Hot metal added to Water, Heat Capacity Problem

In summary, to find the final temperature of a mixture of 100.0 g copper at 100 C and 50.0 g water at 26.5 C, we can use the equation q = q(copper) + q(water) and set the heat lost by the copper equal to the heat gained by the water. This can be further simplified using the equation q = (specific heat)(mass)(change in Temp.) and taking into account that the final temperature of both substances will be equal. Solving for Tfinal will give us the answer.
  • #1
Nick_273
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Homework Statement



A 100.0 g copper sample (specific heat 0.385 J/g K) at 100 C is added to 50.0 g of water at 26.5 C. What is the final temperature of the copper-water mixture?

Homework Equations



q = q(copper) + q(water)

q = (heat capacity)(change in Temp.)

q = (specific heat)(mass)(change in Temp.)


The Attempt at a Solution



So far i have found the heat capacity of copper to be 0.385 J/K

I know the metal loss of heat must equal the waters gain in heat but i do not know how to calculate the gain/loss.
 
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  • #2
It seems you have the idea. To find the final temperature, try setting -qcopper = (specific heat)(mass)(change in Temp.) equal to qwater = (specific heat)(mass)(change in Temp.)

Another thing to keep in mind that should help you solve for final temperature, is that the at the end, the temperature of the water and the copper are going to be equal. So, if you think about what (change in Temp) really is, you should find yourself with an equation and one unknown, Tfinal, and from there you should be able to solve for temperature at the end.
 

1. What happens when hot metal is added to water?

When hot metal is added to water, several processes occur simultaneously. The water near the metal surface is rapidly heated, causing it to expand and rise due to its lower density. This creates convection currents, which help distribute the heat throughout the rest of the water. As the water continues to heat up, some of it may evaporate into steam. The metal itself will also heat up and eventually reach the same temperature as the water.

2. Why is it important to consider the heat capacity when adding hot metal to water?

Heat capacity is a measure of how much energy is required to raise the temperature of a substance. In the case of hot metal added to water, the heat capacity of the water is important because it determines how much the temperature of the water will change. If the heat capacity of the water is low, it will heat up quickly and potentially reach boiling point, whereas a higher heat capacity will result in a slower temperature increase.

3. How does the heat capacity of water compare to other substances?

The heat capacity of water is relatively high compared to other common substances. This is because water has a high specific heat capacity, meaning it requires a lot of energy to raise its temperature. For example, it takes four times as much energy to raise the temperature of water by 1 degree Celsius compared to the same amount of iron. This is why water is often used as a coolant in industrial processes.

4. Can the temperature of water continue to rise indefinitely when hot metal is added?

No, the temperature of the water will eventually reach an equilibrium point where the heat being added by the hot metal is equal to the heat being lost through convection and evaporation. At this point, the temperature will remain constant unless more heat is added or removed.

5. How does the type of metal being added affect the heat capacity of the water?

The type of metal being added can have an impact on the heat capacity of the water. Some metals have a higher heat capacity than others, meaning they will require more energy to raise the temperature of the water. Additionally, some metals may have a lower boiling point, so they may cause the water to reach boiling point quicker than others. Overall, the type of metal will affect the rate at which the water heats up and the final equilibrium temperature.

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