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

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Homework Help Overview

The problem involves a scenario where a heated piece of metal is placed into water, and the objective is to determine the heat gained by the water as it reaches thermal equilibrium with the metal. The subject area pertains to thermodynamics and heat transfer principles.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the relevance of the specific heat of the metal and whether it is necessary for solving the problem. There is an exploration of the temperature change of the water and how to calculate the heat gained by it. Questions arise regarding the method to find the specific heat of the metal once the heat gained by the water is known.

Discussion Status

The discussion is ongoing, with participants providing insights into the calculations related to the heat gained by the water. Some guidance has been offered regarding the relationship between the heat gained by the water and the heat lost by the metal, but there is no explicit consensus on the next steps or final calculations.

Contextual Notes

Participants note the lack of specific heat for the metal and question how to approach the problem without this information. There is also a mention of the initial and equilibrium temperatures of the water and metal, which are critical to the calculations.

astru025
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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!
 
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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.
 
You are told that the water was originally 20 degrees celsius and increased to 26.5 degrees celsius, 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?
 
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?
 
Once I know the heat gained by the water how can I find the specific heat of the metal?
 
astru025 said:
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.

astru025 said:
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...
 
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?
 
astru025 said:
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?
 
I do not know that. Do I use the same equation I used to find change in temp of the water?.
 
  • #10
astru025 said:
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?
 

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