The water at the bottom of the Niagara Falls, which are 50 m high, should be warmer than that at the top. Explain why it is and calculate the temperature rise.

The heat capacity of 1 mol water (which weighs 0.018 kg) is 80 J/K.

The acceleration due to gravity is 9.8 m/s².

Solution

Height of Niagara Falls, h = 50m
Let m be the mass of waterfall.
Decrease in potential energy of waterfall is,
U = mgh
U =

0.018 space cross times space 9.8 space cross times 50 space equals space 8.82 space straight J

This potential energy is converted into heat.
Let θ be the rise in temperature.
Therefore,

m g h space equals space m s theta space rightwards double arrow space space straight theta equals fraction numerator m g h over denominator ms end fraction space space space space space space space space space equals open parentheses fraction numerator 8.82 over denominator 0.018 cross times 80 end fraction close parentheses space cross times 0.018 space space space space space space space space space space equals 0.11025 space to the power of degree straight C

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