Question

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? The specific heat of water is 4190 J/(kg?K).

Answer 1

By conservation of energy...

PE = Q

mgh = mc(delta T) ... mass cancels

(9.8)(51) = (4190)(delta T)

delta T = .119^o C warmer