James Joule (after whom the unit of energy is named) claimed that the water at the bottom of Niagara Falls should be warmer than the water at the top, 51 mm above the bottom. He reasoned that the falling water would transform its gravitational potential energy at the top into thermal energy at the bottom, where turbulence brings the water almost to a halt ...

The complete question is;

James Joule (after whom the unit of energy is named) claimed that the water at the bottom of Niagara Falls should be warmer than the water at the top, 51 m above the bottom. He reasoned that the falling water would transform its gravitational potential energy at the top into thermal energy at the bottom, where turbulence brings the water almost to a halt. If this transformation is the only process occurring, how much warmer will the water at the bottom be?

Answer:

Water becomes warmer by a temperature of ΔT = 0.119 K

Explanation:

If we assume that gravitational kinetic energy will be converyrf into thermal enrgy, we will have;

Q = U

So, m•c_w•ΔT = mgh

Where;

c_w is specific heat capacity of water with a value of 4184 J/Kg. K

ΔT is change in temperature indicating how warmer the water will be. Thus making ΔT the subject, we have;

ΔT = gh/c_w

So, ΔT = 9.8 x 51/4184 = 0.119 K