what will be the temperature difference between the water at the top and the bottom of the falls?

Question

A waterfalls is 90m high. Assume that all of the potential energy possessed by the water at the top is completely converted to heat energy. What will be the temperature difference between the water at the top and at the bottom of the falls?

Answer 1

The potential energy at the top is mgh.  You do not know m, but it will not matter, as you will see in a few lines below.  The heat energy of the water at the bottom is mcΔT, where c is the specific heat of water, which you can look up in your physics book.  You want it in units of J/(kg°C).  Set potential and heat energies equal and solve for the temperature rise ΔT.

 

mgh = mcΔT

 

Note the unknown mass cancels out.

 

gh = cΔT

 

ΔT = gh/c

 

Plug in the numbers.