Final answer:
To calculate the total heat energy produced by a coal-burning power plant with 35% efficiency, multiply the power generation rate by the number of seconds in a year and divide by the efficiency. The correct calculation yields 2.25 × 1016 J, which is higher than the options given in the question.
Step-by-step explanation:
The question asks for the total heat energy produced by a coal-burning power plant in one year, given its power generation and efficiency. To find the answer, we need to use the formula for power, which is the rate of energy conversion, and account for the efficiency of the power plant and the total time in one year.
Let's start by determining the total energy output in one year.
Energy output per second (electrical power) = 2.50 × 108 J/s
Since there are 31,536,000 seconds in a year (365 days),
Total electrical energy output in one year = 2.50 × 108 J/s × 31,536,000 s/year = 7.884 × 1015 J
Now, we take into account the efficiency of the power plant, which is 35.0%. This means that only 35% of the heat energy is converted to electrical energy. To find the total heat energy produced, we need to divide the total electrical energy by the efficiency (in decimal form):
Total heat energy produced = Total electrical energy output / Efficiency
Total heat energy produced = 7.884 × 1015 J / 0.35 = 2.252 × 1016 J
Therefore, the correct answer is B) 2.25 × 1016 J, which corresponds to 2.25 × 1016 joules of heat energy produced in one year by the power plant. It's worth noting that this value is more than the ones provided in the answer choices, indicating there might be a mistake in the question or the answer choices themselves.