Question

A waterfall is 84m high. If the half of the potential energy of the falling water gets converted into heat, the rise in temperature of water will be:
A.0.098°C
B. 0.98°C
C. 0.1°C
D. 0.0098°C

Answer 1

When an object falls under the gravitational field, the potential energy is given by product of mass and acceleration due to gravity and height. By the use of law of conservation of energy, when the water falls down and touches the surface, then this potential energy is converted to heat energy.
Formula used:
Potential energy and heat energy is given by:
(i)$P.E.=\text{ }M\text{ }g\text{ }h.$
(ii) $Q=\text{ }M\text{ }c\text{ }T$

Complete answer:
The energy associated with the resting position of the atoms is called potential energy.
Potential energy is given by formula:
$P.E.=\text{ }M\text{ }g\text{ }h.$
According to the law of conservation of energy, the potential energy is converted into kinetic energy and then the kinetic energy gets converted into thermal energy.
As we know, Conduction of heat occurs when two surfaces interact, in this case water touches to the surface, there is transfer of heat from lower temperature to higher temperature.
Now, the heat energy is given by:
$Q=\text{ }M\text{ }c\text{ }T$
Where Q is heat transfer in the system, c is specific heat of the substance, M is mass and T is temperature.
Now according to the condition given in question, half of the P.E gets converted into thermal energy, i.e. heat energy

& \begin{array}{*{35}{l}} 1/2\text{ }Mgh\text{ }=\text{ }McT \\\ T=\text{ }gh\text{ }/2c \\\ T=(10\times 84m)/(2\times 4179.6\text{ }J)\text{ }\left( \text{ }c\text{ }for\text{ }water=4179.6\text{ }J \right) \\\ \end{array} \\\ & T={{0.1}^{0}}C \\\ \end{aligned}$$ Hence, the rise in temperature of water comes out to be T= 0.1°C. **So, the option C is the correct option.** **Note:** The potential energy under the effect of gravitational field, the kinetic energy gets converted into heat.by using the law of conservation of energy the potential energy is converted into thermal energy i.e. Heat energy Q, which is calculated by using specific heat capacity of the substance(c) and change in temperature.