/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 If the proposed plant is built a... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

If the proposed plant is built and produces \(10 \mathrm{MW}\) but the rate at which waste heat is exhausted to the cold water is \(165 \mathrm{MW}\), what is the plant's actual efficiency? A. \(5.7 \%\) B. \(6.1 \%\) C. \(6.5 \%\) D. \(16.5 \%\)

Short Answer

Expert verified
The plant's actual efficiency is approximately 5.7%.

Step by step solution

01

Understanding Efficiency

Efficiency in a thermal power plant is calculated using the formula: \( \text{Efficiency} = \frac{\text{Output Power}}{\text{Input Power}} \times 100 \% \). This formula helps us determine how well the plant converts input energy to output energy.
02

Identify Output Power

The problem states that the plant produces \(10 \mathrm{MW}\) of output power. This means the useful electricity generated by the plant is \(10 \mathrm{MW}\).
03

Identify Input Power

The input power is the total energy input into the system, which is the sum of the output power and the waste heat. We know the waste heat is \(165 \mathrm{MW}\). Thus, the input power is \(165 \mathrm{MW} + 10 \mathrm{MW} = 175 \mathrm{MW}\).
04

Calculate the Actual Efficiency

Substitute the values into the efficiency formula: \( \text{Efficiency} = \frac{10 \mathrm{MW}}{175 \mathrm{MW}} \times 100 \% \).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Thermodynamics
Thermodynamics is the science that deals with the relationships between heat, work, temperature, and energy. This field is crucial in understanding how power plants and engines operate. In a thermodynamic system, energy can be transferred in the form of heat or work. However, energy cannot be created or destroyed. This principle is known as the law of conservation of energy, or the First Law of Thermodynamics.
In the context of the exercise, thermodynamics helps us measure a plant’s efficiency. Efficiency here refers to how much output work is gained from a certain input of energy. Calculating thermal efficiency requires knowing both the input (the total energy supplied to the system) and the output (useful work produced by the system).
It involves understanding part of the Second Law of Thermodynamics as well, which implies that some energy will always be lost as waste heat. This is why no system can reach 100% thermal efficiency; there's always a fraction of energy that doesn't convert to useful work.
Energy Conversion
Energy conversion is a process where energy changes from one type to another. In power plants, they take stored energy in fuels and convert it into electrical energy. The key to this conversion process is how efficiently a plant can transform one type of energy into another.
  • First, fuel is burned in a boiler to convert chemical energy into thermal energy, creating steam.
  • Steam drives a turbine, where thermal energy is converted into mechanical energy.
  • Finally, the mechanical energy is used to drive a generator, transforming mechanical energy into electrical energy.
Yet, not all energy is converted into electricity. Some is lost as waste heat, like the 165 MW mentioned in the exercise. By calculating the efficiency, we determine how well a plant carries out this energy conversion process.
The formula \(\text{Efficiency} = \frac{\text{Output Power}}{\text{Input Power}} \times 100 \%\) helps understand how much of the input energy becomes usable
electricity.
Power Plants
Power plants are facilities that generate electricity. They are vital for powering homes, industries, and cities. Different types of power plants include coal-fired, nuclear, hydroelectric, and solar energy plants. Regardless of the type, they all follow the basic principle of energy conversion, from fuel to electricity.
Thermal power plants, like the one in the exercise, typically involve converting heat energy into electrical energy.
  • They often use water or other fluids to transfer heat in cycles, expelling waste heat in the process.
  • The expelled waste heat is what affects the overall plant efficiency.
  • This waste heat is often released into the environment, such as in cooling towers or bodies of water.
Improving plant efficiency focuses not only on maximizing output but also on effectively managing waste heat and minimizing environmental impact. Hence, assessing efficiency rates, like the calculated 5.7%, determines how effectively a plant performs its role in the energy ecosystem.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A coal-fired power plant that operates at an efficiency of \(38 \%\) generates \(750 \mathrm{MW}\) of electric power. How much heat does the plant discharge to the environment in one day?

The Kwik-Freez Appliance Co. wants you to design a food freezer that will keep the freezing compartment at \(-5.0^{\circ} \mathrm{C}\) and will operate in a room at \(20.0^{\circ} \mathrm{C}\). The freezer is to make \(5.00 \mathrm{~kg}\) of ice at \(0.0^{\circ} \mathrm{C}\), starting with water at \(20.0^{\circ} \mathrm{C}\). Find the least possible amount of electrical energy needed to make this ice and the smallest possible amount of heat expelled into the room.

Three moles of an ideal gas undergo a reversible isothermal compression at \(20.0^{\circ} \mathrm{C}\). During this compression, \(1850 \mathrm{~J}\) of work is done

In one cycle, a freezer uses \(785 \mathrm{~J}\) of electrical energy in order to remove \(1750 \mathrm{~J}\) of heat from its freezer compartment at \(10^{\circ} \mathrm{F}\). (a) What is the coefficient of performance of this freezer? (b) How much heat does it expel into the room during this cycle?

A gasoline engine takes in \(1.61 \times 10^{4} \mathrm{~J}\) of heat and delivers \(3700 \mathrm{~J}\) of work per cycle. The heat is obtained by burning gasoline with a heat of combustion of \(4.60 \times 10^{4} \mathrm{~J} / \mathrm{g}\). (a) What is the thermal efficiency of the engine? (b) How much heat is discarded in each cycle? (c) What mass of fuel is burned in each cycle? (d) If the engine goes through 60.0 cycles per second, what is its power output in kilowatts? In horsepower?

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.