[rhazen]

At a local convenience store, you purchase a cup of coffee, but at 98.4 degrees Celsius, it is too hot to drink.  You add 21.8g of ice that is -2.2 degrees Celsius to the 248mL of coffee.  What is the final temperature of the coffee? (Assume the heat capacity and density of the coffee are the same as water and the coffee cup is well insulated.)

PLEASE HELP ME!  ANYONE! thank-you!
-Renee

[Jorriss]

There are two big considerations as far as I would see ( big ones, there are others you can more or less take more granted).

What is the relevance of the mentioning the cups are well insulated?

If you mix those two liquids together, there will be heat transfer. One will get hotter, one will get colder. When will the heat transfer stop?

[rhazen]

Sorry, but that doesn't help much.  We are studying quantitative aspects of phase changes.  The heating-cooling curve is discussed and so is the Clausius-Clapeyron Equation.  But nothing in the chapter seems to suit the variables.  The coffee cup being insulated is just saying that the outside system temperature does not affect the temp of the coffee.

[Jorriss]

You answered half of the questions I posed then.

Can you think of anything for the second? If you mix two liquids, or two anything together, their temperatures change. Heat moves from hotter to colder. So it'll stop when the system is in thermal equilibrium.

[rhazen]

Ahk. It's okay.  I'm kind of frustrated with this question at this point.  I'm just going to forfeit the point.  Thanks anyway.

[Borek]

This is one of the simplest heat balance problems, heat lost = heat gained.

[rhazen]

I guess that is right.  The solution was the heat of the solution= the heat of the solute + the heat of the solvent + the heat of the mix.  Even though I was given that equation, I am still perplexed.  If I had an example problem I would understand, but I just keep getting abstract hints.  Nevertheless, I still do not understand how to find the answer.

[Borek]

Assume final temperature is T_f. How much heat will be lost by the hot coffee? How much heat will be gained by the ice before it will be at T_f?

[rhazen]

Final temp of coffee=98.4- (-2.2)
Final temp of ice cube=-2.2+98.4

[rhazen]

Okay, so the above is a random guess because you are asking me the same exact question as in the original problem.  I need to find the final temp.  I don't get how to do it!

[rhazen]

Can someone just PLEASE give me the equation to solve this.  Please I am begging on my knees.

[Borek]

You are trying to juggle numbers, that never helps. There is no single "one size fits all" equation for this type of problems, they have to be solved step by step. The sooner you will understand and accept that, the better for you.

You will need to write heat balance, assuming final temperature is an unknown T_f.

Obviously coffee has to get colder, as some of its heat will be used to heat up and melt the ice and later to heat up water from the melted ice. Coffee temperature will change from 98.4 to T_f. Try to express heat given away using this information.