# Question about determing specific heat capacity using waterfall.

1. Jul 4, 2010

### yvan300

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution

We've done specific heat capacity before but i have no idea where to start :D
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jul 4, 2010

### hikaru1221

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: Jul 4, 2010
3. Jul 4, 2010

### yvan300

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. Jul 4, 2010

### hikaru1221

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. Jul 4, 2010

### yvan300

It turns into heat and some sound energy! :P

6. Jul 4, 2010

### hikaru1221

Okay, forget the sound
Now you have one equation: potential energy at the top = heat at the base!

7. Jul 4, 2010

### yvan300

Yes..............??

8. Jul 4, 2010

### hikaru1221

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?

9. Jul 4, 2010

### yvan300

Nope

10. Jul 4, 2010

### hikaru1221

What's the formula for potential energy? What's the one for heat?

11. Jul 4, 2010

### yvan300

I think heat is 1/2 mv(squared), but don't know the one for potential energy.

12. Jul 4, 2010

### hikaru1221

Potential energy = mgh.
Heat = mC.delta(T).
Remember?

13. Jul 4, 2010

### yvan300

Oh yeah

14. Jul 4, 2010

### hikaru1221

Good. Plug the data in, and go straight to the answer. It should be around 4200 J/kgK.

15. Jul 4, 2010

### yvan300

When calculating, you are able to use any value for mass?

16. Jul 4, 2010

### hikaru1221

It's not necessary. Do the calculation, and you will see why.

17. Jul 4, 2010

### yvan300

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. Jul 4, 2010

Thanks man!