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Let's take the most famous scene from Frozen where Elsa creates her ice palace up in the freezing mountains. Now imagine Elsa doing the same thing at sea level, in the summer, where the conditions are approximately SATP (i.e. 25°C and 100 kPa). Assume that the scientific basis of her power is the ability to locally alter temperature to the point of water vapor depositing as ice. My questions are: Are there any consequences (other than the ice generation itself) of converting that much water vapor in the atmosphere to ice? For example, will that cause a huge change in air pressure? Also, exactly how might these effects be altered by Elsa's location (and thus thermodynamic conditions around her)?

EDIT: I am aware that it would take an enormous measure of air to generate a substantial amount of ice. Assume that Elsa has the ability to gather that amount of air—what would then be the atmospheric or thermodynamic consequences?

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    $\begingroup$ How does science-based and magic tags together not contradict? $\endgroup$
    – JDługosz
    Jun 8 '17 at 8:27
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    $\begingroup$ Please note the following: a) because there isn't that much water in the air usually, it might be beneficial if she heated up the air and water source first. I think this is more logical than somehow gathering air. b) I think you should specify just how high those mountains are supposed to be. c) It gets even more complicated since freezing out the air will not create solid chunks (or mountains) of ice but something like snow instead. I think you should specify exactly what happens in order to get an answer. Do you want snow mountains? d) Is she able to spatially confine temperature changes? $\endgroup$
    – Raditz_35
    Jun 8 '17 at 8:39
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    $\begingroup$ @Raditz_35 she dotn't need to heat up the air. When she get water from cooled air, a fresh portion of air will arrive from a wind. Wind wil go automatically because of difference in pressure. It's common process like air from sea drops snow in mountains $\endgroup$
    – ADS
    Jun 8 '17 at 8:50
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    $\begingroup$ @JDługosz, magic is too often considered without consequence, but the scientific consequences of a situation like this can be of far more interest than the magic itself. $\endgroup$
    – Separatrix
    Jun 8 '17 at 8:58
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    $\begingroup$ @lightweaver I still think you should specify this way then - unless the answers are what you are looking for. Maybe I'm completely misunderstanding your question, in this case never mind. I think there are arbitrary numbers of legitimate answers to your question (which doesn't mean that I intent to write one in any case) $\endgroup$
    – Raditz_35
    Jun 8 '17 at 11:07
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In order to create ice from air, these steps are needed:

  1. condensate the vapor to liquid
  2. cool down the liquid
  3. freeze the liquid to ice

Each of these steps release a substantial amount of heat. Let's say that for practicing Elsa is going to create 1 gram of ice (for scale, the ice formed condensing a cube of water 2 cm side would weight 8 grams); this would release (back of an envelope calculation):

  • condensation: 2272 J
  • cooling down from 100 C to 0 C: 418 J
  • freezing: 333.5 J

Total = 3023 J, which is roughly the energy of a mass of 1 kg launched at 77 m/s.

Creating 1 ton of ice imply therefore the removal and release of 3 GJ, corresponding to what you get burning 88 kg of coke (the coal, not the cola).

I guess Elsa is better releasing that heat away from the ice, if the castle has to stand.

The resulting dry air, being denser than humid air, would then tend to flow down, resulting in downward winds similar to phoen.

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  • $\begingroup$ Since you are using four-digit precision elsewhere, you got the density of the ice slightly wrong. It is less than 1 g per cm^3, or ice wouldn't float. $\endgroup$
    – o.m.
    Jun 8 '17 at 5:05
  • $\begingroup$ @o.m. you are right, I was thinking of the water in a cube that size, but in the rush of typing forgot it. Edited to fix it $\endgroup$
    – L.Dutch ♦
    Jun 8 '17 at 5:52
  • $\begingroup$ So the surrounding air would become immensely hot, then? Is temperature the only thing that changes in the air? $\endgroup$
    – lightweaver
    Jun 8 '17 at 7:03
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    $\begingroup$ I'm confused a bit. To condensate vapor you need to cool down the volume of air from which you get water. To get ice you have to breeze this water. Of course, according to law of conservation of energy, something should be warmed up somewhere. But.. this is a magic, and more likely released energy would be too far away from ice palace (just to prevent its melting). [Perhaps a new star will shine in the galactic far-far away]. I suppose air surrounding palace would be cooled down. It's not obvious from your answer since you focused on releasing energy $\endgroup$
    – ADS
    Jun 8 '17 at 7:38
  • $\begingroup$ @ADS you are right, if the mage is skilled should discharge the excess heat somewhere else (I think it is teached in the basic lessons of magic classes) $\endgroup$
    – L.Dutch ♦
    Jun 8 '17 at 7:44
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The pressure around the ice would undoubtedly decrease as the water is condensing leaving behind a vacuum. But this vacuum would quickly suck up and restore the surrounding pressure to what it was before. Obviously in warmer climates it would be more difficult to cool the water vapor into ice. Also, in drier climates it would be harder to create the ice as there is less water content in the air(places such as the desert as oppose to the rainforest). Lastly, it would easier to create ice where there is higher pressure(such as sea level as oppose to Elsa's mountains). This is because freezing point increases with increasing temperature and therefore the water vapor will have to be cooled less.

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To get water from vapor, you need to cool down surrounding air. To freeze water to the ice you need additional cooling. Of course, something should be warmed up to balance the energy. But this something is far far away and out of scope. Let's concentrate on the palace and surrounding area.

Since near palace air has been cooled, processes like blizzard are run [Cold air go down, warm and wet air goes outside and then cools down and releases vapor. The wind has arisen.] We could estimate how big it would be. According to answer from L.Dutch you need 3×106 joules to get 1 ton of ice. The palace is big so could consist of hundreds and thousands tons. Let's get 100,000 tons. We need 3×106×105 = 3×1011 J of energy. According to this estimation this is 106 times smaller than 'a mature hurricane' so we could expect a really tiny blizzard.

Note that hurricane from link has 60 km radius and lasts for 1 day. Because of very fast process you could expect a moderate blizzard but in a very small area.

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