Question

Calculate the number of joules in 1KWh.
A.$6\times {{10}^{-19}}J$
B.$3.6\times {{10}^{6}}J$
C.$60J$
D.$59J$

Answer 1

Hint: We know that Joules and kilowatt-hour are units of energy but, watt is the SI unit of power. So, finding the relationship between power and energy and thereby finding the interconnection of watt with joules will help us get the solution for this question.

Complete step by step answer:
KWh, which is an abbreviation for kilo-watt hour and joules, both are units of energy. ‘ Joule’ being its SI unit.
We should note here that watt is a unit of power and is entirely a different concept from energy.
 Energy is simply the measure of how much work you have to do to get something done and what is power? It is a rate at which energy is used up.
Let us consider the case of you having a cup of coffee in the morning. The amount of energy required for you to lift the coffee mug to your mouth remains constant (say,$1J$ ) irrespective of how slowly/ fastly you do it. Whereas, power is the rate of lifting your coffee mug, that is, if you lift your coffee mug in 1 second, you exert a power of $1J/s$ which corresponds to $1watt$ .
Now, keeping the above example in mind let’s find the number of joules in 1 KWh.
1 KW or 1 kilowatt corresponds to 1000watts, therefore, 1KWh is 1 kilowatt of power for 1 hour which is equivalent to energy of 1000 joules used up for 3600seconds 3.6 million joules.
Mathematically,
$\begin{align}
  & 1watt=1J/s \\
 & 1watt\times 1\sec =1J \\
 & 1000watt\times 1\sec =1000J \\
 & 1000watt\times \left( 60\times 60 \right)\sec =1000\times 3600J \\
 & 1KWh=3600000J \\
 & 1KWh=3.6\times {{10}^{6}}J \\
\end{align}$
So the answer to the question is option B, $3.6\times {{10}^{6}}J$.

Note:
Though MPG stands for miles per gallon, KWh here corresponds to kilowatt times per hour. Also, when we use Joules as a unit of measurement, numbers get so unwieldy, hence we use KWh as a unit while measuring huge loads of energy.