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Chapter 2: Problem 8

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 \(100 \mathrm{MW} / \mathrm{hr}\) so over the year that's \(100^{*} 24^{*} 365.25 \&\) do the math." (a) Carry out the calculation, showing all the units. (b) What is wrong with the statement of the question? (c) Why was the student wrong in saying that the plant produces \(100 \mathrm{MW} / \mathrm{hr} ?\)

Short Answer

Expert verified
a) The plant generates \(876,600 MW/year\). b) The question is wrong in asking for annual power generation 鈥� power is a rate, not a cumulative amount. c) The student was wrong in saying the plant produces \(100 MW/hr\) because power isn't measured in watt-hours, energy is.

Step by step solution

01

Part a: Calculate the Annual Power Generation

First, it's crucial to recognize that power is measured in watts (W), not watt-hours. Watts represent the rate of energy use over time. So, a 100 MW power plant is capable of generating 100 MW of power every hour. To calculate the plant's annual power generation, multiply this rate by the number of hours in a year: \(100 MW * 24 hours/day * 365.25 days/year \). The units of hours and days will cancel out, leaving you with the answer in MW per year.
02

Part b: Identify the Question's Mistake

The question's mistake is in its confusion regarding the difference between energy and power. Power is the rate of energy production or consumption, while energy is the amount of power used over a period of time. The unit for power is the watt (W) and the commonly used unit for energy is the watt-hour (Wh) or joule (J). Asking about the power a power plant generates annually doesn't make sense as power denotes a rate, not a cumulative amount.
03

Part c: Explain the Student's Error

The error in the student's response is similar to that of the question's. The student tried to represent power in units of \(MW/hr\), which is incorrect. Power is the rate of energy production or consumption, not the ratio of energy to time. The amount of power a plant generates doesn't change with time, it remains constant unless the plant's capacity changes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Power generation calculation
To understand how much power a 100-MW power plant generates annually, we need to clarify some key concepts. Power is a measure of how fast energy is being produced or used. The unit of power is the watt (W). MegaWatt (MW) is equivalent to a million watts. It indicates the capability to produce or consume energy at a rapid rate.

When we say a plant produces 100 MW, it's producing 100 million watts per hour, continuously. To find out how much energy it produces annually, we multiply the power by the number of hours in a year. This incorporates continuous operation over every hour of the year.
  • 100 MW is the power rating.
  • There are 24 hours in a day, and 365.25 days in a year (accounting for leap years).
Calculation becomes: \[ 100 ext{ MW} \times 24 ext{ hours/day} \times 365.25 ext{ days/year} \].
Calculating this gives the total energy generation potential over a full year in MegaWatt-hours (MWh). This is quite different from power, which is a rate, not a total amount.
Units of measurement in engineering
Engineering relies heavily on precise units of measurement to ensure clarity and accuracy. The two crucial units here are watt (W) for power and watt-hour (Wh) for energy. It's essential to distinguish between them to avoid confusion.

  • Power: This is measured in watts (W), representing the rate at which work is done or energy is transformed.
  • Energy: This is commonly measured in watt-hours (Wh) or joules (J). It represents the total amount of work done or energy used over a period of time.
In our exercise, the unit MW/yr represents the plant's energy output over a year. It is important to remember that power should not be expressed in time-divided units such as MW/yr. Instead, a plant maintains its output at a constant rate (MW) without changing over time.
The correct unit differentiation prevents engineering errors and ensures the proper application of principles across different scenarios.
Misconceptions about power and energy
Misunderstandings about power and energy can lead to inaccuracies in both engineering practice and communication. Many people mistakenly conflate power and energy or misuse their respective units.

A common misconception, as in our exercise, is attempting to express power in terms of energy over time (e.g., MW/hr). This is incorrect because:
  • Power is a rate, measured in watts, which does not increase with time.
  • Energy, measured in watt-hours or joules, is the total of power applied over a set duration.
Such errors can lead to incorrect calculations and unclear communication. Remember, power is constant when considering a plant's output unless its capacity is deliberately changed or affected by factors such as shutdowns or maintenance.
Recognizing this distinction helps to prevent errors in energy calculations and allows for more effective engineering decisions and discussions.

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