Sometimes reality doesn't match up to our intuitions, and takes us by surprise. Scroll down or click on the links below - and be surprised.
Kilogram for kilogram, the Sun generates power more slowly than the human body
And not just a bit more slowly either. An average kilogram of the Sun generates power about 7000 times more slowly than an average kilogram of human flesh.
If that's true, why is the Sun so much hotter than the human body? It's because the Sun is so much larger than a human body. Nearly all of the human body is only a few centimetres from the surface, and it's easy for heat to escape. On the other hand, nearly all of the Sun is hundreds of kilometres from the surface, and it's not easy for the heat to escape. Therefore the heat builds up, and the Sun reaches a very high temperature despite a very low rate of heat generation.
You get more energy by burning a Scottish oatcake than you do by exploding the same mass of TNT
Or any other biscuit for that matter. Even a Jaffa cake. The energy yield of an oatcake (when burned) is about 18 MJ kg-1 (megajoules per kilogram), whereas the energy yield of TNT (when detonated) is a paltry 4.6 MJ kg-1.
Explosives go bang not because they release a great deal of energy, but because they release their energy very quickly, and therefore produce very high temperatures. In combination with the gases that they produce, this produces very high pressures.
Actually, I'm cheating a little here, because the oatcake can't burn without a supply of oxygen, unlike the TNT which can explode perfectly happily on its own. The amount of oxygen is quite large - I estimate that an oatcake might need about 5 times its own mass in oxygen to burn. If we take that into account, it looks like the energy yield from oatcakes and from TNT is about the same. Nevertheless the point is still made that explosives do not yield particularly large amounts of energy for their mass.
I was told this gem by Jamie Taylor who works at the Institute for Energy Systems at Edinburgh University.
See another oatcake calculation
Concrete is floppier than steel
I used to think of steel as fairly soft and twangy stuff, and concrete as the epitome of rigidity. But it's not so. If you made two equally-proportioned bars of concrete and steel, and hung a small weight on the end of each, the concrete bar would deflect about 7 times as far as the steel bar.
So how come we quite often see pieces of steel bending (in a spring for example), but we never see a bent piece of concrete? The answer is that although concrete is stiffer than steel, it's much weaker in tension - you don't have to pull it very hard before it breaks. Anything that's bent is in tension on the outside of the bend, and this is concrete's undoing: if we try to bend concrete beam it will break before it has bent far enough for the bend to be obvious. In other works, we never see bent pieces of concrete because they've always snapped first.
Reinforced concrete has steel rods embedded in it. These take the tensile loads that the concrete can't take on its own.
The molecules in a cubic centimetre of air travel a total of one million light-years every second
(A light year is the distance travelled by light in one year - about 5 million million miles)
Gases (like air) consist of large numbers of molecules (or atoms in some cases) flying around bumping into each other. The molecules move with a wide range of speeds, but at at everyday temperatures and pressures, air molecules have typical speeds of about 500 metres per second. In one cubic centimetre of air, there are about 30,000,000,000,000,000,000 air molecules. Multiplying these two numbers together gives the total distance travelled by all the molecules in one second.
This result is so startling not because of what it tells us about the speeds of the air molecules - they are high but not astronomically so - but because it brings home with a vengeance how gigantic the numbers of molecules are even in a small volume of gas. They each move a distance we could walk in a few minutes, but between them they travel a distance that is many orders of magnitude above comprehensibility.
(You may wonder how I can talk about a typical molecule moving 500 metres, when we are talking of a mere 1 cubic centimetre of air. The answer is that the molecules are constantly colliding and changing direction. The path of any molecule is extremely contorted, and could easily lie completely within the cube. And even if a molecule does leave the cube, it doesn't matter. It's very likely that another molecule will have wandered into the cube to take its place.)
See some more details of the calculation
Some more detailed information
Feeble Sun
To compare the per-kilogram energy outputs of the human body and the Sun, we need to know the mass and total power output of both.
Mass of the Sun. This is very close to 2 x 1030 kg from science data books).
Total power output of Sun. The Sun loses all of its energy by radiation. Above the Earth's atmosphere, 1.5 × 1011 metres from the Sun, the intensity of radiation is 1370 W m-2. A spherical surface at this distance from the Sun would have an area of 2.84 × 1023 m2. Assuming that the Sun radiates energy equally strongly in all directions, the total power passing through this surface would be 1370 × 2.84 × 1023 = 3.87 × 1026 W. Ignoring any losses from absorption on the way, this gives us an estimate for the total power output of the Sun.
(You can check this result by noting that the surface temperature of the Sun is 5800K, and using the Stefan-Boltzmann law. You get very good agreement).
Mass of a person. People vary a lot in mass, but a typical adult might weigh 65 kg.
Power output of a person. For a person whose weight is steady, their energy output must equal their energy input. People vary a lot in how much they eat, but 2000 kcal, or about 8.6 × 106 J, is a reasonable estimate for daily energy input. Divided by the number of seconds in the day, this gives an average power of of about 97 W.
Power outputs per kilogram of the Sun and a human being. We divide the total power output by the mass in each case to get 1.9 × 10-4 W kg-1 for the Sun and 1.5 W kg-1 as the overall power per kilogram of a human being. The human being's power output per kilogram is nearly 8000 times that of the Sun.
The Sun gets so hot because, compared to the human body, it is really very short of surface area. Its surface area per kilogram is about 3 × 10-12 m2 kg-1. The corresponding figure for our 65 kg person is about 0.028 m2 kg-1. Thus a human being is about 10 thousand million times more lavishly endowed with surface area than the Sun is. The Sun gets so hot because there's hardly anywhere for the heat to get out!
The explosive oatcake
Assuming that we could somehow explode an oatcake (by incorporating a suitable oxidiser into the recipe), how big a bang would we get? This isn't an easy question (for me) to answer, but I'm going to have a go. The oatcake's energy will initially produce a large quantity of heat, a lot of which will ultimately be converted into kinetic energy as the hot gas expands and the reaction products fly away. I'm going to ask two questions. First, if all the oatcake's energy was converted to heat, how hot would the reaction products be? Second, if all the oatcakes's energy was converted to kinetic energy, how fast would the reaction products be moving?
There's a complication here, because unlike TNT, an oatcake needs an external supply of oxygen to burn, and this adds greatly to the mass of the reaction products. I don't know the chemical composition of an oatcake, but it contains a lot of carbon and a lot of hydrogen. Each carbon atom will react with about 3 times its mass of oxygen to produce carbon dioxide, and each hydrogen atom will react with about 8 times its mass of oxygen to produce water. So as a complete ball-park guess, let's suppose that the reaction products are 5 times the mass of the oatcake.
Let's answer the second question first, because it's easier. The kinetic energy E of an object of mass m moving at velocity v is given by E = 0.5 × m × v2. If the 18 MJ of energy derived from 1 kg of oatcake is all converted into the kinetic energy of 5 kg of reaction products, the velocity of those reaction products would then be about 2700 m s-1. That's about 8 times the speed of sound. Even if only a quarter of the energy were converted into kinetic energy, the reaction products would still be going at half this velocity.
For the heat calculation, we need to estimate the specific heat capacity of the reaction products. Consultation of tables suggests to me that a figure of 2000 J kg-1 K-1 might not be too far wide of the mark. If that's the case, then the reaction products would have an initial temperature of about 1800°C. I've made two big guesses in coming to this answer, so it could be wildly out. But it was fun trying.
Return to item about explosive oatcakes
Floppy concrete
The technical way of expressing the stiffness of a material is by its Young's Modulus. The bigger the Young's Modulus, the stiffer the material. The Young's Modulus for structural steel is about 200 GNm-2, and that for high-strength concrete is a mere 30 GNm-2. (Those units are giganewtons per square metre. The units of Young's Modulus are the same as those of pressure.)
Return to item about concrete and steel
Mega-distance molecules
I looked up the average speed of air molecules in a book.
To work out the number of air molecules in one cubic centimetre, I used the fact that one mole of a perfect gas contains 6 × 1023 molecules (Avogadro's Number), and at standard temperature and pressure occupies 22.4 litres. I then worked out the number of molecules in a cubic centimetre (0.001 litres) by multiplying Avogadro's Number by 0.001/22.4. This gave me about 2.7 × 1019 molecules.
It turns out that this number has a name: it's called the Loschmidt Number.