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

[astru025]

Homework Statement

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.

Homework 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.

The Attempt at a Solution

Not really sure how to go about this problem. Any help in the right direction would be greatly appreciated!

 

[gneill]

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.

 

[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?

 

[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?

 

[astru025]

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

 

[gneill]

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?

Yes.

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

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...

 

[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?

 

[haruspex]

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?

What was the change in temperature of the metal?

 

[astru025]

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

 

[haruspex]

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

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