Why don't ice cubes spontaneously form in a cup of water

[Lymitra]

Why don't ice cubes spontaneously form in a cup of water? Someone was explaining to me that for ice cubes to spontaneously form, the water molecules would have to go to a more ordered state. I know about the spontaneous symmetry breaking that occurs when water is at 0'C, but I was wondering if it's possible for the rest of the universe's entropy to increase more than the decreased entropy caused by the ice cubes forming. That way, the Second Law of Thermodynamics is not violated, and it still allows the ice cubes to form. Is this a question of chance then, that we'd have to wait a long enough cosmological time span for the entropy in all other areas of the universe to suddenly increase to such an extent as to make up for the ice cubes forming?

Thanks for answering.

 

[Vanadium 50]

Before thinking about the second law of thermodynamics, you need to think about the first. Heat flows from a body at higher temperature to one at a lower temperature. So your cup won't cool down below the temperature of the ambient air.

 

[stewartcs]

Before thinking about the second law of thermodynamics, you need to think about the first. Heat flows from a body at higher temperature to one at a lower temperature. So your cup won't cool down below the temperature of the ambient air.

Actually the second law places the constraint on the direction of heat flow, not the first.

CS

 

[Vanadium 50]

You're right.

My brain is clearly broken.

 

[stewartcs]

You're right.

My brain is clearly broken.

Just a Freudian slip I'm sure!

CS

 

[mgb_phys]

They would sometimes if you waited long enough - statistical mechanics is just a matter of playing the odds.

 

[Phrak]

They would sometimes if you waited long enough - statistical mechanics is just a matter of playing the odds.

31 days 9 hours. No ice observed. Will keep posted february.

 

[Mapes]

I was wondering if it's possible for the rest of the universe's entropy to increase more than the decreased entropy caused by the ice cubes forming.

You are describing exactly the process of cooling to 0°C and freezing. Thermal energy and entropy leave the water and move to the surrounding area; of course, the process is only spontaneous if the surroundings are at <0°C, as Vanadium 50 notes. Energy is conserved, and some extra entropy is produced because of the temperature gradient.

Freezing would be spontaneous at room temperature if you could increase the Gibbs free energy of the water phase significantly more than the ice phase. For example, a large enough increase in pressure will make the liquid phase energetically unfavorable because its specific volume is larger than that of the solid phase.

EDIT: The first line of the last paragraph should read "if you you could increase the Gibbs free energy of the water phase significantly more than you increase the Gibbs free energy of the ice phase." You only need G_\mathrm{water}&gt;G_\mathrm{ice} for spontaneity.

 

[turin]

Maybe the ice is forming and melting rapidly all the time, and it's just happening too fast and at too small a scale for you to see?