Question

Verify the energy unit equivalence that \(1\;kWh= 3.60 \times {10^6}\;J\).

Short answer

The required solution has been proved.\(1kWh = 3.60 \times {10^6}J\) .

Step-by-step solution

Definition of Power

The power of a process is the amount of some type of energy converted into a different type divided by the time interval\(\Delta t\)in which the process occurred:

\(P = \frac{{\Delta E}}{{\Delta t}}......(1)\)

The SI unit of power is the watt\((W)\).

\(1\) Watt is\(1\)joule/second.

Verifying the unit

The energy is expressed in terms of power and time from Equation\((1)\):

\(E = P\Delta t\)

Where the energy\(E\)is measured in joules, the power\(P\)in watts, and the time\(\Delta t\)in seconds:

\((J) = (W.s)......(2)\)

To convert \(kWh\) into\(W.s\), multiply by the following conversion factors:

\(\begin{aligned} 1kWh &= (1kW)\left( {\frac{{1000W}}{{1kW}}} \right)(1h)\left( {\frac{{60\min }}{{1h}}} \right)\left( {\frac{{60s}}{{1\min }}} \right) \\ &= 3.60 \times {10^6}W.s \\ \end{aligned} \)

Use Equation \((2)\) to substitute for \(W.s\) :

\(1\;kWh= 3.60 \times {10^6}\;J\)

Hence, it is verified that \(1\;kWh= 3.60 \times {10^6}\;J\).