Physics 2022 JAMB Past Questions - Question 27:  A waterfall is 420m 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 = 4.20 * 103Jkg-1K-1g=10-2]

Correct Answer

A

Explanation

To calculate the temperature difference of the water between the top and bottom of the waterfall, we can use the potential energy of the water and the concept of conservation of energy.

The potential energy of the water at the top of the waterfall is given by the formula:
\[ PE = mgh \]
where
PE = potential energy,
m = mass of the water,
g = acceleration due to gravity (approximately 9.81 m/s^2),
h = height of the waterfall.

At the top of the waterfall, all of the potential energy is converted to kinetic energy, and at the bottom of the waterfall, all of the kinetic energy is converted back to potential energy. Assuming no heat is lost, we can equate the potential energy at the top to the potential energy at the bottom.

So, we have:
\[ mgh = \frac{1}{2}mv^2 \]
where
v = velocity of the water at the bottom of the waterfall.

We can cancel out the mass "m" from both sides of the equation, and solve for v:
\[ gh = \frac{1}{2}v^2 \]
\[ v^2 = 2gh \]
\[ v = \sqrt{2gh} \]

Now, we can use the kinetic energy formula to find the temperature difference:
\[ KE = \frac{1}{2}mv^2 \]
\[ KE = \frac{1}{2}m(\sqrt{2gh})^2 \]
\[ KE = mgh \]

The kinetic energy at the bottom of the waterfall is equal to the potential energy at the top of the waterfall.

Assuming the water starts at rest at the top of the waterfall, all of the potential energy is converted to kinetic energy at the bottom. This means the temperature difference is 0, assuming no heat is lost.