Calculating the conversion of potential energy to thermal

[jongood]

Homework Statement

Horseshoe Falls, one of the Niagara Falls, has a 53 m drop. Consider one kg of water that
falls over the falls. If, upon hitting the bottom of the falls, all of the water’s potential energy
is converted to thermal energy and this heats the fallen water, calculate the increase in the
water’s temperature.

Homework Equations

Ek = ½ m v2
PE = m x g x h

Thermal: change in E_th = m Cp change in T.

The Attempt at a Solution

So I should be calculate the potential energy of 1 kg of water falling 53 m. Then that that number and convert it to thermal energy. Use the thermal energy number to calculate the change in water temperature?

I calculated the potential energy to be 519.4 J.
Convert Joules to BTU=
519.4 joules = 0.492296212 btu

Now to calculate the increase in the water's temperature, I am not sure if that's the whole fall? I don't think that is possible since the amount of water is always changing. Now if they are talking about the increase in temp of that 1 kg of water... then i have no idea...

Am i on the right track? Thanks

 

[CompuChip]

Yep, sounds like we assume that the kinetic energy of that particular kg of water is used to heat just that bit.

You quoted a formula:

Thermal: change in Eth = m Cp change in T.

What does Cp stand for?

 

[jongood]

Cp is for constant pressure. I copy and pasted it from a PDF lecture so it got jumbled up.

So thermal is heat already right?

As for the water, should i just assume it is 25 c since that is the standard. How would I convert Btu to C?

 

[CompuChip]

Actually Cp is the heat capacity of water - it's a number that says how much Joules you need to heat 1 kg of water by 1 degree Kelvin (or Celcius) - look it up!.

You don't need to assume any temperature, the formula says "change in T", right? Well, that's exactly what you're asked for.

 

[jongood]

Oh yeah. sorry I knew that. It was in my notes but I read it too quickly.

so I am kind of lost here. I know that 1 Btu is what will increase 0.454 kg of water 1 degrees.

Since I have approx .5 Btu of energy but 1 kg of water...

I don't know what formula to use...

 

[CompuChip]

If 1 Btu will increase 0.454 kg of water by 1 degree, then how many Btu do you need to increase 1 kg of water by 1 degree?

 

[jongood]

2.20264317 Btu will be needed. but since I only have .454 Btu, then the water will only increase by approx. .25 degrees C?

 

[CompuChip]

I got a slightly different number, but yes - that is the idea.

If you want to use the internationally accepted SI units rather than the weird British units, you could look up Cp in a standard resource and use the value in Joules :D