with our experiment. (Wonder Quest)
How did I arrive at the answer? First, I looked up the temperature at which water boils at Mt. Everest's altitude: 29,035 feet (8850 m). At that altitude, water boils at 156° F (69° C). The Mt. Everest boiling water is much cooler than boiling water at sea level (212° F, 100° C) because the mountaintop air pressure is only about a third of that at sea level.
By the way, if you don't have tables handy, a good rule of thumb is that the temperature of boiling water decreases by 3.33° C for each kilometer of altitude. Or, in English units: 1.83° F for each 1000 feet of altitude. Knowing this, "people who live in Denver or who backpack in mountains now have an easy way for determining the boiling point at their elevation," says meteorologist Craig Bohren, author of What Light through Yonder Window Breaks?
Furthermore, I assumed that the initial temperature of the egg is as cold as if I had removed it from a refrigerator: 4° C. Then, I turned to Google to find the soft-boil temperature. According to the FDA code, an egg is safe for immediate consumption if I raise the egg's temperature to about 63° C for 15 seconds. This was reassuring since the temperature (69° C) at which water boils on top of Mt. Everest is greater than the necessary cooking temperature (63° C). Therefore, I can actually soft boil the egg.
Now, how long must I cook it? Bohren came up with 24 minutes, based on chemical-reaction speeds. The rate of chemical reactions doubles with every increase in temperature of 10° C — another useful rule of thumb. Boiling an egg involves chemical reactions as the egg protein cooks.
Thus, for every drop in temperature of 10° C, the speed halves and the time it takes doubles. The boiling temperature (69° C) on Mt. Everest is about 30° C lower than at sea level (100° C). Therefore, the time doubles (for the first 10° C), doubles again (four times, for the second 10° C) and doubles again (eight times, for the last 10° increment). Thus the time for boiling increases by a factor of eight.
A soft-boiled egg takes about 3 minutes to cook at sea level. Thus, Bohren predicts the soft-boiled egg will take about 24 minutes on top of Mt. Everest.
Finally, I estimated 17 minutes based on a heat-transfer formula derived by physicist Charles D.H. Williams of Exeter University in England.
But is either estimate right? Like any good scientist, I checked the predictions with an experiment. First pressing a helper into service, I gathered my apparatus: a pot for boiling water, a candy thermometer, a plastic stirring spoon, ice cubes and a couple of 57-g eggs.
We cooled the initially boiling water (93° C temperature, at my altitude) to the temperature at which water boils on Mt. Everest (69° C), put the egg in the hot water, maintained the 69° C temperature for 17 minutes and stirred the water continually to simulate the mixing associated with boiling.
When the timer dinged, we removed the egg from the hot water, and plunged it into ice water to stop the egg cooking. Then we sampled the egg. Good, but the white part of the egg was a tad runny. We repeated the experiment on a second egg, increasing the time to 20 minutes. The results: a perfect soft-boiled egg.
Both Bohren's and William's predictions are consistent with our experiment. (Wonder Quest)
I am delighted! The whole article. Thanks greatly. I'm glad you found it interesting, too. My assistant and I had fun testing our theories in the kitchen. Pretty much right on the time we thought --- about 20 minutes to soft boil an egg on top of the world.
ReplyDeleteCome visit my Q&A science site (WonderQuest.com) any time for answers to the mysteries of life.
April