Question

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?

Short answer

a) The mass corresponding to consumed energy in that year is 88 kg.

b) There is no difference if the energy has generated in oil burning and nuclear or hydroelectric power plants.

Step-by-step solution

Given data

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

Definition of theory of special relativity

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$\mathit{E}\mathbf{=}\mathit{m}{\mathit{c}}^{\mathbf{2}}$.

(a) Determine the mass consumed in that year

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.

(b) Determine any difference in answer if this energy is generated in oil-burning, nuclear, or hydroelectric plants

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.