# Temperature Equilibrium between ice cubes and water

1. Nov 30, 2009

### grouper

1. The problem statement, all variables and given/known data

How many 20 g ice cubes (whose initial temperature is -10 C) must be added to 1 L of water (whose initial temperature is 90 C) for the final mixture to have a temperature of 10 C. Assume that all the ice is melted and that the system is isolated

2. Relevant equations

Q=mcT

3. The attempt at a solution

using m(water)*90 + m(ice)*-10 = m(water+ice)*10

where m(water)= 1 kg
and m(ice)= .02n kg

I got 225 ice cubes, but I'm not sure if I set up the above equation correctly

2. Nov 30, 2009

### Hootenanny

Staff Emeritus
Welcome to Physics Forums.
Why have to ignored the c in your Q=mcT equation?

You also need to include the energy required to melt the ice. In words your equation would be something like

energy required to heat the ice by ten degrees + energy required to melt the ice + energy required to heat the melted ice from zero degrees to the final temperature = energy produced by cooling the water from 90 degrees to the final temperature

Do you follow?

3. Nov 30, 2009

### grouper

I believe when it says "assume that all ice is melted" that means you do not have to account for the energy to melt the ice. Also, I ignored c because it's all water, so all the c's are the same and they cancel out, correct?

4. Nov 30, 2009

### Hootenanny

Staff Emeritus
So you think that it takes no energy to melt ice? Just because everything ends up as water doesn't mean that you can assume that all of it was always water.
c for ice is not the same as c for water.

5. Nov 30, 2009

### grouper

I didn't say that it takes no energy to melt ice, please don't insult my intelligence just because I am asking for help. The PROBLEM says to assume that the ice is already melted, therefore I assumed that the energy required to melt the ice is not a part of this problem. Also, if the ice were already melted, then everything would be water and all water has the same value for c.

6. Nov 30, 2009

### Hootenanny

Staff Emeritus
I apologise if I sound abrupt, but that is what you said. You said that you believe that you can ignore the energy required to melt the ice.
No it doesn't.

7. Nov 30, 2009

### grouper

I believe the problem says that "all ice is melted."

8. Nov 30, 2009

### Hootenanny

Staff Emeritus
Yes, the ice melts eventually. However, that doesn't mean that we can ignore the fact that there was initially ice in the glass.

9. Nov 30, 2009

### grouper

Wow, ok. Now I get what you are saying. I was reading that sentence differently. I wish you had explained that in the first place. Well that sure complicates the problem compared to how I originally did it, but it's still pretty easy. Thank you for your roundabout help, we eventually reached a solution.

10. Nov 30, 2009

### Hootenanny

Staff Emeritus
Sorry, I was trying to guide you to the solution without stating it outright. However, I was obviously a little too obscure here.