Water going down a waterfall, where is it warmer?

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In summary, using the conservation of energy, we can determine that the water at the bottom of the 120m waterfall will be warmer than the water at the top. To calculate the temperature difference, we can use the formula E = (m)(c)(ΔT), where E is the heat energy, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. By equating the potential energy at the top of the waterfall to the thermal energy at the bottom, we can solve for ΔT and determine the temperature difference between the top and bottom of the waterfall.
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aeromat
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Homework Statement


Consider a waterfall that is 120m high. How much warmer is the water at the bottom of the waterfall than at the top? The specific heat capacity of water is 4186J/ kg*°C.


Homework Equations


Conservation of Energy


The Attempt at a Solution



Eg [top] = Ek [just before the water hits the ground]
(m)(g)(h) = 1/2(m)(v)^2


I don't know how to compare the warmness of the top to the bottom, or how to get it calculation-wise. Does this have to do with:

E = (m)(c)(T)?
Where "E" is the heat energy?
 
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  • #2
It's a straightforward conservation of energy.

(1) Potential energy before the fall > (2) Kinetic energy just before it hits > (3) Thermal energy in the water.

You can go straight from (1) to (3)
 
  • #3
But would you mind giving me a hint as to how I would go about with the calculations?
 

FAQ: Water going down a waterfall, where is it warmer?

Why does water get warmer as it goes down a waterfall?

As water moves down a waterfall, it gains kinetic energy due to the force of gravity. This energy is converted to heat through friction as the water rubs against the rocks and other surfaces. This increase in heat causes the water to feel warmer as it reaches the bottom of the waterfall.

Is the water at the top of a waterfall colder than the water at the bottom?

Yes, the water at the top of a waterfall is typically colder than the water at the bottom. This is because the water at the top is exposed to cooler air and has not yet gained the kinetic energy and heat from falling down the waterfall.

How much warmer does the water get as it goes down a waterfall?

The exact amount of temperature increase varies depending on the height and speed of the waterfall, as well as the surrounding environmental conditions. However, on average, water can increase in temperature by a few degrees as it falls down a waterfall.

Does the temperature of the water change throughout the waterfall?

Yes, the temperature of the water can change throughout the waterfall. As the water gains heat from friction and kinetic energy, it may become warmer as it falls. However, this increase in temperature may not be uniform and can vary depending on the specific conditions of the waterfall.

Can water going down a waterfall ever be colder than it was at the top?

It is possible for water to become colder as it goes down a waterfall, but this is less common. If the surrounding air is significantly colder than the water at the top of the waterfall, the water may lose more heat due to the increased surface area exposed to the air as it falls. However, this is not typically the case as water tends to gain heat as it falls down a waterfall.

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