(Courtesy of Wikipedia.)
I have a thing against rabbits. I don’t like them. They fill me with contempt. There’s absolutely no reason for this. It’s an utterly irrational hatred. Because of this particular neurosis, during a conversation with a friend, I happened to say something about vaporizing a rabbit. That sent my loony swamp-bog brain spinning off on another of its tangents, and I started to wonder What would happen if you vaporized a rabbit?
For the sake of this thought experiment, I’m going to start off assuming that a rabbit weighs 1 kilogram. That’s within the mass range listed by Wikipedia, but Wikipedia can’t always be trusted. But by virtue of the fact that they exist, we know that rabbits weigh more than 0 kilograms, and by virtue of the fact that we don’t inhale rabbits and get horrible nibbling-rabbit pneumonia, we know that they probably weigh more than 0.000 000 000 000 001 kilograms (1 picogram, which is about the mass of a bacterium). And from this oft-referenced report from the BBC, of Ralph the Unthinkably Large Bunny (who I must admit is kinda cute), we know that rabbits can reach 7.7 kilograms. So 1 kilogram is not unreasonable.
Now that we’ve got that bit of pedantic obsessiveness out of the way, we can proceed.
Most organisms contain quite a lot of water. The density of a human being is similar to the density of water. (If you can float in a pond or a swimming pool, your density is less than that of water, meaning less than 1,000 kilograms per cubic meter. If you have to tread water, your density is higher than 1,000. For the record, I float.) So, for the sake of simplicity, let’s pretend that our 1-kilogram bunny is made entirely of water, like a really disappointing version of those chocolate Easter bunnies. Let’s also assume that it starts out at typical rabbit body temperatures: 100 Fahrenheit, 38 Centigrade, or 311 Kelvin. In order to vaporize this all-water rabbit, we have to add enough heat-energy to it to raise its temperature to the boiling point, which is 212 Fahrenheit, 100 Centigrade, or 373 Kelvin (Have you noticed that we have way too many fucking temperature units? It’s a pain.) That’s a difference of 62 Kelvin. To find out how much energy we need to boil this rabbit (and make some extremely watery rabbit stew), we need water’s specific heat capacity, which happens to be about 4.18 Joules per gram Kelvin.
Specific heat capacity is one of those nice units that just makes sense. Newton’s gravitational constant is measured in units of (Newtons * square meters) / (square kilograms). What the fuck is a square kilogram? Well, the constant is one of those universal constants that tells you, in a vague way, just how weak a force gravity is. Specific heat capacity, though, makes intuitive sense. Water has a specific heat capacity of 4.18 Joules per gram Kelvin (Not to be confused with Jules per Graham Kevin, who is the president of the Earth in the alternate reality where Canada became a totalitarian superpower). That means that, to increase the temperature of one gram of water by one Kelvin, you have to add 4.18 Joules of heat energy to it. The units tell you exactly what they mean, which is nifty.
Anyway, in order to heat our rabbit-shaped mass of water to boiling temperature, we need to add 259,200 Joules of heat energy. But notice that I said “to heat our rabbit-shaped mass to boiling temperature.” That’s not the same as actually making it boil. For that, we need to add extra energy. This extra energy won’t increase the temperature at all, but it will get the water over the hump and vaporize it. This extra energy is quantified by another constant: the specific heat (or enthalpy) of vaporization. For water, this is 2,260,000 Joules per kilogram. That means we need 2,260,000 more Joules to turn our rabbit-shaped water balloon into a rabbit-shaped cloud of steam. So, all told, we’re concentrating 2,500,000 Joules into a volume on the order of 1,000 cubic centimeters. 2,500,000 Joules is about the energy released in the explosion of half a kilogram of TNT, which seems to me (citation needed) like a decent fraction of a stick of dynamite.
Unfortunately, energy alone isn’t going to get us the explosion we’re looking for. Just because we have the equivalent of a stick of dynamite doesn’t mean we’re going to have the same explosion as a stick of dynamite. That energy is all bound up in the rabbit-shaped cloud of steam.
What will get us the explosion we’re looking for, however, is the fact that we’ve got a cloud of hot gas compressed to the density of water and eager to expand. From the ideal gas law (and assuming a rabbit volume of 1,000 cubic centimeters), the cloud will begin at a pressure of 1,699 atmospheres (172.19 megapascals). That’s about half the pressure generated by the burning gunpowder in a .357 magnum cartridge. Maybe not enough to kill you, but certainly enough to make your ears ring. And enough to make you stand in the meadow blinking while a fine mist of rain falls around a little crater in the grass, asking yourself what the hell just happened.
But you know what? Rabbits aren’t just made of water. They’re made of all sorts of weird shit like water, tubulin, hemoglobin, cadherin, vitamin D, collagen, phospholipids, and more rabbit-semen than anybody wants to think about. And from cooking (and from that one scene in The Lord of the Rings) we know that heating a rabbit up to boiling won’t destroy all of its chemical bonds.
I want to make sure this rabbit is gone. I mean gone. Vaporized. I want to rip its fucking molecules apart, so that there’s no trace of fucking rabbit left. I should probably talk to my therapist about this. But for now, I’ll finish what I started.
As it turns out, I can still reasonably assume that the whole 1-kilogram rabbit is made of water, because the hydrogen-oxygen bonds in water are some of the strongest you’ll find in ordinary materials (carbon-hydrogen bonds are stronger, but not by much; nitrogen-nitrogen bonds are much stronger, but there’s not a lot of gaseous nitrogen floating around in a rabbit’s tissues, so we don’t need to worry about it). We’re looking at 55.56 moles of rabbit (NOT 55.56 moles of rabbits; disgusting shit happens when you try to assemble a mole of small mammals). The bond-dissociation energy for the hydrogen-oxygen bond in water is a shade under 500,000 Joules per mole, and there are two such bonds in every water molecule, so the total energy will be about 1,000,000 joules per mole. That means that completely vaporizing a rabbit will require something like 55,500,000 Joules, which is (roughly) equivalent to the detonation of 10 kilograms of TNT. 10 kilograms of TNT works out to just over 6 liters, so imagine two three-liter soda bottles (or six big liter-size beer steins, or a 1-gallon jug and a half-gallon jug) filled to the brim with TNT. That’s more explosives than you find in some artillery shells. You know what that means?