Question

A typical household uses 500 kWh of energy in I month. How much mass is convened to produce this energy?

Short answer

The mass to produce energy for household consumption is $2\times {10}^{-8}\text{kg}$.

Step-by-step solution

Identification of given data

The energy consumption of household is $E=500\text{kWh}$

Energy Consumption

The energy used by all the electrical appliances of house hold in a month for working hour is electrical consumption. This energy is equated to rest energy of mass used.

Determination of mass to produce energy for household consumption

The mass to produce energy for household consumption is given as:

$$\begin{gathered} E=\Delta m{c}^2 \\ \Delta m=\frac{E}{c^2} \end{gathered}$$

Here, c is the speed of light and its value is $3\times {10}^8\text{m}/\text{s}$,

Substitute all the values in the equation.

$$\begin{gathered} \Delta m=\frac{\left(500\text{kWh}\right)\left(\frac{{10}^3\text{J}/\text{s}}{1\text{kW}}\right)\left(\frac{3600\text{s}}{1\text{h}}\right)}{{\left(3\times {10}^8\text{m}/\text{s}\right)}^2} \\ \Delta m=2\times {10}^{-8}\text{kg} \end{gathered}$$

Therefore, the mass to produce energy for household consumption is $2\times {10}^{-8}\text{kg}$.