Question

Explain, in terms of the definition of power, why energy consumption is sometimes listed in kilowatt-hours rather than joules. What is the relationship between these two energy units?

Short answer

The energy consumption is listed in kilowatt-hours rather than joules because the unit Joule is too small to use for everyday electrical energy consumption.

Step-by-step solution

Definition of Concepts

Power consumption: Power consumption is defined as the rate at which energy is being consumed.

Mathematically power is given as,

\(P = \frac{E}{t}\)

Here,\(P\)stands for power,\(E\)stands for energy used, and\(t\)stands for time.

The expression for energy consumed is obtained by rearranging equation (1.1),

\(E = Pt\)

In larger unit power is measured in terms of kilowatt\(\left( {{\rm{kW}}} \right)\)and time is measure in hours\(\left( {\rm{h}} \right)\).

Therefore, the larger unit of power is,

\(\begin{aligned}{}E &= \left( {{\rm{kW}}} \right) \times \left( {\rm{h}} \right)\\ &= {\rm{kWh}}\end{aligned}\)

Explain the relationship between kilowatt-hour and joule

One kilowatt-hour of energy equals,

\(\begin{aligned}{}E& = 1{\rm{ kWh}}\\ &= 1000{\rm{ W}} \times {\rm{1 h}}\\ &= \left( {1000{\rm{ J}} \cdot {{\rm{s}}^{ - 1}}} \right) \times \left( {1{\rm{ h}}} \right) \times \left( {\frac{{60{\rm{ min}}}}{{1{\rm{ h}}}}} \right) \times \left( {\frac{{60{\rm{ sec}}}}{{1{\rm{ min}}}}} \right)\\ &= 3.6 \times {10^6}{\rm{ J}}\end{aligned}\)

Therefore, one kilowatt-hour of energy consumption equals \(3.6 \times {10^6}{\rm{ J}}\).