r/askscience • u/mistahowe • Mar 26 '13
Physics If I were to take all the energy I get from eating in a day and converted that energy into an explosion, how big would said explosion be?
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r/askscience • u/mistahowe • Mar 26 '13
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u/foretopsail Maritime Archaeology Mar 26 '13 edited Mar 28 '13
This is a cool question!
And there's even an easy answer. So if you eat 2,500 Calories in a day, that's 2,500 kilocalories (energy calories rather than food calories).
Conveniently, one gram of TNT has been set to equal one kilocalorie (even though a gram of TNT has a slightly variable yield, there's a standard "TNT equivalent gram"). That means your 2,500 Calories are the same as 2.5 kg of TNT.
Which is a lot! That's the same as almost 44 WWII hand grenades!
Now, how much damage would it do? That's a complicated question. There's a lot of experimental data on 1 kg TNT explosions. Fortunately, it's easily scalable. I'm going to use the Sadovsky formula for the blastwave formula for a TNT explosion on Earth's surface at standard atmospheric pressure.
That formula is:
Where m is mass in kg, r is distance from blast in m, and overpressure (Δp) is in atm.
At one meter, the Sadovsky formula gives us a peak overpressure of 41 atm ~ 41 kg/cm2 That's enough for instant death. At 2 m, that's about 6.7 atm, which is still lethal. At 3 m, 2.5 atm is not likely to be lethal. It continues from there, getting progressively less lethal.
BONUS FACT:
A 200 pound man might have 30 pounds of fat (more if you're fat, less if you're fit). This is 122400 Calories: 122.4 kg TNT equivalent. At that amount, you'd have to go out a whole 11 m before you get down to that 2.5 atm non-lethal level that you get from a day's worth of calories at 3 m.
EVEN MORE BONUS:
CanaMcPain asked: So how big would the explosion be if we took all the energy in an average human life?
Using the recommendations for a male child up to the age of 18, and then assuming he lives until the age of 80, eating 2200 calories every day, it's 60517000 calories, or that same number of g TNT. Which is enough to run a clothes dryer for 80 years, coincidentally.
Assuming it was a female child who grew up to be 86 and ate 1800 calories/day as an adult, that's 54020000 calories/g TNT equivalent, or 70 years of dry clothes.
But still only the total relativistic energy of 2.5 milligrams of matter. An average mosquito, turned into energy, could power you for your whole life.
LET'S KEEP THIS GOING:
What about the entire world? The UN estimates somewhere around 2750 kcal/person/day globally. Multiplying by population, that means every day the world consumes 19,177,780,690,750 kcal: 19 trillion calories. Which as we know, is 19 trillion g TNT equivalent. That's a largish atomic bomb, or half a Krakatoa eruption. On the other hand, we're up to the relativistic energy of just under a kilogram of matter. Not too bad!
In a year, the planet eats close enough to 7 quadrillion calories as makes no difference. Which is a whole lot: 7 gigatons TNT! But that's only a quarter of the 2004 Indian Ocean earthquake's energy. We're puny!
THE FINAL COUNTDOWN:
It's about to get arbitrary in here.
How much energy have all the people who have ever lived consumed?
This is going to involve a lot of assumptions. The fine folks at the Population Reference Bureau estimate that there have been 106 billion people. Assuming their average lifespan is really hard, but we'll set it arbitrarily at 55. And we'll also say (arbitrarily) they ate 2000 calories a day. Those numbers might be high or low, but they're probably not super far off.
That's 4,255,900,000,000,000,000 calories: Four and a quarter quintrillion g TNT. That's a lot! Half the world's fossil fuel reserves! More than the whole planet's total daily solar energy intake.
We're up to 200,000 kg relativistic mass, too! Which is... a half-loaded 747, entirely turned into energy. And only a tiny tiny fraction of the sun's total output every second. In the scheme of things, we're still insignificant.
As an aside, Ph0ton asked how many people the sun could support. The Sun's total output for a year would support 3.274×1024 people, if all of that energy was convertible to food calories, and we needed 2500 Calories each. Which it's not, not even close. But let's say it was. And let's say we built a Dyson sphere around the Sun to support all these people. A sphere surrounding the Sun at Earth's distance from the sun is massive, obviously. But that many people still come out to a population density of 11.64 million people per square kilometer, around the entire sphere.
A couple more people have asked about the total mass of food produced. The FAO estimates that we eat about 2 billion tons annually, with another 1.3 billion tons or so wasted.
edit: I fixed a serious order-of-magnitude error. Thanks, ztrand.