What will happen when a large amount of water at 0C....

[Joe brewer]

Homework Statement

What will happen when a large amount of water at 0 C is mixed with ice at - 20 C? Assume ideal conditions.

Homework Equations

N/A

The Attempt at a Solution

I think the ice will rise in temp (without melting) but no new ice will be formed. Is this right?

 

[jedishrfu]

If the ice rises in temperature then what gets cooler?

 

[Joe brewer]

Oh so there will be more ice formed but it will equilibrate at a temp between - 20 C and 0 C. Is that right?

 

[jedishrfu]

What do you think and why?

 

[Joe brewer]

What do you think and why?

Well I think that the ice can't melt, but the temp must equilibrate. So the heat will flow from the water to the ice. This will form more ice and raise the temp of the new ice until equilibrium is reached. Better?

 

[Herman Trivilino]

What will happen when a large amount of water at 0 C is mixed with ice at - 10 C?

 

[Joe brewer]

What will happen when a large amount of water at 0 C is mixed with ice at - 10 C?

The same thing except it would equilibrate at a higher temp (still below zero). Probably less ice formed as well. Am I on the right track here?

Edit: or if there is enough ice, All of the water would turn to ice in both cases because all the water has to decrease in temperature. Since the L_f of water is fairly low, you would either have enough heat in the water to bring all of the ice up to nearly 0C without any phase change or all of the water would freeze at slightly below 0C as well. This would depend on the proportion between water and ice. Is that right?

 

[Herman Trivilino]

The same thing except it would equilibrate at a higher temp (still below zero). Probably less ice formed as well. Am I on the right track here?

What if the ice were at a temperature of -5° C?

Edit: or if there is enough ice, All of the water would turn to ice in both cases because all the water has to decrease in temperature.

That's why there's a "large" amount of water. How large? Large enough to keep at least some of it in the liquid state.

By the way, what's the significance of the special temperature of 0° C? If you had a 50/50 mixture of ice/water at that temperature and you transferred a small amount of heat energy to the mixture what would happen to it?

 

[Joe brewer]

0C is when any amount of water and ice would be at equilibrium.

At -5 C presumably the ice would increase in temp and some of the water would freeze.

 

[Herman Trivilino]

So ice at -20 °C will warm up.

Ice at -10 °C will warm up.

Ice at -5 °C will warm up.

Do you see where this is going?

 

[Joe brewer]

Yep! Basically as long as the ice is below zero, equilibrium will be at an intermediate temperature and will have x amount of additional ice.

 

[Herman Trivilino]

You've already told us this ...

0C is when any amount of water and ice would be at equilibrium.

 

[Chestermiller]

Yep! Basically as long as the ice is below zero, equilibrium will be at an intermediate temperature and will have x amount of additional ice.

What would happen if the intermediate temperature happened to be - 10 degrees. How would it know to stop at - 10 degrees? You just told us that if you have ice at - 10 degrees in water at 0 degrees, the ice would heat up and more ice would form, and the ice would reach another intermediate temperature somewhere between -10 and 0. What if the new intermediate temperature happened to be - 5 degrees. How would it know to stop at - 5 degrees?

Chet

 

[Joe brewer]

So it would all turn to ice no matter what?

 

[Chestermiller]

So it would all turn to ice no matter what?

No. There would be ice and water left in the end, but the final temperature would be ?

 

[Joe brewer]

No. There would be ice and water left in the end, but the final temperature would be ?

Well, I was thinking somewhere between zero and the temp of the ice. Would it always be zero but the amount of ice would just increase? That's the only way I can think of that allows any water to be left over.

 

[Herman Trivilino]

Well, I was thinking somewhere between zero and the temp of the ice. Would it always be zero but the amount of ice would just increase? That's the only way I can think of that allows any water to be left over.

That's the only equilibrium temperature at which a mixture of ice and water can exist. So looking at the way the problem is stated, the reference to a "large" amount of water is a hint that the author intends it to be a sufficient amount so that there is still some liquid water left in the container. As long is there is still some liquid, and some solid, and it's in equilibrium, there is only one possible thermometer reading.

 

[Chestermiller]

Well, I was thinking somewhere between zero and the temp of the ice. Would it always be zero but the amount of ice would just increase? That's the only way I can think of that allows any water to be left over.

Why do you feel this way? If you had ice floating in ice water inside an insulated container at 0C, do you feel like all the water would turn to ice. Where would all the heat given off when the water turned to ice go to? You are aware that, in order for water to turn to ice at 0 C, you need to remove the heat of freezing, correct?

Chet

 

[Joe brewer]

Let me walk you through what I'm thinking
1.ice is added
2.water gives up heat to ice, heating it up and turning into ice (still at 0c)
3.this continues until all the ice(old and new) is at 0c
4.water is still at 0c

On another note, Is this how (re) crystallization works?

 

[Herman Trivilino]

You got it.

This is how freezing works. I'm not sure what you mean about crystallization.
.

 

[Chestermiller]

Let me walk you through what I'm thinking
1.ice is added
2.water gives up heat to ice, heating it up and turning into ice (still at 0c)
3.this continues until all the ice(old and new) is at 0c
4.water is still at 0c

On another note, Is this how (re) crystallization works?

What recrystallization? After step 4, you have ice at 0 C sitting in a pool of ice water at 0 C. Game over. Nothing more happens. The system is now at equilibrium. To get more water to freeze, you would have to physically remove heat from the system.

Chet