Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: stocks58 on 04/09/2012 02:56:51
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So I was just thinking about this the other day and want to know where I went wrong. Let me preface this by saying i have not had a science class since high school 10 years ago so...
if I have a 100g apple said apple has a mass of 10.2
according to e=mc2 that apple is 9.17^17 joules
if there are 4.2 kj in a food calorie
then an apple contains 21,826,911,480,000 calories?
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then an apple contains 21,826,911,480,000 calories?
That only works when you combine an apple and an anti-apple.
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E=mc2 is iconic, and inspiring - but in practice it is exceedingly difficult to turn matter into energy!
Perhaps the easiest way to see this is to look at a periodic table (eg http://www.ptable.com/), and compare the mass of 4 hydrogen atoms (each 1.00794 grams/mole) with the mass of 1 helium atom (4.00260).
Together the 4 hydrogen atoms add up to 4.03176, which means that if you could fuse them together to make helium, you would release roughly 0.029 as energy, a mass to energy conversion yield of less than 0.1%. And it takes huge amounts of energy to create the right conditions where hydrogen fusion reactions could occur - and even then you can't capture all of this energy, because neutrinos are such slippery little suckers....
Hydrogen fusion, despite its incredibly small mass conversion ratio, produces enough energy to keep the Sun burning, and inspire several large research projects looking at controlled fusion power plants.
It's just as well you don't get all this energy from an apple - because those bazillion calories certainly exceeds your recommended daily intake of gamma rays!
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Another way to get a lot of energy out of an apple is to let it get swept up in the accretion disk of a black hole.
Before it disappears forever beyond the event horizon, it will radiate strongly in X-Rays, as it is shredded and spaghettified (a technical term).
Of course, it would take more energy than found in the mass of an apple to transport an apple to our nearest known black hole in a reasonable number of millennia. http://www.space.com/7678-black-hole-closer-earth-thought.html
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Stock58
Apart from bad physics you seem to have mixed your units up a little if you want energy in Joules you must use kilograms as your units of mass.
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if I have a 100g apple said apple has a mass of 10.2
according to e=mc2 that apple is 9.17^17 joules
if there are 4.2 kj in a food calorie
then an apple contains 21,826,911,480,000 calories?
You're off slightly, as Syphrym said. You need to convert the apple's mass to kilograms before plugging it into E=mc2. I get roughly 2 x 1012 Calories, assuming my math is right. Not a big deal.
However, when you eat an apple, your body can only extract energy from a fraction of the chemical bonds present in that apple. Even if you could get energy from all the chemical bonds, it would only be a tiny fraction of the energy in nuclear bonds. And if you could break the nuclear bonds, you'd still be left with a lot of energy in the form of fundamental particles that haven't been broken down. The only way to release all the energy in an apple is to somehow annihilate all the particles in it and release all their mass as energy. As Clifford said, you could do this with antimatter.
Of course, if your stomach was made of antimatter, you'd have bigger problems than a calorie overdose from eating an apple...
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One should mention that there is chemical energy, and nuclear energy.
Chemical energy is that energy held in the chemical bonds of a structure, for example carbon-carbon bonds and carbon-hydrogen bonds in so called carbon chains.
So, for example, your apple will have fructose (C6H12O6) This is combined with oxygen from the air:
C6H12O6 + 6O2 (from the air) --> 6CO2 + 6H2O + ENERGY
Of course, there are also many other carbohydrates and hydrocarbons in the apple too.
So, what you read as about 100 calories in an apple is only the energy that is released when your body breaks the chemical bonds in in the apple (metabolizes).
Our sun creates energy by fusion, mostly of Hydrogen which is in the apple. But, only a small fraction of the matter is actually converted to energy. Antimatter reactions are currently the only way in which 100% of the energy of a substance is converted into energy. However, while positrons, or anti-electrons are not uncommon, larger particles essentially do not occur in nature are are difficult to create in the lab. And, certainly your body is unable to derive energy from fusion, fission, or antimatter reactions.
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I think we should be careful using calories, the true calorie is defined with the old CGS system ie one gram of water thru one degree Centigrade but the nutritionist use the kilo calorie ie one kilogram of water thru one degree centigrade without stating that that is the unit they are using.
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The standard notation is to us a capital letter to indicate a kilocalorie, i.e. 1 Calorie = 1 kilocalorie = 1000 calories. Food energy is generally measured in Calories (kilocalories), as you say.
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A McDonalds apple pie has about that number of calories !!