A Waterfall Is 100m High And The Difference In Temperature Between The Water At The Top And That At The Bottom Is 0.24 K. Obtain A Value For The Specific Heat Capacity Of Water In J/kg K Explaining The Steps In Calculations; Make Any Assumptions (g=10m/s)?

Using the equation:

Gravitational potential energy = mass x gravitational force x height (E = mgh),

And assuming that this is a conservative system where there is no energy loss (to the surroundings, air resistance, etc), we can therefore equate:

Loss of gravitational potential energy = gain in molecular kinetic energy of water

(Temperature, is fundamentally the measurement of kinetic energy of the molecules in a body)

hence,
mgh = specific heat capacity x change in temperature x mass
gh = specific heat capacity x change in temperature
10 x 100 = specific heat capacity x 0.24
1000/0.24 = specific heat capacity
specific heat capacity = 4170 (to 3 significant figures)