Heat and internal energy of water temperature

In summary, using the equation Q=mcΔT, we can calculate the temperature of the water at the bottom of Niagara Falls by equating the change in potential energy to the heat absorbed by the water. By rearranging the equation, we can solve for the final temperature, which is equal to the initial temperature plus the change in potential energy divided by the specific heat capacity.
  • #1
mizzy
217
0

Homework Statement


Water at the top of Niagara Falls has a temperature of 10.0degrees celsius. If it falls a distance of 50.0m and all of its potential energy goes into heating the water, calculate the temperature of the water at the bottom of the falls.


Homework Equations



W = change in kinetic energy + change in potential energy

The Attempt at a Solution


i know there's potential energy on top and none at the bottom. There's not kinetic energy at the top and there is at the bottom. But how do i put temperature into this equation?
 
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  • #2
The change in potential energy of the water = heat absorbed by water


You should know the equation Q=mcΔT
 
  • #3
so distance isn't included in the equation? and mass?
 
  • #4
mizzy said:
so distance isn't included in the equation? and mass?

The height is a distance and the mass will not really matter.
 
  • #5
so, mgh = mc(T-Ti)

then solve for Tf?

therefore,

mgh = mc(Tf - Ti)
gh = cTf - cTi
gh + cTi = cTf
gh/c + Ti = Tf
 
  • #6
Yes that should work.
 
  • #7
Thanks
 

1. What is the difference between heat and internal energy?

Heat is a form of energy that is transferred from one object to another due to a temperature difference. Internal energy refers to the total energy of the particles within a substance, including both kinetic and potential energy.

2. How does water temperature affect its internal energy?

As water is heated, its internal energy increases. This is because the molecules within the water gain kinetic energy and move faster, increasing the substance's overall internal energy.

3. Does the specific heat of water change with temperature?

Yes, the specific heat of water does change with temperature. Water has a higher specific heat at lower temperatures, meaning it requires more energy to raise its temperature compared to other substances.

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

Water has a relatively high heat capacity compared to other substances. This means that it can absorb and store a large amount of heat energy without experiencing a significant change in temperature.

5. Can internal energy be converted into heat?

Yes, internal energy can be converted into heat. When the molecules within a substance have high amounts of internal energy, they can transfer this energy to other particles through collisions, resulting in an increase in temperature, which we feel as heat.

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