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Water in a river is at a temperature of T = 10 degrees Celsius. It then flows over a waterfall and down a height h = 50 m to the pool below.

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Question 1:
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What is the gravitational potential energy of a cube of
water 2 meters on a side, at the top of the falls?
What is the kinetic energy of the same cube just before
it hits the pool?

Answer: The volume of the cube is V = (2 m)^3 = 8 m^3. The density of water is rho = 1000 kg/m^3. Therefore, the mass of the cube is m = (density)*(volume) = (1000 kg/m^3)*(8 m^3) = 8,000 kg The gravitational potential energy of this cube is PE = mgh = (8000 kg)*(9.8 m/s^2)*(50 m) = 3.92 x 10^6 J As it falls, the PE is converted to KE. Just before it hits the pool, all the PE has been turned into KE: KE = 3.92 x 10^6 J

(If you don't know how to do problem 1, assume that the amount of kinetic energy is 1,000,000 Joules).

Assume that 25% of the water's kinetic energy is turned into heat, raising the temperature of the same 2-m cube of water.

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Question 2:
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What is the temperature of the water at the bottom of the falls?

Answer: If 25% of the kinetic energy is turned into heat energy, then the total amount of heat energy in the cube is Heat energy = 0.25*(3.92 x 10^6 J) = 980,000 J The heat energy goes into raising the temperature of this cube of water: heat energy = (specific heat)*(mass)*(change in temp) We can solve for the change in temperature: heat energy change in temp = ------------------------ (specific heat)*(mass) 980,000 J = ------------------------ (4186 J/kg*C)*(8000 kg) = 0.029 Celsius degrees The temperature at the bottom of the falls is final temp = (initial temp) + (change in temp) = 10 + 0.029 = 10.029 degrees C

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Question 3:
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Convert the final temperature of the water in the pool
from Celsius to Fahrenheit, and to Kelvin.

Answer: temp K = temp C + 273.15 = 10.029 + 273.15 = 283.30 K temp F = (temp C)*(9/5) + 32 = (10.029)*(1.8) + 32 = 50.05 degrees F

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This page maintained by Michael Richmond.
Last modified Dec 19, 1997.
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Copyright © Michael Richmond. This work is licensed under a Creative Commons License.