Phase Transition in a Pure Water System

[LittleMissScare-All]

Hello, I'm a highschool student and there has been this question bugging me ever since my physics teacher insisted my point of view was wrong but it never sat right with me so I want to share it and get a proper explanation.
Consider a perfectly isolated system containing an infinite mass of pure water at 0°C. The system is maintained under ideal conditions where the freezing point of water and the melting point of ice are both 0°C. If a minute quantity of ice at -1°C, approximately the size of a dust particle, is introduced into the system, will a phase transition occur such that all of the liquid water solidifies?
thank you

 

[Dale]

I assume that by “infinite mass” you just mean “large mass”. An infinite mass of water would form a black hole.

No, you would get a very small additional amount of ice formation. Remember, to go from water at 0 C to ice at 0 C, the water must give up a substantial amount of latent heat. So a small amount of water at 0 C will give up latent heat and become ice at 0 C, and the ice at -1 C will receive that heat and warm up to ice at 0 C.

 

[LittleMissScare-All]

I assume that by “infinite mass” you just mean “large mass”. An infinite mass of water would form a black hole.

No, you would get a very small additional amount of ice formation. Remember, to go from water at 0 C to ice at 0 C, the water must give up a substantial amount of latent heat. So a small amount of water at 0 C will give up latent heat and become ice at 0 C, and the ice at -1 C will receive that heat and warm up to ice at 0 C.

Sorry for the infinite mass error I tried to emphasize a scale since this is an imaginary problem in hand.
I completely forgot about the latent heat part, thank you for answering

 

[Dale]

There is a related phenomenon that may be closer to what you want. If the water is very cool and still and the container is very smooth then it is possible to “supercool” the water. This means that you have liquid water at some temperature lower than 0 C, say -10 C. The temperature is low enough to form ice, but without a good site for ice crystal formation it may not.

The small speck of ice at -1 C, even though it is warmer than the supercooled water, can serve as a crystallization starter, also called a nucleation site. So then you will very rapidly get the formation of ice until the whole system becomes a mix of ice and water at 0 C

 

[LittleMissScare-All]

There is a related phenomenon that may be closer to what you want. If the water is very cool and still and the container is very smooth then it is possible to “supercool” the water. This means that you have liquid water at some temperature lower than 0 C, say -10 C. The temperature is low enough to form ice, but without a good site for ice crystal formation it may not.

The small speck of ice at -1 C, even though it is warmer than the supercooled water, can serve as a crystallization starter, also called a nucleation site. So then you will very rapidly get the formation of ice until the whole system becomes a mix of ice and water at 0 C

This was exactly how I thought it would work out minus the warmer ice supercooled water part, thank you for sharing

 

[DaveE]

OK, then please let me know if this is correct for the phase transition of supercooled water.

The latent heat of fusion is about 80 cal/g, which would correspond to a temperature change in liquid water of 80C. So if you have supercooled water at -10C, after the phase change you would have about 12.5% ice and 87.5% water at a temperature of 0C. This is because there is only enough energy released (from -10C to 0C) to freeze 12.5% of the water. To freeze all of the water it would have to start at -80C.

 

[Dale]

Yes, or at least that is my understanding on the topic.

 

[gmax137]

I need to re read Vonnegut's Cat's Cradle.