Question about determing specific heat capacity using waterfall.

[yvan300]

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

 

[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?

 

[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 :)

 

[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?

 

[yvan300]

It turns into heat and some sound energy! :P

 

[hikaru1221]

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

 

[yvan300]

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

Yes.....??

 

[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?

 

[yvan300]

Nope

 

[hikaru1221]

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

 

[yvan300]

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

 

[hikaru1221]

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

 

[yvan300]

Oh yeah

 

[hikaru1221]

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

 

[yvan300]

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

 

[hikaru1221]

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

 

[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

 

[yvan300]

Thanks man!