Question

On a website devoted to answering engineering questions, viewers were invited to determine how much power a 100-MW power plant generates annually. The answer declared to be best was submitted by a civil engineering student, who stated, "It produces 100 MW/hr so over the year that's 100*24*365.25 & do the math." a. Carry out the calculation, showing all the units. Answer b. What is wrong with the statement of the question? c. Why was the student wrong in saying that the plant produces 100 MW/hr?

Answer 1

Answer:

(a) The plant generates 3,153,600,000 MJ a year.

(b) The problem with the question is that "power" is not "generated". What is generated is Energy, and Power is the rate of generation of Energy.

(c) The student is wrong because the plants generates 100 MJ of energy a second. "MW/hr" is not a unit of energy or power, so it has no sense.

Maybe he get confused with MW-h, which is a unit of energy, used to measure electrical consumption.

Explanation:

(a) The power of the plant (100 MW) is the rate at which electrical energy is produced. It has units of [energy]/[time].

In this case, the plant produces 100 MJ/s. The energy produced can also be expressed in other units, like MJh.

To calculate the energy generated in one year, we have

$Energy = Power * Time = \\\\Energy = 100 MW*1year\\\\Energy = (100 \frac{MJ}{s})*(1 year*\frac{365 days}{1year}* \frac{24hours}{1day}*\frac{3600s}{1hour})\\\\Energy=(100 \frac{MJ}{s})*(31,536,000s)=3,153,600,000MJ$

The plant generates 3,153,600,000 MJ a year.

(b) The problem with the question is that "power" is not "generated". What is generated is Energy, and Power is the rate of generation of Energy.

(c) The student is wrong because the plants generates 100 MJ of energy a second. "MW/hr" is not a unit of energy or power, so it has no sense.

Maybe he get confused with MW-h, which is a unit of energy, used to measure electrical consumption. That unit represents the amount of energy consumed or generated by a 1 MW unit in one hour. It is equivalent to 3600 MJ (1 MW-h = 3600 MJ).

In this unit, the 100 MW plant generates 876,000 MWh.