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Cold, when all is said and done, makes a disappointing superweapon.
I mean, the comic book movies are pretty convincing. The hot superhero shoots a lava jet at the cold supervillain, whose ice ray (not to be confused with a freeze ray) sets out an opposite jet, they meet in the middle and cancel each other out in a brilliant contest of CGI. You get Frozone making walls of ice out of thin air. Or you get the Terminator, freezing in liquid nitrogen and shattering like the hopes of a Hillary voter on election night.
The trouble is that you can only make things so cold. You end up stuck against absolute zero. Heat is molecules moving; you slow ’em down you make things colder. You slow ’em enough that they stop all motion, that’s absolute zero. You can’t slow ’em even further; if you get ’em running backwards that means they’re moving again and things are heating up.
Absolute zero comes at roughly three hundred degrees C below room temperature. Lava, according to this source I just googled, at it’s coldest runs about 700 C. If you’re trying to balance that with your coldness you’ll need at least twice as much ice-ray as lava to get the job done. There’s more room in the attic than the basement.
That’s only taking the raw temperature into account. What exactly are you projecting? We called it an ice-ray up above. Let’s say you’re shooting ice-cubes. Man, doesn’t that just make it sound lame. But it does allow you to make your daring heist! Tunnel under the Gotham Gold Depository. Heat the room until the gold all melts and drips through the floor drain. Freeze it again and make your escape! What could possibly go wrong?
The melting point of gold is around 1,000 C. You’re going to want that down to about 30 C (room temperature) in order to pick the stuff up and cart it away. That’s the bad news. The good news is that gold has a much lower heat capacity than water. “Heat capacity” is a measure of how much energy you have to put into a thing to change its temperature. If you put a metal pot on a stove that metal pot will heat up real quick. The water inside it though, that’ll take some time to boil.
There’s a formula, H = mCΔT, which lets you determine how much energy you’re talking about. “m” is your mass, “C” is your heat capacity, and ΔT is how far ‘long the thermometer you want to move it. Let’s say you’re heating your water about 300, from absolute zero to room temperature. And you’re cooling your gold about a thousand, also to room temperature. Since water has a heat capacity of around 4 J/(g*K) (That’s pronounced ‘Joules per gram-Kelvin’, by the way) and gold sits around 0.13 J/(g*K), or roughly a 40th of water’s, that means you’ll end up using all the ‘cold’ in about a kilogram of water to cool off about ten kilos of gold. Profitable!
There’s one more wrinkle; the heat of formation. Broadly speaking, it takes less energy for a thing to be a solid than for it to be a liquid or a gas. A solid just sits there; liquids have their molecules wandering around. If you drop a single ice-cube in molten gold that ice cube will take some of that heat just to turn from a solid to a liquid. It’ll take more to turn from a liquid to a gas. That’s the good news for your heist. The bad news is that you’ve got to pay the piper on the other end too; it’ll take some cooling to turn your liquid gold solid. Not going to run the numbers on how much; not until someone points me to a gold depository situated on nice, easy tunneling.
All that’s discussed using some sort of super-sciency absolute zero ice cube slinger. What if we talk about a more realistic “cold-ray.” I’m thinking basically a Super Soaker that shoots liquid nitrogen. Taking another quick jaunt through the search engines we find this:
Specific heat of Nitrogen is 1.04 J/(g*K).
Latent Heat of Vaporization of Nitrogen is 2.7928 kJ/mol.
Oh, and the boiling point is at -195.8 C. Let’s say that we keep our liquid nitrogen stored at -200 C, for the convenience of the math. (You can store it at higher pressures so you don’t have to get it so darn cold, but that kinda defeats the point of our scheming.) If you spray a hapless bystander with a kilogram of liquid nitrogen how much of their body heat are you taking away?
Call it 250 kJ of energy to do the raw temperature change. Add in the fact the poor sap has to boil the nitrogen away (Heat of formation, heat of vaporization, same concept really), that’s another 200 kJ of energy. 450 kJ of freezing. What does that do for you?
The specific heat of a human body is around 3.5 J/(g*K). (Mankind, being mostly water, has much of water’s high heat capacity. Use this to your advantage when the robots attack!) Run those numbers back, 450 kJ = 50 kg*3.5 kJ/(kg*K) * ΔT. On a small adult (~110 lbs) you’d drop their temperature by about two, three degrees C.
On the one hand, three degrees is a lot; that much temperature change is enough for mild hypothermia. On the other hand, you’re assuming they’re just standing there and taking it, and that none of this is splashing, and oh-by-the-way that their human body isn’t also actively heating them. You’ll cause significant local tissue damage, but significant local tissue damage never makes the evening news. Certainly, you won’t leave your victims frozen in dramatic poses.
And when you get right down to it, a kilogram is a lot to carry around. How many kilos are you rucking? How heavy is the bottle that you’re keeping your liquid nitrogen in? How many security guards can you freeze before you have to call the whole bank-robbery off?
Why don’t you just shoot them again?