Temperature Equilibrium between ice cubes and water

[grouper]

Homework Statement

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

Homework Equations

Q=mcT

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

 

[Hootenanny]

Welcome to Physics Forums.

Homework Statement

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

Homework Equations

Q=mcT

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

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?

 

[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?

 

[Hootenanny]

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.

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.

Also, I ignored c because it's all water, so all the c's are the same and they cancel out, correct?

c for ice is not the same as c for water.

 

[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.

 

[Hootenanny]

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.

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.

The PROBLEM says to assume that the ice is already melted

No it doesn't.

 

[grouper]

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

 

[Hootenanny]

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

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

 

[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.

 

[Hootenanny]

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.

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