Question

What is power? How do you differentiate kilowatt from kilowatt hour? The Jog Falls in Karnataka state are nearly 20 m high. 2000 tonnes of water falls from it in a minute. Calculate the equivalent power if all this energy can be utilized? ($g=10m/{{s}^{2}}$ )

Answer 1

In the question we are asked to define power and differentiate between kilowatt and kilowatt hour. Then we are given the height of a waterfall and the amount of water falling from the falls per minute. To find the equivalent power of the falls we know the equation for power and from the given details we can find the work done by the falls. Thus by substituting the obtained values in the equation, we get the solution.

Formula used:
Power, $P=\dfrac{W}{t}$
Work, $W=P.E=mgh$

Complete step by step answer:
First let us see what power is and the difference between kilowatt and kilowatt hour.
As we know power is defined as the rate of doing work or we can say it is the work done in unit time, i.e.
$P=\dfrac{W}{t}$, where ‘P’ is power, ‘W’ is the work done, ‘t’ is the time taken.
Watt (W) is the SI unit of power. It is expressed as Joule/s (J/s).
1000 Watt (W) = 1 Kilowatt (KW)
Hence kilowatt is the unit of power expressed as KiloJoules/s (KJ/s).
Kilowatt hour is the unit of energy. It can be defined as the energy consumed by a power of 1 Kilowatt during a time of 1 hour. Hence we can express it as,
$\begin{aligned} & 1kWh=1kw\times 1hr \\\ & \Rightarrow 1kWh=1000W\times 3600\sec \\\ & \Rightarrow 1kWh=1000J/s\times 3600\sec \\\ & \Rightarrow 1kWh=36\times {{10}^{5}}J \\\ \end{aligned}$
The SI unit of energy is given as Joules (J).
Now in the question it is given the height of Jog falls in Karnataka.
h = 20 m
We are also given the mass of the water falling per minute,
m = 2000 tonnes
We know that $1\text{tonne}={{10}^{3}}kg$
Therefore the mass of water becomes,
$m=2000\times {{10}^{3}}kg$
$\Rightarrow m=2\times {{10}^{6}}kg$
Now let us calculate the work done by the falls. Here the work done is equivalent to the potential energy of the falls.
Therefore,
$W=mgh$
$\begin{aligned} & \Rightarrow W=\left( 2\times {{10}^{6}} \right)\left( 10 \right)\left( 20 \right) \\\ & \Rightarrow W=4\times {{10}^{8}}J \\\ \end{aligned}$
Then the power of the falls when all this energy is utilized will be,
$\begin{aligned} & P=\dfrac{W}{t} \\\ & \Rightarrow P=\dfrac{4\times {{10}^{8}}}{60} \\\ & \Rightarrow P=\dfrac{2}{3}\times {{10}^{7}}W \\\ \end{aligned}$
Hence the power of Jog falls is $\dfrac{2}{3}\times {{10}^{7}}W$ .

Note:
Potential energy is simply the energy by virtue of the position of an object relative to other objects. It is also defined as the energy held by a body due to its position relative to other bodies.
Potential energy mainly depends on the force acting on the two relative objects.
Hence the potential energy due to gravitational force is given as,
$P.E=mgh$
Since in the case of waterfalls, water falls from it due to the effect of gravity.
Hence we take the work done by the waterfalls as the potential energy.