There's been lots of coverage of a trio of dead blue whales near the town of Trout River in Newfoundland. As the whales decay, they're expanding more and more as their internal cavities fill with noxious gases.
|Image from the Chicago Sun-Times|
It's possible that the whales will eventually burst, like the one below did with a bit of help from a biologist with a very long-handled knife. (It's a pretty nasty video, so don't click it if you're eating lunch.)
As disgusting as that is, it's not particularly dangerous. The real threat could come from the gases inside the decaying animals. Much of the volume of the bloated whales is likely taken up by methane, which is quite flammable, and potentially explosive.
We at Physics Buzz (well I and the Mathlete anyway) were wondering what might result if the whale were to explode rather than just pop. Based on our calculations, that lady in the picture above is in much more danger than she realizes. In fact, it might make sense for the local authorities to consider evacuating some of the nearby buildings, or at least posting a no smoking sign or two.
Check out our calculations below to see just how big a boom we think the whale might make if the worst were to happen (hint - it's really, really big).
According to our favorite infallible resource (Wikipedia, not Francis) a full grown blue whale weighs about 180 metric tons, which we will round to 200 tons for approximation purposes.
Whales, like most animals are made primarily of water, so it's fair to approximate their density at that of water, one gram per milliliter, which is a kilogram per liter. So a full grown whale's volume is about
(200 tons)(1000 kg/ton)(1 liter/kg)=200,000 liters
Therefore, if a bloated whale doubles in volume due to entrapped gas, there must be about 200,000 liters of gas in it.
Assuming that gas is mostly methane, with a chemical formula of CH4 (one carbon atom and four hydrogen atoms), we know from chemistry class that an Avogadro number of the molecules (that is, one mole) can be calulated by multiplying the total atomic number of the molecule by grams.
Carbon is has an atomic number of 12, and hydrogen has an atomic number 1. A carbon plus four hydrogens gives us a total mass of 16 grams per mole.
Typically, a mole of gas takes up about 25 liters of volume at room temperature and pressure, so the total weight of methane in a whale bloated to twice its normal size is
(200,000 liters of methane)(16grams /25 liters)(1 kg/ 1000 grams) = 128 kg of methane.
Going back to Wikipedia again, a kilogram of methane contains about 55.5 megajoules of energy, so the amount of energy in the gas inside the whale is about
(128 kg methane)(55.5 megajoules/kg)=7,104,000,000 joules = 7.1 gigajoules.
TNT contains about 4 gigajoules per ton, so a whale bloated to twice its normals size contains methane with energy comparable to (7 gigajoules)(1 ton TNT/4 gigajoules)= 1.75 tons of TNT
Now, we at the buzz have no idea how likely it would be for all the methane in a bloated whale to explode at once, but if it happened, it would be like detonating a full size pick up truck loaded to the brim with TNT.
One thing is certain, it would be a lot bigger than this little experiment involving a fresh whale carcass and a mere half ton of dynamite.
In this case, blubber rained down over a quarter mile away, and it was less than a third of the explosive potential we're talking about with the blue whales in Newfoundland.
So if you happen to own one of those buildings near the whale in Trout River, I'd recommend three things
1) Don't light a match
2) Get out
3) Make sure your homeowner's insurance is paid up