Kerepakupai Vena in Venezuela, more commonly known as Angel Falls, is the world\

Question

Kerepakupai Vena in Venezuela, more commonly known as Angel Falls, is the world's highest waterfall with a height of 979 m and 47 different plunges. The longest plunge (for the water) is 807 m. At the bottom of the fall, the kinetic energy of the water is converted into thermal energy. This results in a temperature increase of the water. If the water has a temperature of 14.7°C when it gets to the bottom of the plunge, what was the temperature at the top of the plunge? The specific heat of water is 1.00 kcal/(kg · °C).

Explanation / Answer

Longest plunge for water is 807m. So the water falls through a height h = 807m and its temperature raises by when it reaches the bottom

At the height h the potential energy of water is = mgh, there is no Kinetic enery at height h. When the water falls through a height h, all this potential energy is converted to kintetic energy at the bottom where water has no potential energy. So for a mass m of water, applying consrvation of energy we get;

mgh = Kinetic energy at the botttm

So Kinetic energy at the botttm is KE = mgh

Now this KE is lost and converted to heat. Let the thermal energy be Q, then

Q = KE = mgh

if it raises the temperature of water by , then we have Q = ms, where s is specific heat of water

So mgh = ms

or = gh/s = (9.8m/s2)(807m)/(4186J/kg-K)

or = 1.889K

so the temperature is raised by = 1.889K or 1.889 0C.

So the temperature at the top of the plunge was T = 14.7°C - 1.889 0C = 12.810C.

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