## Question

A waterfall is 420 m high, calculate the difference in temperature of the water between the top and bottom of the waterfall assuming no heat is lost. [Specific heat capacity of water (C_{w}) is 4.20 x 10^{3} JKg^{-1}K^{-1}, gravitational force (g) = 10 m/s^{-2}].

## Answer

The final answer to the above question which is the difference in temperature of the waterfall is 1.0^{0}C.

### Explanation

**Data:** We need to extracting the relevant information from the question.

We will now have the following data given to us:

- Height (h) = 420m

2. Specific heat capacity of water (C_{w}) = 4.20 x 10^{3} JKg^{-1}K^{-1}

3. Gravitational force (g) = 10 m/s^{2}

**Unknown:** We will now check the question and look for what we need to find.

Temperature difference (Δθ) = ?

**Formula:** The formula is the equation that will help us to solve the problem.

The potential energy of the waterfall at 420m above the ground level (mgh) will be converted into internal energy (mcΔθ) in the form of heat as the water hits the ground. Therefore, the formula we are using is mcΔθ

**Solution**

From mgh = mcΔθ

By making Δθ subject of the formula, we will now obtain

Δθ = gh/C_{w} = (10 x 420) / (4.20 x 10^{3}) = 1.0^{0}C.

Therefore, when a waterfall is 420 m high, the difference in temperature of the water between the top and bottom of the waterfall is 1.0^{0}C.