# Homework Help: Heat capacity

1. Aug 1, 2010

### jinx007

An ice cube of 75 g is drop into a glass containing 330 g of water at a temperature of 22 ' Celsius. The ice is at 0 ' Celsius and melts so that the temperature of the water decreases.

Calculate the final temperature of the water when all the ice has melted. Assume that no heat lost to the glass or the surrounding.

Specific latent heat of fusion of ice = 3.3 x 10^5 J/kg

specific heat capacity of water = -4.2 x 10^3 J/kg K

2. Aug 1, 2010

### Staff: Mentor

Call the final temperature X.

How much energy is required to melt the ice?

How much energy is required to heat the melted ice water from 0 degrees to X?

How much energy must be removed from the warm water to bring it down from 22 degrees to the final temperature?

3. Aug 1, 2010

### jinx007

Energy to melt ice to water at 0 ' Celsius = q = m lf

Energy to melt ice to water from 0 to X using q = mcQ
0.075 x -4.2 x 10^3 x( X - 0)

The last part i cannot understand..please check whether i am on the right track, please explain to me a bit more in detail

4. Aug 1, 2010

### Staff: Mentor

Yes, you're on the right track. Hint: The energy you must add to the ice to melt it and then heat it up must equal the energy removed from the warm water.

You'll set up an energy equation and then solve for X.

5. Aug 1, 2010

### jinx007

"""...How much energy must be removed from the warm water to bring it down from 22 degrees to the final temperature?..."""

How should i calculate the energy that must be removed from the warm water to bring it from 22 to X

should i use q = mcQ
0.33 x -4.2 x 10^3 x ( 22 - Q )

by the way the upper part i understand.

6. Aug 1, 2010

### Staff: Mentor

The equation you want is the same one that you used to find the heat you need to add to warm the ice water:

Q = mcΔT = mc(22 - X)

7. Aug 1, 2010

### jinx007

So if i round up all what i understand the answer should be like that:

m lf + 0.075 x -4.2x10^3 x (x-0) = 0.33 x -4.2 x 10^3 (22-x)

when i solve i will have the value of X that is the temperature

8. Aug 1, 2010

### Staff: Mentor

Looks good. (But get rid of the minus sign in front of the specific heat.) Don't forget to plug in the values for m and lf.