Question

The height of the waterfall has been found to be as $210m$ assuming that the surface on which the water is falling will be perfectly insulated and all the kinetic energy of water will be dissipated as heat. What will be the rise in temperature of the water?
$g=10m{{s}^{-2}}$, the specific heat of water will be $C=1000calk{{g}^{-1}}{{C}^{-1}}$ and $1kcal=4200J$
$\begin{aligned} & A.0.1{}^\circ C \\\ & B.0.5{}^\circ C \\\ & C.1{}^\circ C \\\ & D.0.25{}^\circ C \\\ \end{aligned}$

Answer 1

Here the complete potential energy of the waterfall will be converted into the heat energy. The potential energy will be equivalent to the product of the mass, acceleration due to gravity and the height of the body. The heat energy will be equivalent to the product of the mass, specific heat of water and the change in temperature. This will help you in answering this question.

Complete step by step answer:
here the complete potential energy of the waterfall will be converted into the heat energy.
The potential energy will be equivalent to the product of the mass, acceleration due to gravity and the height of the body. The heat energy will be equivalent to the product of the mass, specific heat of water and the change in temperature. This can be written as an equation given as,
$mgH=mC\Delta T$
It has been given in the question that the mass of the water will be given as,
$m=1kg$
Acceleration due to gravity can be written as,
$g=10m{{s}^{-2}}$
Height of the waterfall has been given as,
$H=210m$
Specific heat of water has been written as,
$C=1000calk{{g}^{-1}}{{C}^{-1}}=4200J$
Substituting the values in the equation can be written as,
$10\times 210=4200\times \Delta T$
Rearranging this equation can be written as,
$\Delta T=0.5{}^\circ C$

So, the correct answer is “Option B”.

Note: The first law is otherwise called the law of Conservation of Energy which says that the energy will not be created or destroyed in an isolated system. The second law of thermodynamics also says that the entropy of any isolated system will be always enhancing.