Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Ice crystals are spatially ordered, and in every randomness there is a low possibility of temporarily order. If given enough boiling water, and sufficient time, could local clusters water molecules happen to be in a crystalized state?

This may seem absurd, but I believe it must be possible, imagine dropping an ice cube in boiling water(and water vapor) in a perfect closed system, the ice cube melts while the water keeps boiling (because of the water vapor), then because of Poincare recurrence theorem, there will be an similar ice cube after a sufficiently long but finite time.

EDIT: The temperature is 100 Celsius and 1 atm (not at triple point)

share|improve this question
2  
Do not hold your breath. It is the same answer to "what is the probability that all the air ends up in the upper right corner of the room and we suffocate". –  anna v Jan 12 at 15:29
    
So is there a small chance it might snow in the upper right hand corner of the room? –  Jitter Jan 12 at 15:48
1  
@Jitter, no it'll snow in the lower left corner, so we'll die w/o even getting a single run down the slope :-) –  Carl Witthoft Jan 12 at 15:57
1  
At the triple point of water, the probability is quite high. –  Olin Lathrop Jan 12 at 15:58
    
@OlinLathrop true, but I don't think you can convince water to boil at the triple point. –  Carl Witthoft Jan 12 at 17:13

1 Answer 1

Please read this article in the wiki

In statistical mechanics, Boltzmann's equation is a probability equation relating the entropy S of an ideal gas to the quantity W, which is the number of microstates corresponding to a given macrostate :

Boltzman formula

In this formula connecting the statistical probability to entropy arising from thermodynamics one sees that all microstates are counted in. This would include the subset of microstates that are postuled in the question.

To get a probability number, one would have to do all the permutations of molecules at that temperature and pressure to appear in the volume under consideration and take the ratio to all the possible configurations with the rest of the molecules. In normal temperatures and pressures this would be a very very very small number for boiling water, and I am not willing to do the calculations for it. In addition one would have to include the phase transition into the calculations also ( or the binding of water molecules in the two forms).

In a supersaturated vapor, as in a cloud chamber or up high in the atmosphere where the jets leave track, the probability is quite high once a seed appears that the phase transition will happen, but that is another story.

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.