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The height of a waterfall is 50 m. If $g = 9.8m{s^{ - 2}}$, the difference between the temperature at the top and the bottom of the waterfall is (A) ${1.17^{\rm O}}C$(B) ${2.17^{\rm O}}C$(C) ${0.117^{\rm O}}C$(D) ${1.43^{\rm O}}C$

Last updated date: 10th Sep 2024
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Hint: The potential energy of the water is converted into heat energy this relation between potential energy and heat energy can be as $mgh = ms\Delta t$. We will put all the values and find the change in the temperature of the water.

It is given in the question that the height of the waterfall is 50 m. Then we have to find the difference between the temperature at the top and the bottom of the waterfall.
Here the potential energy of the water is converted into heat energy this relation between potential energy and heat energy can be as $mgh = ms\Delta t$. Here m is the mass of the water, g is the gravitational force which is equal to $9.8m{s^{ - 2}}$, h is the height of the waterfall s is the specific heat and $\Delta t$ is the temperature change.
We know that $1J = 4.2C$, so we get $1000J = 4200C$.
So, we get s = 4200 C.
The relation between the potential energy and heat is $mgh = ms\Delta t$.
On cancelling the similar terms from both sides, we get-
$gh = s\Delta t$
$\Delta t = \dfrac{{gh}}{s}$
On putting the values of g, h, and ‘s’ in $\Delta t$ we get-
$\Delta t = \dfrac{{9.8 \times 50}}{{4200}}$
$\Delta t = \dfrac{{490}}{{4200}}$
$\Delta t = {0.117^{\rm O}}C$
Thus, the difference between the temperature at the top and the bottom of the waterfall is $\Delta t = {0.117^{\rm O}}C$.

Therefore, option c is correct.