Assume that a certain city consumes electrical energy at an average rate of 2.0 × 10⁹ W.What would be the mass change in producing enough energy to keep this city running for 21 weeks? (c = 3.00 × 10⁸ m/s) A)0.28 kg B)0.32 kg C)0.39 kg D)0.48 kg

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To find the mass change, we can use the equation derived from Einstein's theory of relativity, $E = mc^2$, where $E$ is the energy, $m$ is the mass, and $c$ is the speed of light. First, we need to calculate the total energy consumed by the city over 21 weeks.Given:- Average power consumption = $2.0 \times 10^{19}$ W (Watts are Joules per second)- Time = 21 weeks = $21 \times 7 \times 24 \times 60 \times 60$ seconds (converting weeks to seconds)- Speed of light, $c = 3.00 \times 10^8$ m/sThe total energy consumed, $E$, can be calculated as power multiplied by time:$$E = P \times t = 2.0 \times 10^{19} \times (21 \times 7 \times 24 \times 60 \times 60)$$To find the mass change, $m$, we rearrange the equation $E = mc^2$ to $m = \frac{E}{c^2}$.Substituting the values:$$m = \frac{E}{(3.00 \times 10^8)^2}$$After calculating $E$ with the given values and then calculating $m$, we find that the mass change is approximately 0.28 kg, which corresponds to option A. This calculation demonstrates the principle of mass-energy equivalence, showing how a relatively small mass change can produce a significant amount of energy.

Assume That a Certain City Consumes Electrical Energy at an Average