[Physics] How fast can water from a lake be frozen


Warning: this question contains spoilers for the first episode of 2018 TV series Lost in Space by Netflix.

On the series, the Robinsons spaceship, Jupiter, falls on a planet, and it’s submerged in the water of a glacier that melted. Judy enters the water and swim to the spaceship to get a battery. A minute later, she can’t get out because the water freezes too quickly, holding her on the ice.

Accordingly to what was said on the episode, we know:

  • The planet's environment: "earth-like atmosphere, air-pressure and gravity"
  • The lake's depth: "once the water freezes, the Jupiter's gonna be locked in 50 feet of solid ice."
  • The temperature: "in six hours, the sun's gonna go down, and indications are, it will drop to 60 degrees below zero"

So, given this information, I would like to know if it’s possible for water to freeze so quickly like that?

Note: I’m no expert on physics, so I appreciate if you could use a not so technical language.

Best Answer

As we don't know anything about the intial temparature of the water, another fun but unlikely explanation would be to consider what we call supercooled water.

Basically, at atmospheric pressure, water below 0°C doesn't have to be solid. Sure enough, it would be its most natural state. But actually if you cool down some very pure, very steady water, you can pretty easily get... a very cold liquid below 0°C. This is all because in order for the water molecules to re-arrange into Crystal of ice, they need some support to rely on, a little seed to grow around (we call that a nucleus). So if there is no impurity in that water, then you can cool it down without freezing it ! You have to be careful to keep it steady too, because the energy of a shock would give the kick it needs to start the crystallization. You can find plenty of YouTube videos demonstrating this phenomenon. So if we assume that your water is already below zero, and in a supercooled state, then the swimmer in it would kickstart the crystallization, which would happen very quickly. For all I know, it is plausible that she'd then get trapped Under ice.

Your stroy makes me think of that because there is a horrible but pretty cool legend about a lake in Russia called the Ladoga lake. Alledgedly, during the Siege of Leningrad in 1942, in a cold winter's night, a fire started in the forest, scaring off a thousand of horses. Those who could run away from the flames plunged into the cold waters of the lake. And suddenly, with a sound of broken glass, the lake froze as the horses were jumping in it, trapping hundreds of them them in ice. I think it's Hubert Reeves who first suggested that the lake might have been in supercooled state, which could explain this sudden freezing, with the carateristic sound of shattered glass. However most people suggest it's just bullshit, as the water would have to be insanely pure and steady (which is not very natural). Furthermore, I have never seen an experiment about supercooled wtaer on such big scales. I don't know if this would hold.

So in short, supercooled water might be an (unlikely) way to justify it. But not so bad regarding series standards :)

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