Solved: A power station with an efficiency of 0.4

Problem 1E A friend said the temperature inside a particular oven is 500 and the temperature inside a particular star is 50,000. You’re unsure whether your friend meant Celsius degrees or kelvins. How much difference does it make in each case?

Problem 1P What is the ideal efficiency of an automobile engine in which fuel is heated to 2700 K and the outdoor air is 270 K?

Problem 1RQ What is the origin and meaning of the word ?thermodynamics??

The temperature of the Sun’s interior is about \(10^{7}\) degrees. Does it matter whether this is degrees Celsius or kelvins? Explain.

Problem 2P Consider an ocean thermal energy conversion (OTEC) power plant that operates on a temperature difference between deep 4°C water and 25°C surface water. Show that the Carnot efficiency of this plant is 7%.

Problem 2RQ Is the study of thermodynamics concerned primarily with microscopic processes or with macroscopic ones?

Problem 3E When heat flows from a warm object in contact with a cool object, do both objects undergo the same amount of temperature change?

Problem 3P On a chilly 10°C day, your friend who loves cold weather says she wishes it were twice as cold. Taking this literally, show that the temperature she wishes for would be ?131.5°C.

Problem 3RQ By how much does the volume of gas at 0°C contract for each decrease in temperature of 1 Celsius degree when the pressure is held constant?

Problem 4E Heat always flows spontaneously from an object with a higher temperature to an object with a lower temperature. Is this the same thing as saying that heat always flows from an object with a greater internal energy to one with a lower internal energy? Explain.

Problem 4P Imagine a giant dry-cleaners bag full of air at a temperature of ?35°C floating like a balloon with a string hanging from it 10 km above the ground. Estimate what its temperature would be if you were able to yank it suddenly back to Earth’s surface.

Problem 4RQ By how much does the pressure of gas at 0°C decrease for each decrease in temperature of 1 Celsius degree when the volume is held constant?

Problem 5P Calculate the ideal efficiency of an engine wherein fuel is heated to 2700 K and the surrounding air is 300 K.

Problem 5RQ If we assume the gas does not condense to a liquid, what volume is approached for a gas at 0°C cooled by 273 Celsius degrees?

Problem 6E If you vigorously shake a can of chicken broth back and forth for more than a minute, will the temperature of the broth increase? (Try it and see.)

Problem 6RQ What is the lowest possible temperature on the Celsius scale? On the Kelvin scale?

Problem 7E When air is quickly compressed, why does its temperature increase?

Problem 7P A power station with an efficiency of 0.4 generates 108 W of electric power and dissipates 1.5 × 108 J of heat energy each second to the cooling water that flows through it, which increases its temperature by 3 Celsius degrees. Knowing that the specific heat of water in SI units is 4184 J/kg·°C, show that 12,000 kg of warmed water flows through the plant each second.

Problem 7RQ What else besides molecular kinetic energy contributes to the internal energy of a substance?

Problem 8E Suppose you do 100 J of work in compressing a gas. If 80 J of heat escapes in the process, what is the change in internal energy of the gas?

Problem 8P Construct a table of all the possible combinations of numbers that can come up when you throw two dice. Your friend says, “Yes, I know that 7 is the most likely total number when two dice are thrown. But ?why 7?” Based on your table, answer your friend, and explain that, in thermodynamics, the situations that are likely to be observed are those that can be formed in the greatest number of ways.

Problem 8RQ Is the principal concern in the study of thermodynamics the ?amount of internal energy in a system or the ?changes? in internal energy in a substance?

Problem 9E Why does the bottom of a tire pump feel hot when you pump air in the tire, but when air is released, the valve stem feels cool?

Problem 9RQ How does the law of the conservation of energy relate to the first law of thermodynamics?

When you blow up a balloon, do you slightly warm the balloon? When air is allowed to rush out of it, how, if at all, does the temperature of that expanding air change?

Problem 10RQ What is the relationship between heat added to a system, change in its internal energy, and external work done by the system?

Problem 11E What happens to the gas pressure within a sealed gallon can when it is heated? When it is cooled? Why?

Problem 11RQ What happens to the internal energy of a system when mechanical work is done on it? What happens to its temperature?

Problem 12E Is it possible to wholly convert a given amount of mechanical energy into thermal energy? Is it possible to wholly convert a given amount of thermal energy into mechanical energy? Cite examples to illustrate your answers.

Problem 12RQ What condition is necessary for a process to be adiabatic?

Problem 13E Why does cold mountain air become warm when it descends into a valley?

Problem 13RQ If work is done ?on a system, does the internal energy of the system increase or decrease? If work is done ?by? a system, does the internal energy of the system increase or decrease?

Problem 14E Everybody knows that warm air rises. So it might seem that the air temperature should be higher at the tops of mountains than clown below. But the opposite is most often the case. Why?

Problem 14RQ How do meteorologists express the first law of thermodynamics?

Problem 15E What is the ultimate source of energy in coal, oil, and wood? Why do we call energy from wood renewable but energy from coal and oil nonrenewable?

Problem 16E What is the ultimate source of energy in a hydroelectric power plant?

Problem 15RQ What is the adiabatic form of the first law?

Problem 16RQ What generally happens to the temperature of rising air? Of sinking air?

Problem 17E The combined molecular kinetic energies of molecules in a cool lake are greater than the combined molecular kinetic energies of molecules in a cup of hot tea. Pretend you partially immerse the teacup in the lake and that the tea ?absorbs? 10 calories from the water and becomes hotter, while the water that gives up 10 calories becomes cooler. Would this energy transfer violate the first law of thermodynamics? The second law of thermodynamics? Defend your answers.

What is a temperature inversion?

Problem 18E Why is thermal pollution a relative term?

Problem 18RQ Do adiabatic processes apply only to gases? Defend your answer.

The box “Thermodynamics Dramatized” shows the crushing of an inverted steam-filled can placed in a pan of water. Would the water need to be cold? Would crushing occur if the water were hot but not boiling? Would it crush in boiling water? (Try it and see!)

Problem 19RQ How does the second law of thermodynamics relate to the direction of heat flow?

Problem 20E Why is it advantageous to use steam that is as hot as possible in a steam-driven turbine?

Problem 20RQ What three processes occur in every heat engine?

How does the ideal efficiency of an automobile relate to the temperature of the engine and the temperature of the environment in which it operates? Be specific.

Problem 21RQ What exactly is thermal pollution?

Problem 22E What happens to the efficiency of a heat engine when the temperature of the reservoir into which thermal energy is transferred is lowered?

Problem 22RQ How does the second law relate to heat engines?

Problem 23RQ Why is the condensation part of the cycle in a steam turbine so essential?

Problem 23E Under what conditions would a heat engine be 100% efficient?

Problem 24E To increase the efficiency of a heat engine, would it be preferable to produce the same temperature increment by increasing the temperature of the reservoir while maintaining the temperature of the sink constant, or to decrease the temperature of the sink while maintaining the temperature of the reservoir constant? Explain.

Problem 24RQ Distinguish between high-quality energy and low-quality energy in terms of organized and disorganized energy. Give an example of each.

Problem 25E Could you cool a kitchen by leaving the refrigerator door open and closing the kitchen door and windows? Explain.

Problem 25RQ How can the second law be stated with regard to high-quality and lower-quality energy?

Problem 26E Could you warm a kitchen by leaving the door of a hot oven open? Explain.

Problem 26RQ With respect to orderly and disorderly states, what do natural systems tend to do? Can a disorderly state ever transform to an orderly state? Explain.

An electric fan not only doesn’t decrease the temperature of air, but it actually increases air temperature. How, then, are you cooled by a fan on a hot day?

Problem 27RQ What is the physicist’s term f? easure of amount of disorder?

Problem 28E Strictly speaking, why will a refrigerator containing a fixed amount of food consume more energy in a warm room than in a cold room?

Problem 29E A refrigerator moves heat from cold to warm. Why does this not violate the second law of thermodynamics?

Problem 30E What happens to the density of a quantity of gas when its temperature is decreased and its pressure is held constant?

Problem 31E If you squeeze an air-filled balloon and no heat escapes, what happens to the internal energy of the gas in the balloon?

Problem 32E In buildings that are being electrically heated, is it at all wasteful to turn all the lights on? Is turning all the lights on wasteful if the building is being cooled by air- conditioning?

Problem 28RQ Distinguish between the first and second laws of thermodynamics in terms of whether or not exceptions occur.

Problem 37E According to the second law of thermodynamics, is the universe moving to a more ordered state or to a more disordered state?

Problem 35E Molecules in the combustion chamber of a rocket engine are in a high state of random motion. When the molecules are expelled through a nozzle in a more ordered state, will their temperature be more, less, or the same as their initial temperature in the chamber before being exhausted?

Problem 34E Defend the statement that 100% of the electrical energy that goes into lighting a lamp is converted to thermal energy. Are the first and the second laws of thermodynamics violated?

Problem 38E Do adiabatic parcels occur in the atmosphere, in the ocean, or in both?

Problem 33E Why can the drinking bird in Figure 17.4 in the previous chapter be considered a heat engine?

Problem 39E The ocean possesses enormous numbers of molecules, all with kinetic energy. Can this energy be extracted and used as a power source? Defend your answer.

Problem 40E Why do we say a substance in a liquid phase is more disordered than the same substance in a solid phase?

Problem 42E Water evaporates from a salt solution and leaves behind salt crystals that have a higher degree of molecular order than the more randomly moving molecules in the saltwater. Has the entropy principle been violated? Why or why not?

Problem 41E Comment on this statement: The second law of thermodynamics is one of the most fundamental laws of nature, yet it is not an exact law at all.

Problem 36E Is the total energy of the universe becoming more unavailable with time? Explain.

Problem 43E Water put into the freezer compartment of your refrigerator goes to a state of less molecular disorder when it freezes. Is this an exception to the entropy principle? Explain.

Problem 44E As a chicken develops from an egg, it becomes more ordered with time. Does this violate the principle of entropy? Explain.

Problem 45E The United States Patent and Trademark Office rejects claims for perpetual motion machines (in which energy output is as great or greater than energy input) without even investigating them. Why is this?

Problem 46E It is generally assumed that perpetual motion machines are impossible to construct. Is it inconsistent to say that molecules are in perpetual motion?

Problem 47E A classmate says that all this stuff about no perpetual motion is bunk; that atoms, planets, stars, and everything are in perpetual motion. What distinction is being missed here?

Problem 48E (a) If you spent 10 minutes repeatedly shaking and throwing down a pair of coins, would you expect to see two heads come up at least once? (b) If you spent an hour shaking a handful of 10 coins and throwing them down, would you expect to see all 10 come up heads at least once? (c) If you stirred a box of 10,000 coins and tossed them repeatedly on the floor all day long, would you expect to see all 10,000 appear as heads at least once?

What is the origin and meaning of the word thermodynamics?

Is the study of thermodynamics concerned primarily with microscopic processes or with macroscopic ones?

By how much does the volume of gas at \(0^{\circ} \mathrm{C}\) contract for each decrease in temperature of 1 Celsius degree when the pressure is held constant? Text Transcription: 0^circ C

By how much does the pressure of gas at \(0^{\circ} \mathrm{C}\) decrease for each decrease in temperature of 1 Celsius degree when the volume is held constant? Text Transcription: 0^circ C

What is the lowest possible temperature on the Celsius scale? On the Kelvin scale?

If we assume the gas does not condense to a liquid, what volume is approached for a gas at \(0^{\circ} \mathrm{C}\) cooled by 273 Celsius degrees? Text Transcription: 0^circ C

Is the principal concern in the study of thermodynamics the amount of internal energy in a system or the changes in internal energy in a substance?

How does the law of the conservation of energy relate to the first law of thermodynamics?

What is meant by a system?

What happens to the internal energy of a system when mechanical work is done on it? What happens to its temperature?

What is the relationship among heat added to a system, change in the system’s internal energy, and external work done by the system?

What condition is necessary for a process to be adiabatic?

If work is done on a system, does the internal energy of the system increase or decrease? If work is done by a system, does the internal energy of the system increase or decrease?

How do meteorologists express the first law of thermodynamics?

What is the adiabatic form of the first law?

What generally happens to the temperature of rising air? Of sinking air?

What is a temperature inversion?

Do adiabatic processes apply only to gases? Defend your answer.

How does the second law of thermodynamics relate to the direction of heat flow?

What three processes occur in every heat engine?

What exactly is thermal pollution?

How does the second law relate to heat engines?

Why is the condensation part of the cycle in a steam turbine so essential?

Distinguish between high-quality energy and low-quality energy in terms of organized and disorganized energy. Give an example of each.

How can the second law be stated with regard to high-quality and lower-quality energy?

With respect to orderly and disorderly states, what do natural systems tend to do? Can a disorderly state ever transform into an orderly state? Explain.

What is the physicist’s term for measure of amount of disorder?

Distinguish between the first and second laws of thermodynamics in terms of whether or not exceptions occur.

What is the third law of thermodynamics?

What is the zeroth law of thermodynamics?

\(\text { Ideal efficiency }=\frac{\mathbf{T}_{\text {hot }}-\mathrm{T}_{\text {cold }}}{\mathrm{T}_{\text {hot }}}\) Show that the ideal efficiency is 90% for an engine in which fuel is heated to 3000 K and the surrounding air is 300 K.

\(\text { Ideal efficiency }=\frac{\mathbf{T}_{\text {hot }}-\mathbf{T}_{\text {cold }}}{\mathbf{T}_{\text {hot }}}\) Calculate the ideal efficiency of an engine in which fuel is heated to 2700 K and the surrounding air is 200 K.

What is the ideal efficiency of an automobile engine that operates between the temperatures \(600^{\circ} \mathrm{C}\) and \(320^{\circ} \mathrm{C}\)? (Why is your answer not 47%?)

On a chilly \(10^{\circ} \mathrm{C}\) day, your friend who loves cold weather says she wishes it were twice as cold. Taking this literally, show that the temperature she wishes for would be \(-131.5^{\circ} \mathrm{C}\).

Consider an ocean thermal energy conversion (OTEC) power plant that operates on a temperature difference between deep \(4^{\circ} \mathrm{C}\) water and \(25^{\circ} \mathrm{C}\) surface water. Show that the Carnot efficiency of this plant is 7%.

Imagine a giant dry-cleaner’s bag full of air at a temperature of \(-35^{\circ} \mathrm{C}\) floating like a balloon with a string hanging from it 10 km above the ground. Estimate what its temperature would be if you were able to yank it suddenly back to Earth’s surface.

Wally Whacko claims to have invented a heat engine that will revolutionize industry. It runs between a hot source at \(300^\circ\)C and a cold sink at \(25^\circ\)C. He claims that his engine is 92% efficient. a. What error did he make in his choice of temperature scales? b. What is the actual maximum efficiency of his engine?

A power station with an efficiency of 0.4 generates \(10^{8} \quad \mathrm{W}\) of electric power and dissipates \(1.5 \times 10^{8} \quad \mathrm{J}\) of heat energy each second to the cooling water that flows through it, which increases its temperature by 3 Celsius degrees. Knowing that the specific heat of water in SI units is \(4184 \quad \mathrm{J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\), show that 12,000 kg of warmed water flows through the plant each second. Text Transcription: 10^8 W 1.5 times 10^8 J 4184 J / kg cdot ^circ C

Construct a table of all the possible combinations of numbers that can come up when you throw two dice. Your friend says, “Yes, I know that 7 is the most likely total number when two dice are thrown. But why 7?” Based on your table, answer your friend, and explain that, in thermodynamics, the situations that are likely to be observed are those that can be formed in the greatest number of ways.

Consider a 6.0-g steel nail 8.0 cm long and a hammer that exerts an average force of 600 N on the nail when it is being driven into a piece of wood. The nail becomes warmer. Show that the increase in the nail’s temperature is \(17.8^{\circ} \mathrm{C}\). (Assume that the specific heat capacity of steel is \(450 \quad \mathrm{J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\).) Text Transcription: 17.8^circ C 450 J / kg cdot ^circ C

A friend said the temperature inside a particular oven is 500 and the temperature inside a particular star is 50,000. You’re unsure whether your friend meant Celsius degrees or kelvins. How much difference does it make in each case?

The temperature of the Sun’s interior is about \(10^{7}\) degrees. Does it matter whether this is degrees Celsius or kelvins? Explain.

When heat flows from a warm object in contact with a cool object, do both objects undergo the same amount of temperature change?

If you vigorously shake a can of chicken broth for more than a minute, will the temperature of the broth increase? (Try it and see.)

When air is quickly compressed, why does its temperature increase?

Suppose you do 100 J of work in compressing a gas. If 80 J of heat escapes in the process, what is the change in the internal energy of the gas?

Why does the bottom of a tire pump feel hot when you pump air in the tire, but when air is released, the valve stem feels cool?

When you blow up a balloon, do you slightly warm the balloon? When air is allowed to rush out of it, how, if at all, does the temperature of that expanding air change?

What happens to the gas pressure in a sealed gallon can when it is heated? When it is cooled? Why?

Why does cold mountain air become warm when it descends into a valley?

What is the ultimate source of energy in coal, oil, and wood? Why do we call energy from wood renewable but energy from coal and oil nonrenewable?

What is the ultimate source of energy in a hydroelectric power plant?

How does the ideal efficiency of an automobile relate to the temperature of the engine and the temperature of the environment in which it operates? Be specific.

What happens to the efficiency of a heat engine when the temperature of the reservoir into which thermal energy is transferred is lowered?

Under what conditions would a heat engine be 100% efficient?

To increase the efficiency of a heat engine, would it be preferable to produce the same temperature increment by increasing the temperature of the reservoir while maintaining the temperature of the sink constant, or to decrease the temperature of the sink while maintaining the temperature of the reservoir constant? Explain.

Could you cool a kitchen by leaving the refrigerator door open and closing the kitchen door and windows? Explain.

Could you warm a kitchen by leaving the door of a hot oven open? Explain.

An electric fan not only doesn’t decrease the temperature of air but actually increases the air temperature. How, then, are you cooled by a fan on a hot day?

Strictly speaking, why will a refrigerator that contains a fixed amount of food consume more energy in a warm room than in a cold room?

A refrigerator moves heat from cold to warm. Why doesn’t this violate the second law of thermodynamics?

What happens to the density of a quantity of gas when its temperature is decreased and its pressure is held constant?

If you squeeze an air-filled balloon and no heat escapes, what happens to the internal energy of the gas in the balloon?

In buildings that are being electrically heated, is it at all wasteful to turn all the lights on? Is turning all the lights on wasteful if the building is being cooled by air conditioning?

Why can the drinking bird in Figure 17.4 in Chapter 17 be considered a heat engine?

Molecules in the combustion chamber of a rocket engine are in a high state of random motion. When the molecules are expelled through a nozzle in a more ordered state, will their temperature be higher than, lower than, or the same as their initial temperature in the chamber before being exhausted?

Is the total energy of the universe becoming more unavailable with time? Explain.

According to the second law of thermodynamics, is the universe moving to a more ordered state or to a more disordered state?

The ocean possesses enormous numbers of molecules, all with kinetic energy. Can this energy be extracted and used as a power source? Defend your answer.

Do adiabatic parcels occur in the atmosphere, in the ocean, or in both?

Why do we say a substance in a liquid phase is more disordered than the same substance in a solid phase?

Water evaporates from a salt solution and leaves behind salt crystals that have a higher degree of molecular order than the more randomly moving molecules in the saltwater. Has the entropy principle been violated? Why or why not?

Water put into the freezer compartment of your refrigerator goes to a state of less molecular disorder when it freezes. Is this an exception to the entropy principle? Explain.

As a chicken develops from an egg, it becomes more ordered with time. Does this violate the principle of entropy? Explain.

The United States Patent and Trademark Office rejects claims for perpetual motion machines (in which energy output is as great as or greater than energy input) without even investigating them. Why is this?

Discuss whether or not it is possible to wholly convert a given amount of mechanical energy into thermal energy. Is it possible to wholly convert a given amount of thermal energy into mechanical energy? Cite examples to illustrate your answers.

Heat always flows spontaneously from an object with a higher temperature to an object with a lower temperature. Is this the same as saying that heat always flows from an object with greater internal energy to one with less internal energy? Discuss why or why not.

Everybody knows that warm air rises. So it might seem that the air temperature should be higher at the tops of mountains than down below. Discuss why the opposite is most often the case.

Hovering over the surface of our skin is a layer of air some 3 millimeters in thickness that acts as a thermal blanket. On a hot day, what effect does a breeze on bare skin have on your skin? What effect does it have on a cold day?

The temperature in Boston was \(40^{\circ} \mathrm{F}\) when it was \(80^{\circ} \mathrm{F}\) in St. Petersburg, FL. What is your response to a friend who suggests that it was twice as hot in St. Petersburg on that day? Text Transcription: 40^circ F 80^circ F

The combined molecular kinetic energies of molecules in a cool lake are greater than the combined molecular kinetic energies of molecules in a cup of hot tea. Pretend you partially immerse the teacup in the lake and the tea absorbs 10 calories from the water and becomes hotter, while the water that gives up 10 calories becomes cooler. Would this energy transfer violate the first law of thermodynamics? The second law of thermodynamics? Discuss your answers.

Why is thermal pollution a relative term?

The Thermodynamics Dramatized! box shows the crushing of an inverted steam-filled can placed in a pan of water. Does the water need to be cold? Would crushing occur if the water were hot but not boiling? Would the can crush in boiling water? Discuss this, and then try it and see!

Defend the statement that 100% of the electric energy that goes into lighting a lamp is converted to thermal energy. Are the first and the second laws of thermodynamics violated?

Discuss this statement: The second law of thermodynamics is one of the most fundamental laws of nature, yet it is not an exact law at all. Why not?

A classmate says that all this stuff about no perpetual motion is bunk; that atoms, planets, stars, and everything are in perpetual motion. What distinction is being missed here?

It is generally assumed that perpetual motion machines are impossible to construct. Is it inconsistent to say that molecules are in perpetual motion?

(a) If you spent 10 minutes repeatedly shaking and throwing down a pair of coins, would you expect to see two heads come up at least once? (b) If you spent an hour shaking a handful of 10 coins and throwing them down, would you expect to see all 10 come up heads at least once? (c) If you stirred a box of 10,000 coins and tossed them repeatedly on the floor all day long, would you expect to see all 10,000 appear as heads at least once? Discuss.

Why is it advantageous to use steam that is as hot as possible in a steam-driven turbine?