Question

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) \[{1.43^{\rm O}}C\]

Answer 1

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.

Complete step by step answer:
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.

Additional information:
The specific heat is the amount of heat required to raise the temperature of the water by one-degree Celsius. Specific heat capacity can be used to identify an unknown substance. Because specific heat capacity is the physical property of a substance.

Note:
One can make a mistake that they may take the value of s as 4.2 but we have to take the value of s as 4200 because we are finding the change in temperature of the water and the unit of mass i.e., water is taken in kg.