Agents Of Physics

I was binge-netflixing Agents Of Shield (great show) the other day on vacation. In one episode, a character with the power to cool stuff freezes all the water around a battleship in just a few seconds, preventing it from moving. This man wasn't an alien, just subjected to a machine and a bit of "lightning bolt hit him" handwave, so he's prolly guided by physics, even in-universe.

When I watched this, I thought: where's all this energy going? Seriously: he dropped the temperature of the water to 0 degrees from ambient, then froze it. That has to be a substantial amount of energy. How much is it?

The answer actually depends on what season it is. According to the Agents of Shield wikia (of course it exists), this took place in the Port of Casablanca. The coastal temperature swings between 17-23 degrees celcius each year. It looked reasonably chilly during the scene, and everyone was wearing a jacket so I'll assume that this took place in one of the cooler seasons with 18.5 degree water.

The enthalpy of fusion of water (energy to freeze) is about 6 Kilojoules per Kilogram, and the energy to drop water by 18.5 degrees is about 77.5 kj. That's a pretty substantial amount of energy; added together, that's about 20 grams of TNT per kg of water frozen. Speaking of which, my new favorite unit for measuring specific heat is the kilogram of TNT per degree kelvin, which I propose to name the "shockwave enthalpy":

Unit cancellation is weird.

Now we need the volume of the water frozen. Looking at a still of the scene,

You can see that the ship in question looks like a sort of battleship. I'm not well-versed enough in shippery to know exactly what kind of ship that is, but it looks like it has a gun, and the first battleship I could find was 260 meters long, and perhaps 30m wide (a sharp eyed redditor found a width of 21m, so the calculation is under 10% off.). Good enough for a first approximation. Now, the ice penetrates quite deep. It looks like it's half as deep as the ship is wide, so we can say that it's perhaps 10m deep, and a perfect half-annulus, which gives us a volume of about 163,363 m^3, which is (breaking out scientific notation) 1.6×10^8 kg of water. Given that the displacement of $battleship is about 35 million kg, that seems about right. To freeze it from ambient, we get 1.36×10^10 joules of energy. That is a crapton. Actually, it's 3.2 metric craptons of tnt equivalent (a cube 13 meters per side):

To put that in perspective, you know that huge explosion on Mythbusters? With the cement truck? That was only 1/8th the energy this dude just sucked out of the water.

Also, that amount of energy is the same as that contained in 73,000 strips of standard 44 kCalorie bacon.

So the area was as cold as a bonfire of a hundred thousand strips of bacon is hot.

That's a nice unit.


This was fun; I think I'll be doing this more often here; perhaps make it into a weekly thing.


(Note: I hope I didn't mess up anywhere. Please do let me know if you spot anything wrong.)