Chapter 40, Problem 54A

The total U.S. consumption of electricity in 2001 was approximately $4\times {10}^{12}kilowatt\text{-}hours$, or approximately $4\times {10}^{19}J$. Show that this much energy is equivalent to converting approximately 160 kg of mass to energy (roughly speaking, the mass of a small motorcycle).

To determine

To Prove: The total consumption of the electricity in 2001 in US is equivalent to convert the $160\text{kg}$ mass to energy.

Answer to Problem 54A

It is proved that total consumption of the electricity in 2001 in US is equivalent to convert the $160\text{kg}$ mass to energy.

Explanation of Solution

Given info:

Total US consumption of electricity in 2001, $C=4\times {10}^{12}\text{kWh}=1.4\times {10}^{19}\text{J}$ .

Mass for the energy conversion, $m=160\text{kg}$

Formula Used:

The expression to calculate the energy converted from mass is,

$E=m{c}^2$

Where,

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

Calculation:

Substitute the given values in the above expression.

$\begin{array}{c}E=\left(160\text{kg}\right){\left(3\times {10}^8\text{m}/\text{s}\right)}^2\\ =1.44\times {10}^{19}\text{J}\\ =\left(1.44\times {10}^{19}\text{J}\right)\left(\frac{1\text{kWh}}{3.6\times {10}^6\text{J}}\right)\\ =4\times {10}^{12}\text{kWh}\end{array}$

The energy produced by the mass is same as the total consumption of electricity in 2001 in US.

Conclusion:

Thus, it is proved that total consumption of the electricity in 2001 in US is equivalent to convert the $160\text{kg}$ mass to energy.