Question

Define $1KWh$. Give the relation between $1KWh$ and Joule.

Answer 1

Hint: KWh or Kilowatt-hour is a unit of energy used for commercial purposes. First, define 1 KWh. Then to convert 1 KWh into the SI unit joule, use the relationship between power, energy and time.

Formula used:
$P=\dfrac{E}{t}$

Complete step by step answer:
The full form of KWh is Kilowatt-hour and it is a unit of energy.
The definition of 1 KWh is as follows:
1 KWh is the amount of energy consumed by an electric appliance working with a power of 1Kilowatt i.e. $1000Watts$, in a time interval of 1 hour. So when an appliance with power of 1000W operates for 1 hour, we say that it has consumed 1 KWh amount of energy.

Let us now convert 1 KWh in another SI unit of energy, i.e. Joules.
We know that watt is a unit of power and hour is a unit of time.
Also, power (P) is the rate of energy (E) consumed per unit time (t).
i.e. $P=\dfrac{E}{t}$.
$\Rightarrow E=Pt$ ….. (i).

This means that if the appliance operates with a power P for a time interval t, then the energy that it consumes is equal to $E=Pt$.
In this case, $P=1000watts$
And
$t=1hour\\
\Rightarrow t =60\times 60s\\
\Rightarrow t =3600s$.
Substitute the value of P and t in equation (i).
$ E=(1000)(3600)\\
\therefore E =3.6\times {{10}^{6}}Joules$.
And here, $E=1KWh$. Therefore, this implies that $1KWh=3.6\times {{10}^{6}}Joules$.

Hence, we found a relation between 1KWh and joule.

Note: Some students may get confused between Kilowatt-hour and watts. Since the unit Kilowatt-hour has watt in it, they may think that it’s a unit of power. However, we just now stated that it’s a unit of energy. For commercial purposes, 1 kilowatt-hour is considered 1 unit.