Question

A coal-burning power plant generates electrical power at a rate of 950 megawatts (mw), or 9.50 × 108 j/s. the plant has an overall efficiency of 32.1% for the conversion of heat to electricity. given this efficiency, how much heat energy in joules is produced in one year of operation, to generate the above electrical power?

Answer 1

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.