The Learned of Chemistry, lend me your brains!

[Collin152]

I've encountered a problem, and I can't wrap my mind around it. Lord knows my teacher can't explain it well.
Given an amount of water and it's original temperature, a given amount of ice melted in the water, and the temperature of the water after the ice has melted, and then having determined the volume of the water after it melted, how can one determine the energy needed to melt the ice?
If you can help me, both I and my friend (as she get's it no more than I do) will be in your debt.
Also, there will be cake.

[Logic]

I've encountered a problem, and I can't wrap my mind around it. Lord knows my teacher can't explain it well.
Given an amount of water and it's original temperature, a given amount of ice melted in the water, and the temperature of the water after the ice has melted, and then having determined the volume of the water after it melted, how can one determine the energy needed to melt the ice?
If you can help me, both I and my friend (as she get's it no more than I do) will be in your debt.
Also, there will be cake.
I think this could be figured out using a third medium, such as calories. I have not taken chemistry in a long time, so I have little doubt that there are flaws with my theory.

[Cobra_Ikari]

I've encountered a problem, and I can't wrap my mind around it. Lord knows my teacher can't explain it well.
Given an amount of water and it's original temperature, a given amount of ice melted in the water, and the temperature of the water after the ice has melted, and then having determined the volume of the water after it melted, how can one determine the energy needed to melt the ice?
If you can help me, both I and my friend (as she get's it no more than I do) will be in your debt.
Also, there will be cake.

...guessing off the top of my head (it's been years since I've done something like this)...the volume change gives you an amount of ice, and the temperature change takes into account some of the energy?

I've no clue, to be honest.

[Logic]

...guessing off the top of my head (it's been years since I've done something like this)...the volume change gives you an amount of ice, and the temperature change takes into account some of the energy?

I've no clue, to be honest.

Well, the knowns are:

1: Beginning volume of water before ice is put into it
2: Beginning temperature of the water before ice is put into it
3: Volume of ice.
4: New temprature of the water after the ice has melted.
5: New volume of water after ice has melted

With the desired unknown is amount of energy required to melt the ice into water.

I think that the temperature of the ice before it is placed in the water should be a known, because it will undoubtably take more energy to melt ice that is near the freezing/melting point than something that is 100 degrees colder than that. I recant my previous statement. I have no idea how this is supposed to be solved without trial and error.

[Elvaris]

It's a Law of Conservation of Energy problem.

On one side of the equation, you have the energy required to melt the ice plus the energy required to raise the water formed by the melted ice to the final temperature (assuming the ice started at its melting point, otherwise you also have a term to change the temperature of the ice...)

On the other side of the equation, you have the amount of energy required to lower the initial quantity of water from its original temperature to its final temperature.

Two of the three terms are simple specific heat times volume problems, allowing you to solve for the third (ignoring energy contributions from the atmosphere, viscosity, or any other complications real life imposes on science...)