# Heat loss/Heat Gained

1. Dec 8, 2009

### cashellz77

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

heat Lost Heat Gained
M=.213 kg M=.868
C=2090 J/kg K C=4186 J/kg K
To=0 To=26.5
T=? T=?

2. Relevant equations

Q=mc(delta T

3. The attempt at a solution I can not figure this out , I have tried and tried with no luck.

2. Dec 8, 2009

### Andrew Mason

Heat flows from the hotter to the colder until they reach the same temperature. So you know that the temperature of each mass will be the same when equilibrium is reached. You have to determine the final temperature.
Your equation for the heat flow is correct. So the equations for the change in temperature in terms of initial and final temperature are:

$$Q_1 = m_1C_1(T_1 - T_f)$$

$$Q_2 = m_2C_2(T_f - T_2)$$

What is the relationship between Q1 and Q2? That will enable you to solve for Tf.

AM

Last edited: Dec 8, 2009
3. Dec 8, 2009

### Delphi51

Welcome to PF, Cashelz.
I don't think you have typed in the whole question - not exactly sure what the question is!

Generally in these heat questions you write
heat lost by one material = heat gained by the other
mC*ΔT = mC*ΔT

I think your ΔT for the water will be (26.5 - T) where T is the final temperature.
For the other material, looks like ΔT = (T - 0).
Try putting all the info into the equation and see if you can find T.

4. Dec 8, 2009

### cashellz77

Hello Thankyou!! The queastion reads An ice cube with a mass of .213kg and a temp. of0.00c is placed in a Styrofoam cup containing .868 of water at a temp. of 26.5 c . What is the final temp. of the water after the ice cube has melted?

5. Dec 8, 2009

### Delphi51

Glad you gave us the question! Our previous answers do not apply to this question, which involves the melting of ice. It takes heat to melt ice, called the heat of fusion. So
heat lost by water = heat of fusion of ice + heat gained by ice after melting

You should look up "heat of fusion" in your book and get the formula for it.