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As you can see in this demonstration and read in this Wikipedia article if you were to place a cup of liquid nitrogen in a low pressure environment then it would reach a triple point and begin to solidify. However I do not understand why.

As we know lowering the atmospheric pressure reduces the boiling point of a liquid. This is because there are less, in this case, nitrogen particles above the liquid nitrogen, allowing more particles from the liquid to escape into a gas state. However I do not understand what effect this has on it's solid state. Yes, I've seen the phase diagram but a liquid turns to a solid when the energy of its particles lowers to the point they form an ordered structure. The only thing I can think of that would lower the freezing point is that at lower pressure since atoms more easily escape from the liquid into the vapor phase the liquid is left with all the low energy atoms, which turns it to a solid. I couldn't find any relevant information on this.

Another thing I don't understand is why is the temperature of the nitrogen falling? It starts at ~ -196 C but according to the diagram and Wikipedia then falls to ~ -210 C causing it to form solid layers. Considering how cold it is it should only be absorbing temperature from the environment and thus increasing its temperature. Is this linked to my hypothesis above?

To summarize:
1. Considering the linked video and article - what is the mechanism that causes the nitrogen to become solid at lower pressures? Is it because high energy atoms leave the liquid, thus leaving only their low energy brethren behind?
2. Why is the temperature of the nitrogen falling? Is it linked to the hypothesis from 1. where the leaving high energy atoms, by leaving only low energy particles, lower the temperature of the system?

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