Final answer:
To determine how much mass is destroyed to produce a continuous 1000 MW of electricity at 35.0% efficiency for one year, one must use Einstein's equation, E=mc^2, and take into account the total energy output as well as the efficiency of the power plant.
Step-by-step explanation:
The question is asking how much mass would need to be converted into energy to produce a continuous 1000 MW of electric power for one year at an efficiency of 35.0%. Using Einstein's equation, E=mc^2, we can find the total energy in joules that corresponds to the electrical energy produced. Taking into account the efficiency of the conversion, we can then find out how much mass would be equivalent to that amount of energy.
The total energy E that a power plant producing 1000 MW for one year (which is 3.16 × 107 seconds) at 35.0% efficiency would produce can be calculated by:
E = Power × Time × Efficiency = 1000 MW × 3.16 × 107 s × 0.35
To find the mass m, we rearrange the equation:
m = E/c2
where c is the speed of light in a vacuum (approximately 3 × 108 m/s). Doing the calculations, we can determine the amount of mass that would be destroyed to produce the specified amount of electricity.