In one year the United States consumption of electrical energy was about $\mathbf{2}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{12}}\mathbf{}\mathit{k}\mathit{W}\mathbf{.}\mathit{h}\mathbf{.}$

(a) How much mass is equivalent to the consumed energy in that year?

(b) Does it make any difference to your answer if this energy is generated in oil-burning, nuclear, or hydroelectric plants?

In a year the United States consumption of electrical energy is $2.2\times {10}^{12}k\mathrm{Wh}$

Special relativity is an explanation of how speed affects mass, time and space. The theory includes a way for the speed of light to define the relationship between energy and matter-small amounts of mass (m) can be interchangeable with enormous amounts of energy (E), as defined by the classic equation$\mathit{E}\mathbf{=}\mathit{m}{\mathit{c}}^{\mathbf{2}}$.

The Einstein’s equation is as follows:

$E=m{c}^2$...(i) Here, the mass is m, and the speed of light is c.

Rearrange expression (i)

$m=\frac{E}{c^2}$...(ii)

Substitute $2.2\times {10}^{12}kWh$for E and $3\times {10}^{8}m{s}^{-1}$for c in expression (ii),

role="math" localid="1663054865235" $$\begin{gathered} m=\left(2.2\times {10}^{12}kWh\right)\frac{\left(3.6\times {10}^{6}J\right)}{1kWh} \\ m=88kg \end{gathered}$$

Hence, the mass corresponding to consumed energy in that year is 88 kg.

The energy consumed in the process of all burning and nuclear or hydroelectric plants is $2.2\times {10}^{12}kWh$.

Hence, there is no difference if the energy has generated in oil burning and nuclear or hydroelectric power plants.