Question

Kilowatt-hour is the unit of energy. $1kW-h=1kW\times 1h$. Determine how many joules equals to $1kW-h$.

Answer 1

Step 1: Given data
$1kW-h=1kW\times 1h$
We also know that:
$$\begin{gathered} 1W=1\frac{J}{s} \\ 1h=(60\times 60)s=3600s \end{gathered}$$
Step 2: Convert $1kW-h$ into Joules.
$1kW-h$ is the amount of power consumed by an electric appliance rated $1kW(={10}^{3}W)$ in $1$ hour.
Put the value of kilowatt in joule/second and the value of hour in seconds.
$$\begin{gathered} 1kW-h=1kW\times 1h \\ =1\times {10}^{3}W\times 1h \\ ={10}^3\frac{J}{s}\times 3600s \\ ={10}^3\times 3600J \\ =3.6\times {10}^6\hspace{0.17em}J \end{gathered}$$

Thus, $1kW-h$ is equal to $3.6\times {10}^6\hspace{0.17em}J$.