Question about determing specific heat capacity using waterfall.

In summary, the water temperature at the top of a waterfall is 22 degrees celcius. The water temperature at its base, 210 m lower, is 22.5 degrees celcius.
  • #1
yvan300
13
0

Homework Statement


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

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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  • #2
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?
 
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  • #3
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 :)
 
  • #4
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?
 
  • #5
It turns into heat and some sound energy! :P
 
  • #6
Okay, forget the sound :biggrin:
Now you have one equation: potential energy at the top = heat at the base!
 
  • #7
hikaru1221 said:
Okay, forget the sound :biggrin:
Now you have one equation: potential energy at the top = heat at the base!

Yes.....??
 
  • #8
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:
 
  • #9
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!
 

Related to Question about determing specific heat capacity using waterfall.

1. How is specific heat capacity calculated?

Specific heat capacity is calculated by dividing the amount of heat required to raise the temperature of a substance by the mass of the substance and the change in temperature. This can be represented by the formula Q = mcΔT, where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

2. How does a waterfall help in determining specific heat capacity?

A waterfall can be used to determine specific heat capacity by providing a controlled environment for the heat transfer process. By measuring the temperature of the water before and after the waterfall, the amount of heat transferred can be calculated and used in the specific heat capacity formula.

3. What factors can affect the accuracy of using a waterfall to determine specific heat capacity?

The accuracy of using a waterfall to determine specific heat capacity can be affected by factors such as the flow rate of the water, the ambient temperature, and any heat loss from the surrounding environment. It is important to control these factors as much as possible to obtain accurate results.

4. Can specific heat capacity vary for different substances?

Yes, specific heat capacity can vary for different substances. This is due to differences in the molecular structure and composition of each substance. For example, water has a higher specific heat capacity compared to most other substances, meaning it requires more heat to raise its temperature.

5. How is specific heat capacity useful in practical applications?

Specific heat capacity is useful in practical applications such as designing heating and cooling systems, determining cooking times for different foods, and understanding the thermal properties of materials. It is also important in industries such as engineering and chemistry, where heat transfer and temperature control are crucial.

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