Final answer:
The heat energy produced by a coal-burning power plant with a 32.1% efficiency and an electrical power output of 950 MW is approximately 9.33 × 10^16 joules in one year.
Step-by-step explanation:
To calculate the heat energy produced by the power plant, we must consider the plant's efficiency and the rate at which it generates electrical power. Since the plant has a 32.1% efficiency, only 32.1% of the total heat energy produced is converted into electrical energy. The rate at which electrical power is generated is given as 9.50 × 108 joules per second (J/s), which is equivalent to 950 megawatts (MW).
First, we calculate the total heat energy produced per second by dividing the electrical power produced by the efficiency (in decimal form):
Heat energy per second = Electrical Power / Efficiency = 9.50 × 108 J/s / 0.321 = 2.96 × 109 J/s
Next, we determine the total heat energy produced in one year by multiplying the heat energy produced per second by the number of seconds in a year:
Heat energy per year = Heat energy per second × Seconds in a year
Heat energy per year = 2.96 × 109 J/s × (60 s/min × 60 min/hr × 24 hr/day × 365 days/year)
Heat energy per year = 2.96 × 109 J/s × 31,536,000 s/year = 9.33 × 1016 J/year
Therefore, the coal-burning power plant produces approximately 9.33 × 1016 joules of heat energy in one year to generate the specified electrical power.