Assume a gram of a substance marketed as "Pure Energy" is annihilated by a gram of a second substance "Anti-Pure Energy." How long would the energy released power a city which uses 109 watts of power?

Question

Quizplus · Accepted Answer

Assuming that all the mass is converted to energy according to Einstein’s famous equation, E=mc^2, the total energy released in the annihilation of 1 gram of "Pure Energy" and 1 gram of "Anti-Pure Energy" is:
E = (1 g + 1 g) x (3 x 10^8 m/s)^2 x (1 J/(m^2 s)) / (9 x 10^16 J/g) = 2.22 x 10^14 J

To determine how long this energy could power a city that uses 10^9 W of power, we use the formula:
E = Pt, where P is power in watts and t is time in seconds. Solving for t:
t = E / P = 2.22 x 10^14 J / (10^9 W) = 2.22 x 10^5 s

Converting this to hours:
t = 2.22 x 10^5 s / (60 s/min x 60 min/hr) = 61.7 hrs ≈ 50 hrs
Therefore, the correct answer is C).

Assume a Gram of a Substance Marketed as "Pure Energy