### Exploding Whale Fermi Problem

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

1. The problem with this story of comparing 200000 Liter of gas in a rotting whale with the detonation of the said amount of TNT is this:

1 The gas in the Whale in would be a mixture of Methane with CO2 with hardly any free Oxygen. Typically the gas would roughly also contain other combustible decomposition products containing Nitrogen and some Sulphur. . .Mercaptans and probably Hydrogen Sulfide as well. . . These are the foul smelling gases of decomposing flesh and some biomass the wale had been eating. The CO2 could roughlybe 40% or more of the total mass of gas.

2 After bursting due to carcass rupturing the gas has fist to mix with air in order to ignite. This is a rather slow process and that MUST occur before the gas can ignite. If an ignition source would be present tight there you only get a huge slowly expanding and rising flame. . .spectacular but in NO WAY as devastating as the explosion if the said amount of TNT, which would have at least Twice the Energy content compared to the gas.

3 3 The Methane CO2 Mixture containing half the energy would not “explode” but would, relatively slowly burn instead because of the need for the gas to mix with air. . .and only the mixed gas would burn, some of that gas would not even burn properly and produce smoke. . .that is actually a Pyrolysis process. . .
The whale would remain mostly as a large lump of flesh behind. . . only some of the guts would be flung out from the bursting carcass and not be launched very far away at all, and the flames would predominantly rise up into the air. . No Big Danger at all to anyone, unless they are close by and are engulfed by the flames that would develop at ground level.

4 A TNT Explosion is NOT a burning process but a “detonation” that takes at most a few milliseconds. . . if that long. . . it depend on how the amount of TNT is arranged. The combustion speed in a detonation is up to 10 km/second for some explosives. . TNT probably “only: 8 km/s J.. . .If it was a single ball then the detonation would be over in 10 to 50 Microseconds, depending on how big a package it would be. . . .If the TNT is arranged in a long stretch of separate cases with some space between them then a series of detonation would result in a Chain reaction IF the detonation starts at one end. The Chain Reaction explosions would then maybe a thousand times longer and be as long as a in the order of 10 milliseconds. . .This would depend on the spacing between the cases.
This is the great difference between burning a fuel (even if it is already mixed with Oxygen) and a detonation process. . .In case if the Gas from a decaying Whale the burning of the 200000 L gas mixture might take 5 seconds or even more as the gas rises into the air as it is mixed. . . .

Compare that with a detonation that will require between 10 and 50 microseconds.

2. what if tiny holes are made ? Will it just blow up or help the gases ease out calmly ?

1. Ever try to put tiny holes in a balloon? Same effect as you can see in the videos where TNT isn't used

3. Conrad, thank you for you're extensive comment.

I would like to point out that we are doing a Fermi Problem, and that we were speculating how big the explosion would be IF the gas were to detonate. Yes, you would need a special set of circumstances for that to happen, but that doesn't change the fact that there's a lot of chemical energy in there.

It's a little like noting that the chemical potential energy in a candy bar is comparable to the energy in a quarter stick of dynamite. No, your candy bar is not going to release all its energy in one burst, but IF it did it would take your head off.

Unlike a candy bar, however, methane can burn, often violently (en.wikipedia.org/wiki/Methane#Safety). Natural gas leaks (consisting primarily of methane, BTW) have led to numerous explosions that have leveled houses. Here's a case from last week: http://www.dailyherald.com/article/20140426/news/140428580/

One way I could imagine it occurring is if the whale burst, creating a cloud of methane that disperses until it reaches an explosive methane/oxygen ratio. A small spark or flame, perhaps in the pilot light of a stove in one of those houses near the whale, could create an effective fuel/air bomb (http://en.wikipedia.org/wiki/Thermobaric_weapon#Fuel-air_explosive).

Is it likely? Probably not. Is it physically possible, yes - after all, that's why houses with gas leaks can explode.

Methane, by the way, is more dense than air, so it wouldn't rise. If there was no wind, it would spread out in the local area, going from a rich, but non-flammable concentration to a potentially explosive mix, and ultimately dispersing, provided it didn't detonate along the way.

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