# Finding heat gained by water when hot metal is placed in it.

1. Nov 12, 2013

### astru025

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

A 85 gram piece of metal is heated to 98°C and placed into 200mL of water insulated at 20°C. If the equilibrium temperature is 26.50, find the heat gained by the water.

2. Relevant equations

200 mL = 200 g.
85 g x 98 degrees celsius x specific heat of metal = 200 g x 20 degrees celsius x 4.180 J x g x C.

3. The attempt at a solution
Not really sure how to go about this problem. Any help in the right direction would be greatly appreciated!

2. Nov 12, 2013

### Staff: Mentor

Note that you weren't given a specific heat for the metal. So the information about the metal is likely spurious (not required). Just look at the water.

3. Nov 12, 2013

### HallsofIvy

You are told that the water was originally 20 degrees Celcius and increased to 26.5 degrees Celcius, a difference of 6.5 degrees. What is the heat is required to raise the temperature of 200 ml of water by 6.5 degrees?

4. Nov 13, 2013

### astru025

So would I take 200 g x 6.5 degrees celsius x 1 cal/ g C ? I come up with 1300 cal, would this be the heat gained by the water?

5. Nov 13, 2013

### astru025

Once I know the heat gained by the water how can I find the specific heat of the metal?

6. Nov 13, 2013

### Staff: Mentor

Yes.

The same form of equation applies. What was the temperature change for the metal? The heat that changed the water's temperature came from the metal, so...

7. Nov 13, 2013

### astru025

Specific heat is measured in cal/ g C. I have 1300 cal. which is the heat that changed the waters temperature and this heat came from the metal. So do I take 1300 cal. / 85 g. x 98 degrees celsius?

8. Nov 13, 2013

### haruspex

What was the change in temperature of the metal?

9. Nov 14, 2013

### astru025

I do not know that. Do I use the same equation I used to find change in temp of the water?.

10. Nov 14, 2013

### haruspex

You know the initial temperature. At equilibrium, what will be the difference in temperature between the metal and the water?