Question

A certain household has consumed 250 units of energy during a month. How much energy is this in joules?

Answer 1

We know that the kWh is a commonly used billing unit for electric utilities. The cost of these utilities is calculated by multiplying the power consumption in kilowatts by the operating time in hours and is essentially priced per kilowatt.
First find out how many $Js^{-1}$ is one watt. We know that a watt is equivalent to one joule per second. Then determine the number of seconds in an hour. Multiplying these two quantities will result in a measure in joules, equivalent to the number of kilowatts consumed in an hour. This should give you the necessary conversion factor to determine the given energy in joules.

Formula used:
Conversion: $1\;kWh = 3.6 \times 10^6 J$

Complete step-by-step answer:
The commercial unit of energy is kilowatt hour (kWh).
We know that $1\;kilowatt(kW) = 10^3\;watt(W) = 10^3\;Js^{-1}$
And $1\;hr = 60 \times 60 = 3600\;s$
Therefore, $1\;kWh = 1\;kW \times 1hr$
$\Rightarrow 1\;kWh = 10^3 \times 3600 .\; Js^{-1}s$
Therefore $1\;kWh = 3.6 \times 10^6 J$
We are given that a certain household consumes 250 units of energy during a month.
This means that their energy consumption is $250\;kWh$
We derived that $1\;kWh = 3.6 \times 10^6 J$
$\Rightarrow 250\;kWh = 250 \times 3.6 \times 10^6\;J = 900 \times 10^6\;J = 9 \times 10^8\;J$
Therefore, this household consumes $9 \times 10^8\;J$ or $900\;MJ$ of energy in a month.

Note: Do not get confused between energy and power and their units.
Energy is just the work performed and is measured in joules, or watt seconds, whereas power is the rate of delivery of this energy and is measured in watts, or joules per second. Energy is a whole quantity or component, whereas power is an instantaneous quantity. Energy is an interchangeable quantity whereas power cannot be transformed from one form to another.