Question

(a) What is a commercial unit of energy ? It is equal to how many joules?
(b) An electric oven is rated $2500\,W$. How much energy does it use in 4 hours?

Answer 1

Hint: The SI unit joule is insufficient for expressing very large amounts of energy. As a result, we use a larger unit known as the kilowatt hour (kWh) to express electricity. The kWh is the commercial unit of electricity (kilowatt hour). It is used to calculate how much energy is used in a home.

Complete step by step answer:
(a) The SI unit of energy becomes small when large amounts of energy are to be expressed. As a result, the commercial unit is employed. The commercial unit of energy is the kilowatt-hour. The amount of energy consumed by a system in one working hour at a constant rate of one kilowatt is known as one kilowatt-hour. The Joule is the SI unit of energy.
\[1{\text{ }}kWh{\text{ }} = {\text{ }}1kW \times 1h{\text{ }} \\
\Rightarrow 1{\text{ }}kWh{\text{ }}= {\text{ }}1000W \times 1h{\text{ }} \\
\Rightarrow 1{\text{ }}kWh{\text{ }}= {\text{ }}1000\left( {J/s} \right)\times 3600{\text{ }}s{\text{ }} \\
\therefore 1{\text{ }}kWh{\text{ }}= {\text{ }}3.6\times {10^6}\;J\]

Therefore, \[3.6{\text{ }}{10^6}\] Joules equals one unit of electrical energy.

(b) The power, the energy and the time of the oven is related as,
$Power = \dfrac{{Energy}}{{time\,taken}}$
$E = P \times t$
On substituting the values we get,
$E = 25000\,W \times \,4hr \\
\Rightarrow E = 100,000\,Whr \\
\Rightarrow E = \dfrac{{100,000}}{{1000}}\,KWhr \\
\therefore E = 100\,KWhr \\ $
Therefore, in 4 hours $100\,KW$ energy will be used.

Note: Although this unit is not a regular unit in any formal measurement scheme, it is still widely used. Despite the fact that the prices for the domestic and commercial sectors are different, the same unit has been used in both sectors. The measurement unit would be in kilowatt-hours, even though the large sectors consume less electricity.