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

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1. Oct 8, 2015

### Joe brewer

1. The problem statement, all variables and given/known data
What will happen when a large amount of water at 0 C is mixed with ice at - 20 C? Assume ideal conditions.

2. Relevant equations
N/A

3. 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?

2. Oct 8, 2015

### Staff: Mentor

If the ice rises in temperature then what gets cooler?

3. Oct 8, 2015

### 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?

4. Oct 8, 2015

### Staff: Mentor

What do you think and why?

5. Oct 8, 2015

### Joe brewer

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?

6. Oct 8, 2015

### Mister T

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

7. Oct 8, 2015

### Joe brewer

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?

Last edited: Oct 9, 2015
8. Oct 9, 2015

### Mister T

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

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?

9. Oct 9, 2015

### 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.

10. Oct 9, 2015

### Mister T

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?

11. Oct 9, 2015

### 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.

12. Oct 9, 2015

### Mister T

You've already told us this ...

13. Oct 9, 2015

### Staff: Mentor

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

14. Oct 9, 2015

### Joe brewer

So it would all turn to ice no matter what?

15. Oct 9, 2015

### Staff: Mentor

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

16. Oct 9, 2015

### Joe brewer

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.

17. Oct 9, 2015

### Mister T

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.

18. Oct 9, 2015

### Staff: Mentor

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

19. Oct 10, 2015

### Joe brewer

Let me walk you through what I'm thinking
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?

20. Oct 10, 2015

### Mister T

You got it.

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