A continuous stream of water falls through a vertical distance of 100 m - AQA - A-Level Physics - Question 8 - 2017 - Paper 2

To find the temperature difference ( \Delta T ), we can use the equation that relates gravitational potential energy to thermal energy gained:

$mgh = mc\,\Delta T$

Where:

• $m$ is the mass of water (cancels out)
• $g$ is the gravitational acceleration ($9.81 \, m/s^2$)
• $h$ is the height of the waterfall ($100 \, m$)
• $c$ is the specific heat capacity of water ($4200 \, J kg^{-1} K^{-1}$)
• $\Delta T$ is the temperature difference

Rearranging the equation gives:

$\Delta T = \frac{gh}{c}$

Substituting the values:

$\Delta T = \frac{(9.81 \, m/s^2)(100 \, m)}{4200 \, J kg^{-1} K^{-1}}$

Calculating gives:

$\Delta T = \frac{981}{4200} \approx 0.233 K$

Thus, the temperature difference is approximately 0.23 K.