Question about determing specific heat capacity using waterfall.

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Homework Help Overview

The problem involves determining the specific heat capacity of water based on temperature changes observed at a waterfall, where the temperature at the top is 22.0 degrees Celsius and at the base is 22.5 degrees Celsius, with a height difference of 210 meters. Additionally, it poses a hypothetical scenario regarding the temperature change if the waterfall were twice as tall.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the conservation of energy as water falls, considering potential and kinetic energy. They explore how kinetic energy relates to temperature changes and question how to link these concepts mathematically.

Discussion Status

Participants are actively engaging with the problem, discussing equations for potential energy and heat transfer. Some have provided guidance on the relevant formulas, while others are working through the implications of energy conservation in this context. There is a collaborative effort to clarify the relationships between the different forms of energy involved.

Contextual Notes

Participants note the problem's construction may be unconventional, and there is an emphasis on understanding the energy transformations rather than simply applying formulas. The discussion includes questions about the necessity of mass in calculations and the appropriateness of values used.

yvan300
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Homework Statement


The temperature at the top of a popular waterfall is 22.0 degrees celsius. The temperature at its base, 210 m lower, is 22.5 degrees celsius.

1)Caluclate the specific heat capacity of the water.

2) If the waterfall was twice as tall, determine by how much the water temperature would change from its initial value.




Homework Equations





The Attempt at a Solution



We've done specific heat capacity before but i have no idea where to start :D

 
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I think this problem is awkwardly made up (so don't apply this problem to practice!). Anyway, it's a good one to test new knowledge.
Consider 1 kg of water falling from the top to the base. Assume that the energy is conserved (!). Now what form of energy does the water store when: 1- it's at the top, and 2- it's at the base?
 
Last edited:
Well, at the top, there would be potential energy and as it falls to the bottom, it would gain kinetic energy. Since kinetic energy is linked to temperature, that explains the temperature rise. But still the problem is linking everything together to give the answer. LOl :)
 
Okay. Before it "touches" the base, it has kinetic energy, right? After that, it's stopped. So kinetic energy is changed into another form. What form is it?
 
It turns into heat and some sound energy! :P
 
Okay, forget the sound :biggrin:
Now you have one equation: potential energy at the top = heat at the base!
 
hikaru1221 said:
Okay, forget the sound :biggrin:
Now you have one equation: potential energy at the top = heat at the base!

Yes.....??
 
Can you write down the potential energy of 1kg water at the top, and the heat of 1kg water to raise its temperature from 22 to 22.5 degrees? :smile:
 
Nope
 
  • #10
What's the formula for potential energy? What's the one for heat?
 
  • #11
I think heat is 1/2 mv(squared), but don't know the one for potential energy.
 
  • #12
Potential energy = mgh.
Heat = mC.delta(T).
Remember?
 
  • #13
Oh yeah
 
  • #14
Good. Plug the data in, and go straight to the answer. It should be around 4200 J/kgK.
 
  • #15
When calculating, you are able to use any value for mass?
 
  • #16
It's not necessary. Do the calculation, and you will see why.
 
  • #17
Ok so since p.e. mgh

Then p.e. is 1kg * 10m/s * 210

2100 J

And this is converted to 2100 J of kinetic energy

Since Eh = mc *temperature change

2100 = 1 * c *.5

which is 4200 :D
 
  • #18
Thanks man!
 

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