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Thermodynamics: An Engineering Approach

Yunus A. Cengel, Michael A. Boles

Chapter 8

Exergy - all with Video Answers

Educators

RZ

Chapter Questions

01:11

Problem 1

What final state will maximize the work output of a device?

Mitchell Cutler
Mitchell Cutler
Numerade Educator
01:08

Problem 2

Is the exergy of a system different in different environments?

Mitchell Cutler
Mitchell Cutler
Numerade Educator
00:30

Problem 3

Under what conditions does the reversible work equal irreversibility for a process?

RZ
Rubeena Zulfiqar
Numerade Educator
00:41

Problem 4

How does useful work differ from actual work? For what kinds of systems are these two identical?

RZ
Rubeena Zulfiqar
Numerade Educator
00:58

Problem 5

How does reversible work differ from useful work?

RZ
Rubeena Zulfiqar
Numerade Educator
00:53

Problem 6

Is a process during which no entropy is generated $\left(S_{\mathrm{gen}}=0\right)$ necessarily reversible?

RZ
Rubeena Zulfiqar
Numerade Educator
00:41

Problem 7

Consider an environment of zero absolute pressure (such as outer space). How will the actual work and the useful work compare in that environment?

RZ
Rubeena Zulfiqar
Numerade Educator
03:51

Problem 8

It is well known that the actual work between the two specified states depends on the path followed during the process. Can we say the same for the reversible work?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:37

Problem 9

Consider two geothermal wells whose energy contents are estimated to be the same. Will the exergies of these wells necessarily be the same? Explain.

Mitchell Cutler
Mitchell Cutler
Numerade Educator
01:34

Problem 10

Consider two systems that are at the same pressure as the environment. The first system is at the same temperature as the environment, whereas the second system is at a lower temperature than the environment. How would you compare the exergies of these two systems?

Mitchell Cutler
Mitchell Cutler
Numerade Educator
00:53

Problem 11

What is the second-law efficiency? How does it differ from the first-law efficiency?
$8-12 C$ Does a power plant that has a higher thermal effi-

RZ
Rubeena Zulfiqar
Numerade Educator
01:30

Problem 12

Does a power plant that has a higher thermal efficiency necessarily have a higher second-law efficiency than one with a lower thermal efficiency? Explain.

Mitchell Cutler
Mitchell Cutler
Numerade Educator
00:42

Problem 13

Does a refrigerator that has a higher COP necessar. ily have a higher second-law efficiency than one with a lower COP? Explain.

RZ
Rubeena Zulfiqar
Numerade Educator
01:53

Problem 14

Saturated steam is generated in a boiler by converting a saturated liquid to a saturated vapor at 200 psia. This is done by transferring heat from the combustion gases, which are at $700^{\circ} \mathrm{F}$, to the water in the boiler tubes. Calculate the wasted work potential associated with this heat transfer process. How does increasing the temperature of the combustion gases affect the work potential of the steam stream? Take $T_{0}=80^{\circ} \mathrm{F}$ and $P_{0}=14.7$ psia.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:05

Problem 15

One method of meeting the extra electric power demand at peak periods is to pump some water from a large body of water (such as a lake) to a reservoir at a higher eleva. tion at times of low demand and to generate electricity at times of high demand by letting this water run down and rotate $a$ turbine (i.e., convert the electric energy to potential energy and then back to electric energy). For an energy storage capacity of $5 \times 10^{6} \mathrm{kWh}$, determine the minimum amount of water that needs to be stored at an average elevation (relative to the ground level) of $75 \mathrm{~m}$. Answer: $2.45 \times 10^{10} \mathrm{~kg}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:11

Problem 16

A heat engine that receives heat from a furnace at $1200^{\circ} \mathrm{C}$ and rejects waste heat to a river at $20^{\circ} \mathrm{C}$ has a thermal efficiency of 40 percent. Determine the second-law efficiency of this power plant.

Nathan Nowack
Nathan Nowack
Numerade Educator
02:34

Problem 17

Consider a thermal energy reservoir at $1500 \mathrm{~K}$ that can supply heat at a rate of $150,000 \mathrm{~kJ} / \mathrm{h}$. Determine the exergy of this supplied energy, assuming an environment temperature of $25^{\circ} \mathrm{C}$.

RZ
Rubeena Zulfiqar
Numerade Educator
04:00

Problem 18

A heat engine receives heat from a source at $1100 \mathrm{~K}$ at a rate of $400 \mathrm{~kJ} / \mathrm{s}$, and it rejects the waste heat to a medium at $320 \mathrm{~K}$. The measured power output of the heat engine is $120 \mathrm{~kW}$, and the environment temperature is $25^{\circ} \mathrm{C}$. Determine ( $a$ ) the reversible power, $(b)$ the rate of irreversibility, and $(c)$ the second-law efficiency of this heat engine. Answers: (a) $284 \mathrm{~kW}$. (b) $164 \mathrm{~kW}$. (c) 42.3 percent.

RZ
Rubeena Zulfiqar
Numerade Educator
04:16

Problem 19

Reconsider Prob. $8-18$. Using appropriate software, study the effect of reducing the temperature at which the waste heat is rejected on the reversible power, the rate of irreversibility, and the second-law efficiency as the rejection temperature is varied from 500 to $298 \mathrm{~K}$, and plot the result.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:23

Problem 20

A heat engine that rejects waste heat to a sink at $510 \mathrm{R}$ has a thermal efficiency of 25 percent and a second-law efficiency of 50 percent. Determine the temperature of the source that supplies heat to this engine. Answer: $1020 \mathrm{R}$.

RZ
Rubeena Zulfiqar
Numerade Educator
03:29

Problem 21

A geothermal power plant uses geothermal liquid water at $150^{\circ} \mathrm{C}$ at a rate of $210 \mathrm{~kg} / \mathrm{s}$ as the heat source, and it produces $5.1 \mathrm{MW}$ of net power in an environment at $25^{\circ} \mathrm{C}$. If $7.5 \mathrm{MW}$ of exergy entering the plant with the geothermal water is destroyed within the plant, determine $(a)$ the exergy of the geothermal water entering the plant, $(b)$ the second-law efficiency, and $(c)$ the exergy of the heat rejected from the plant.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:39

Problem 22

A house that is losing heat at a rate of $35,000 \mathrm{~kJ} / \mathrm{h}$ when the outside temperature drops to $4^{\circ} \mathrm{C}$ is to be heated by electric resistance heaters. If the house is to be maintained at $25^{\circ} \mathrm{C}$ at all times, determine the reversible work input for this process and the irreversibility. Answers: $0.685 \mathrm{~kW}, 9.04 \mathrm{~kW}$.

RZ
Rubeena Zulfiqar
Numerade Educator
03:31

Problem 23

A freezer is maintained at $20^{\circ} \mathrm{F}$ by removing heat from it at a rate of $75 \mathrm{Btu} / \mathrm{min}$. The power input to the freezer is $0.70 \mathrm{hp},$ and the surrounding air is at $75^{\circ} \mathrm{F}$. Determine
(a) the reversible power, (b) the irreversibility, and (c) the second-law efficiency of this freezer. Answers: (o) 0.20 hp,

RZ
Rubeena Zulfiqar
Numerade Educator
04:11

Problem 24

The electric power needs of a community are to be met by windmills with 40 -m-diameter rotors. The windmills are to be located where the wind is blowing steadily at an average velocity of $6 \mathrm{~m} / \mathrm{s}$. Determine the minimum number of windmills that need to be installed if the required power output is $1500 \mathrm{~kW}$.

Mitchell Cutler
Mitchell Cutler
Numerade Educator
03:35

Problem 25

Show that the power produced by a wind turbine is proportional to the cube of the wind velocity and to the square of the blade span diameter.

Nathan Nowack
Nathan Nowack
Numerade Educator
03:07

Problem 26

Two constant-pressure devices, each filled with $30 \mathrm{~kg}$ of air, have temperatures of $900 \mathrm{~K}$ and $300 \mathrm{~K}$. A heat engine placed between the two devices extracts heat from the hightemperature device, produces work, and rejects heat to the low-temperature device. Determine the maximum work that can be produced by the heat engine and the final temperatures of the devices. Assume constant specific heats at room temperature.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:14

Problem 27

Can a system have a higher second-law efficiency than the first-law efficiency during a process? Give examples.

Nathan Nowack
Nathan Nowack
Numerade Educator
06:01

Problem 28

A mass of $8 \mathrm{~kg}$ of helium undergoes a process from an initial state of $3 \mathrm{~m}^{3} / \mathrm{kg}$ and $15^{\circ} \mathrm{C}$ to a final state of $0.5 \mathrm{~m}^{3} /$ $\mathrm{kg}$ and $80^{\circ} \mathrm{C}$. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, determine the increase in the useful work potential of the helium during this process.

Nathan Nowack
Nathan Nowack
Numerade Educator
06:50

Problem 29

Which is a more valuable resource for work production in a closed system $-15 \mathrm{ft}^{3}$ of air at 100 psia and $250^{\circ} \mathrm{F}$ or $20 \mathrm{ft}^{3}$ of helium at 60 psia and $200^{\circ} \mathrm{F}$ ? Take $T_{0}=77^{\circ} \mathrm{F}$ and $P_{0}=14.7$ psia.

Nathan Nowack
Nathan Nowack
Numerade Educator
10:11

Problem 30

Which has the capability to produce the most work in a closed system $-1 \mathrm{~kg}$ of steam at $800 \mathrm{kPa}$ and $180^{\circ} \mathrm{C}$ or $1 \mathrm{~kg}$ of $\mathrm{R}-134 \mathrm{a}$ at $800 \mathrm{kPa}$ and $180^{\circ} \mathrm{C}$ ? Take $T_{0}=25^{\circ} \mathrm{C}$ and $P_{0}=100 \mathrm{kPa}$
Answers: $623 \mathrm{~kJ}$ (steam), $47.5 \mathrm{~kJ}(\mathrm{R}-134 \mathrm{a})$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:45

Problem 31

$8-31$ The radiator of a steam heating system has a volume of $20 \mathrm{~L}$ and is filled with superheated water vapor at $200 \mathrm{kPa}$ and $200^{\circ} \mathrm{C}$. At this moment both the inlet and the exit valves to the radiator are closed. After a while it is observed that the temperature of the steam drops to $80^{\circ} \mathrm{C}$ as a result of heat transfer to the room air, which is at $21^{\circ} \mathrm{C}$. Assuming the surround ings to be at $0^{\circ} \mathrm{C}$, determine $(a)$ the amount of heat transfer to the room and $(b)$ the maximum amount of heat that can be

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:08

Problem 32

Reconsider Prob. $8-31 .$ Using appropriate software, investigate the effect of the final steam temperature in the radiator on the amount of actual heat transfer and the maximum amount of heat that can be transferred. Vary the final steam temperature from 80 to $21^{\circ} \mathrm{C}$ and plot the actual and maximum heat transferred to the room as functions of final steam temperature.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:51

Problem 33

A well-insulated rigid tank contains 6 lbm of a saturated liquid-vapor mixture of water at 35 psia. Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is turned on and kept on until all the liquid in the tank is vaporized. Assuming the surroundings to be at $75^{\circ} \mathrm{F}$ and 14.7 psia, determine $(a)$ the exergy destruction and $(b)$ the second-law efficiency for this process.

Jincy M Saji
Jincy M Saji
Numerade Educator
09:12

Problem 34

A piston-cylinder device contains $8 \mathrm{~kg}$ of refrigerant$134 \mathrm{a}$ at $0.7 \mathrm{MPa}$ and $60^{\circ} \mathrm{C}$. The refrigerant is now cooled at constant pressure until it exists as a liquid at $20^{\circ} \mathrm{C}$. If the surroundings are at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$, determine $(a)$ the exergy of the refrigerant at the initial and the final states and $(b)$ the exergy destroyed during this process.

Nathan Nowack
Nathan Nowack
Numerade Educator
05:57

Problem 35

An insulated piston-cylinder device contains $0.018 \mathrm{~m}^{3}$ of saturated refrigerant-134a vapor at 0.6 MPa pressure. The refrigerant is now allowed to expand in a reversible manner until the pressure drops to 0.16 MPa. Determine the change in the exergy of the refrigerant during this process and the reversible work. Assume the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:57

Problem 36

A $12-\mathrm{ft}^{3}$ rigid tank contains refrigerant-134a at 30 psia and 55 percent quality. Heat is transferred now to the refrigerant from a source at $120^{\circ} \mathrm{F}$ until the pressure rises to 50 psia. Assuming the surroundings to be at $75^{\circ} \mathrm{F}$, determine $(a)$ the amount of heat transfer between the source and the refrigerant and $(b)$ the exergy destroyed during this process. Answers: (a) 447 Btu, (b) 77.8.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:09

Problem 37

Oxygen gas is compressed in a piston-cylinder device from an initial state of $12 \mathrm{ft}^{3} / \mathrm{lbm}$ and $75^{\circ} \mathrm{F}$ to a final state of $1.5 \mathrm{ft}^{3} / \mathrm{lbm}$ and $525^{\circ} \mathrm{F}$. Determine the reversible work input and the increase in the exergy of the oxygen during this process. Assume the surroundings to be at 14.7 psia and $75^{\circ} \mathrm{F}$.

Jincy M Saji
Jincy M Saji
Numerade Educator
06:21

Problem 38

A piston-cylinder device initially contains $2 \mathrm{~L}$ of air at $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$. Air is now compressed to a final state of $600 \mathrm{kPa}$ and $150^{\circ} \mathrm{C}$. The useful work input is $1.2 \mathrm{~kJ}$. Assuming the surroundings are at $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$, determine
( $a$ ) the exergy of the air at the initial and the final states,
(b) the minimum work that must be supplied to accomplish this compression process, and (c) the second-law efficiency of this process.

Narayan Hari
Narayan Hari
Numerade Educator
04:15

Problem 39

$8-39$ A $0.8-\mathrm{m}^{3}$ insulated rigid tank contains $1.54 \mathrm{~kg}$ of carbon dioxide at $100 \mathrm{kPa}$. Now paddle-wheel work is done on the system until the pressure in the tank rises to $135 \mathrm{kPa}$. Determine $(a)$ the actual paddle-wheel work done during this process and $(b)$ the minimum paddle-wheel work with which this process (between the same end states) could be accomplished. Take $T_{0}=298 \mathrm{~K}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:23

Problem 40

An insulated piston-cylinder device initially contains $20 \mathrm{~L}$ of air at $140 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$. Air is now heated for 10 min by a $100-W$ resistance heater placed inside the cylinder. The pressure of air is kept constant during this process, and the surroundings are at $27^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$. Determine the exergy destroyed during this process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:21

Problem 41

A rigid tank is divided into two equal parts by a partition. One part of the tank contains $4 \mathrm{~kg}$ of compressed liquid water at $200 \mathrm{kPa}$ and $80^{\circ} \mathrm{C}$ and the other side is evacuated. Now the partition is removed, and the water expands to fill the entire tank. If the final pressure in the tank is $40 \mathrm{kPa}$, determine the exergy destroyed during this process. Assume the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:58

Problem 42

Using appropriate software, study the effect of final pressure in the tank on the exergy destroyed during the process. Plot the exergy destroyed as a function of the final pressure for final pressures between 45 and $5 \mathrm{kPa}$, and discuss the results.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:38

Problem 43

An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains $3 \mathrm{~kg}$ of argon gas at $300 \mathrm{kPa}$ and $70^{\circ} \mathrm{C},$ and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Assuming the surroundings to be at $25^{\circ} \mathrm{C},$ determine the exergy destroyed during this process.

Nathan Nowack
Nathan Nowack
Numerade Educator
05:58

Problem 44

A $50-\mathrm{kg}$ iron block and a $20-\mathrm{kg}$ copper block, both initially at $80^{\circ} \mathrm{C}$, are dropped into a large lake at $15^{\circ} \mathrm{C}$. Thermal equilibrium is established after a while as a result of heat transfer between the blocks and the lake water. Assuming the surroundings to be at $20^{\circ} \mathrm{C}$, determine the amount of work that could have been produced if the entire process were executed in a reversible manner.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:35

Problem 45

Carbon steel balls $\left(\rho=7833 \mathrm{~kg} / \mathrm{m}^{3}\right.$ and $c_{p}=0.465 \mathrm{~kJ} /$
$\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ ) $8 \mathrm{~mm}$ in diameter are annealed by heating them first to $900^{\circ} \mathrm{C}$ in a furnace and then allowing them to cool slowly to $100^{\circ} \mathrm{C}$ in ambient air at $35^{\circ} \mathrm{C}$. If 1200 balls are to be annealed per hour, determine $(a)$ the rate of heat transfer from the balls to the air and $(b)$ the rate of exergy destruction due to heat loss from the balls to the air.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:46

Problem 46

A 70 -lbm copper block initially at $220^{\circ} \mathrm{F}$ is dropped into an insulated tank that contains $1.2 \mathrm{ft}^{3}$ of water at $65^{\circ} \mathrm{F}$ Determine $(a)$ the final equilibrium temperature and $(b)$ the work potential wasted during this process. Assume the surroundings to be at $65^{\circ} \mathrm{F}$.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
02:17

Problem 47

An ordinary egg can be approximated as a $5.5-\mathrm{cm}-$ diameter sphere. The egg is initially at a uniform temperature of $8^{\circ} \mathrm{C}$ and is dropped into boiling water at $97^{\circ} \mathrm{C}$. Taking the properties of egg to be $\rho=1020 \mathrm{~kg} / \mathrm{m}^{3}$ and $c_{p}=3.32 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ determine how much heat is transferred to the egg by the time the average temperature of the egg rises to $85^{\circ} \mathrm{C}$ and the amount of exergy destruction associated with this heat transfer process. Take $T_{0}=25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:14

Problem 48

A piston-cylinder device initially contains $1.4 \mathrm{~kg}$ of refrigerant- $134 \mathrm{a}$ at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. Heat is now transferred to the refrigerant from a source at $150^{\circ} \mathrm{C}$, and the piston, which is resting on a set of stops, starts moving when the pressure inside reaches $120 \mathrm{kPa}$. Heat transfer continues until the temperature reaches $80^{\circ} \mathrm{C}$. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, determine $(a)$ the work done, $(b)$ the heat transfer, (c) the exergy destroyed, and ( $d$ ) the second-law efficiency of this process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:15

Problem 49

A $0.04-\mathrm{m}^{3}$ tank initially contains air at ambient conditions of $100 \mathrm{kPa}$ and $22{ }^{\circ} \mathrm{C}$. Now, a $15-\mathrm{L}$ tank containing liquid water at $85^{\circ} \mathrm{C}$ is placed into the tank without causing any air to escape. After some heat transfer from the water to the air and the surroundings, both the air and water are measured to be at $44^{\circ} \mathrm{C}$. Determine $(a)$ the amount of heat lost to the surroundings and $(b)$ the exergy destruction during this process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:57

Problem 50

$Steam is throttled from $8 \mathrm{MPa}$ and $450^{\circ} \mathrm{C}$ to $6 \mathrm{MPa}$. Determine the wasted work potential during this throttling process. Assume the surroundings to be at $25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:56

Problem 51

$ Refrigerant- 134 a enters an expansion valve at $1200 \mathrm{kPa}$ as a saturated liquid and leaves at $200 \mathrm{kPa}$. Determine $(a)$ the temperature of $\mathrm{R}-134 \mathrm{a}$ at the outlet of the expansion valve and (b) the entropy generation and the exergy destruction during this process. Take $T_{0}=25^{\circ} \mathrm{C}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:20

Problem 52

$Air enters a nozzle steadily at $200 \mathrm{kPa}$ and $65^{\circ} \mathrm{C}$ with a velocity of $35 \mathrm{~m} / \mathrm{s}$ and exits at $95 \mathrm{kPa}$ and $240 \mathrm{~m} / \mathrm{s}$. The heat loss from the nozzle to the surrounding medium at $17^{\circ} \mathrm{C}$ is estimated to be $3 \mathrm{~kJ} / \mathrm{kg}$. Determine $(a)$ the exit temperature and ( $b$ ) the exergy destroyed during this process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:32

Problem 53

$ Reconsider Prob. 8-52. Using appropriate software, study the effect of varying the nozzle exit velocity from 100 to $300 \mathrm{~m} / \mathrm{s}$ on both the exit temperature and exergy destroyed, and plot the results.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:22

Problem 54

$ Reconsider Prob. 8-52. Using appropriate software, study the effect of varying the nozzle exit velocity from 100 to $300 \mathrm{~m} / \mathrm{s}$ on both the exit temperature and exergy destroyed, and plot the results.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:12

Problem 55

$Steam enters a diffuser at $10 \mathrm{kPa}$ and $60^{\circ} \mathrm{C}$ with a velocity of $375 \mathrm{~m} / \mathrm{s}$ and exits as saturated vapor at $50^{\circ} \mathrm{C}$ and $70 \mathrm{~m} / \mathrm{s}$. The exit area of the diffuser is $3 \mathrm{~m}^{2}$. Determine $(a)$ the mass flow rate of the steam and ( $b$ ) the wasted work potential during this process. Assume the surroundings to be at $25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:21

Problem 56

$Argon gas enters an adiabatic compressor at $120 \mathrm{kPa}$ and $30^{\circ} \mathrm{C}$ with a velocity of $20 \mathrm{~m} / \mathrm{s}$ and exits at $1.2 \mathrm{MPa}$, $530^{\circ} \mathrm{C}$, and $80 \mathrm{~m} / \mathrm{s}$. The inlet area of the compressor is $130 \mathrm{~cm}^{2}$. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$, determine the reversible power input and exergy destroyed.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:11

Problem 57

$Air enters a compressor at 14.7 psia and $77^{\circ} \mathrm{F}$ and is compressed to 140 psia and $200^{\circ} \mathrm{F}$. Determine the minimum work required for this compression, in $\mathrm{Btu} / \mathrm{lbm},$ with the same inlet and outlet states. Does the minimum work require an adiabatic compressor?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:11

Problem 58

$Air is compressed by a compressor from $101 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$ to $400 \mathrm{kPa}$ and $220^{\circ} \mathrm{C}$ at a rate of $0.15 \mathrm{~kg} / \mathrm{s}$. Neglect-
ing the changes in kinetic and potential energies and assuming the surroundings to be at $25^{\circ} \mathrm{C},$ determine the reversible power input for this process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:51

Problem 59

Using appropriate software, investigate the effect of compressor exit pressure on reversible power. Vary the compressor exit pressure from 200 to $600 \mathrm{kPa}$ while keeping the exit temperature at $220^{\circ} \mathrm{C}$. Plot the reversible power input for this process as a function of the compressor exit pressure.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:49

Problem 60

The adiabatic compressor of a refrigeration system compresses R-134a from a saturated vapor at $160 \mathrm{kPa}$ to $800 \mathrm{kPa}$ and $50^{\circ} \mathrm{C}$. What is the minimum power required by this compressor when its mass flow rate is $0.1 \mathrm{~kg} / \mathrm{s} ?$ Take $T_{0}=25^{\circ} \mathrm{C}$.

RZ
Rubeena Zulfiqar
Numerade Educator
04:33

Problem 61

Refrigerant $-134 \mathrm{a}$ at $140 \mathrm{kPa}$ and $-10^{\circ} \mathrm{C}$ is compressed by an adiabatic $0.5-\mathrm{kW}$ compressor to an exit state of $700 \mathrm{kPa}$ and $60^{\circ} \mathrm{C}$. Neglecting the changes in kinetic and potential energies and assuming the surroundings to be at $27^{\circ} \mathrm{C}$, determine
( $a$ ) the isentropic efficiency and (b) the second-law efficiency of the compressor.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:23

Problem 62

Airenters a compressor at ambient conditions of $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$ at a rate of $6.2 \mathrm{~m}^{3} / \mathrm{s}$ with a low velocity and exits at $900 \mathrm{kPa}, 60^{\circ} \mathrm{C}$, and $80 \mathrm{~m} / \mathrm{s}$. The compressor is cooled by cooling water that experiences a temperature rise of $10^{\circ} \mathrm{C}$. The isothermal efficiency of the compressor is 70 percent. Determine (a) the actual and reversible power inputs, (b) the second-law efficiency, and ( $c$ ) the mass flow rate of the cooling water.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:06

Problem 63

Combustion gases enter a gas turbine at $900^{\circ} \mathrm{C}, 800 \mathrm{kPa}$ and $100 \mathrm{~m} / \mathrm{s}$ and leave at $650^{\circ} \mathrm{C}, 400 \mathrm{kPa}$, and $220 \mathrm{~m} / \mathrm{s}$.
Taking $c_{p}=1.15 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ and $k=1.3$ for the combustion gases, determine $(a)$ the exergy of the combustion gases at the turbine inlet and $(b)$ the work output of the turbine under reversible conditions. Assume the surroundings to be at $25^{\circ} \mathrm{C}$ and 100 kPa. Can this turbine be adiabatic?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:04

Problem 64

Steam enters a turbine at $9 \mathrm{MPa}, 600^{\circ} \mathrm{C},$ and $60 \mathrm{~m} / \mathrm{s}$ and leaves at $20 \mathrm{kPa}$ and $90 \mathrm{~m} / \mathrm{s}$ with a moisture content of 5 percent. The turbine is not adequately insulated, and it estimated that heat is lost from the turbine at a rate of $220 \mathrm{~kW}$. The power output of the turbine is $4.5 \mathrm{MW}$. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$, determine $(a)$ the reversible power output of the turbine, $(b)$ the exergy destroyed within the turbine, and $(c)$ the second-law efficiency of the turbine. ( $d$ ) Also, estimate the possible increase in the power output of the turbine if the turbine were perfectly insulated.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:36

Problem 65

Refrigerant-134a is condensed in a refrigeration system by rejecting heat to ambient air at $25^{\circ} \mathrm{C}$. $\mathrm{R}-134 \mathrm{a}$ enters the condenser at $700 \mathrm{kPa}$ and $50^{\circ} \mathrm{C}$ at a rate of $0.05 \mathrm{~kg} / \mathrm{s}$ and leaves at the same pressure as a saturated liquid. Determine (a) the rate of heat rejected in the condenser, $(b)$ the $\mathrm{COP}$ of this refrigeration cycle if the cooling load at these conditions is $6 \mathrm{~kW},$ and $(c)$ the rate of exergy destruction in the condenser.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:19

Problem 66

Air enters the evaporator section of a window air conditioner at $100 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$ with a volume flow rate of $6 \mathrm{~m}^{3} / \mathrm{min}$. Refrigerant-134a at $120 \mathrm{kPa}$ with a quality of 0.3 enters the evaporator at a rate of $2 \mathrm{~kg} / \mathrm{min}$ and leaves as saturated vapor at the same pressure. Determine the exit temperature of the air and the exergy destruction for this process, assuming $(a)$ the outer surfaces of the air conditioner are insulated and $(b)$ heat is transferred to the evaporator of the air conditioner from the surrounding medium at $32^{\circ} \mathrm{C}$ at a rate of $30 \mathrm{~kJ} / \mathrm{min}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
06:11

Problem 67

Refrigerant- 22 absorbs heat from a cooled space at $50^{\circ} \mathrm{F}$ as it flows through an evaporator of a refrigeration system. R-22 enters the evaporator at $10^{\circ} \mathrm{F}$ at a rate of $0.08 \mathrm{lbm} / \mathrm{s}$ with a quality of 0.3 and leaves as a saturated vapor at the same pressure. Determine $(a)$ the rate of cooling provided, in $\mathrm{Btu} / \mathrm{h}$, (b) the rate of exergy destruction in the evaporator, and (c) the second-law efficiency of the evaporator. Take $T_{0}=77^{\circ} \mathrm{F}$. The properties of $\mathrm{R}-22$ at the inlet and exit of the evaporator are:
$h_{1}=107.5 \mathrm{Btu} / \mathrm{lbm}, s_{1}=0.2851 \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R}, h_{2}=172.1 \mathrm{Btu} /$ Ibm, $s_{2}=0.4225 \mathrm{Btu} / \mathrm{lbm} \cdot \mathrm{R}$

RZ
Rubeena Zulfiqar
Numerade Educator
02:19

Problem 68

Steam expands in a turbine steadily at a rate of 18,000 $\mathrm{kg} / \mathrm{h}$, entering at $7 \mathrm{MPa}$ and $600^{\circ} \mathrm{C}$ and leaving at $50 \mathrm{kPa}$ as saturated vapor. Assuming the surroundings to be at $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$, determine $(a)$ the power potential of the steam at the inlet conditions and $(b)$ the power output of the turbine if there were no irreversibilities present.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:56

Problem 69

An adiabatic turbine operates with air entering at $550 \mathrm{kPa}, 425 \mathrm{~K},$ and $150 \mathrm{~m} / \mathrm{s}$ and leaving at $110 \mathrm{kPa}, 325 \mathrm{~K}$ and $50 \mathrm{~m} / \mathrm{s}$. Determine the actual and maximum work production for this turbine, in $\mathrm{kJ} / \mathrm{kg}$. Why are the maximum and actual works not the same? Take $T_{0}=25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:17

Problem 70

Air enters a compressor at ambient conditions of 15 psia and $60^{\circ} \mathrm{F}$ with a low velocity and exits at 150 psia, $620^{\circ} \mathrm{F}$, and $350 \mathrm{ft} / \mathrm{s}$. The compressor is cooled by the ambient air at $60^{\circ} \mathrm{F}$ at a rate of $1500 \mathrm{Btu} / \mathrm{min}$. The power input to the compressor is 400 hp. Determine $(a)$ the mass flow rate of air and $(b)$ the portion of the power input that is used just to overcome the irreversibilities.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:36

Problem 71

Hot combustion gases enter the nozzle of a turbojet engine at $230 \mathrm{kPa}, 627^{\circ} \mathrm{C}$, and $60 \mathrm{~m} / \mathrm{s}$ and exit at $70 \mathrm{kPa}$ and $450^{\circ} \mathrm{C}$. Assuming the nozzle to be adiabatic and the surroundings to be at $20^{\circ} \mathrm{C}$, determine $(a)$ the exit velocity and $(b)$ the decrease in the exergy of the gases. Take $k=1.3$ and $c_{p}=$ $1.15 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ for the combustion gases.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
05:32

Problem 72

Ambient air at $100 \mathrm{kPa}$ and $300 \mathrm{~K}$ is compressed isentropically in a steady-flow device to 0.8 MPa. Determine ( $a$ ) the work input to the compressor, $(b)$ the exergy of the air at the compressor exit, and ( $c$ ) the exergy of compressed air after it is cooled to $300 \mathrm{~K}$ at 0.8 MPa pressure.

Nathan Nowack
Nathan Nowack
Numerade Educator
05:48

Problem 73

A $0.6-\mathrm{m}^{3}$ rigid tank is filled with saturated liquid water at $135^{\circ} \mathrm{C}$. A valve at the bottom of the tank is now opened, and one-half of the total mass is withdrawn from the tank in liquid form. Heat is transferred to water from a source of $210^{\circ} \mathrm{C}$ so that the temperature in the tank remains constant. Determine ( $a$ ) the amount of heat transfer and $(b)$ the reversible work and exergy destruction for this process. Assume the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:33

Problem 74

How much exergy is lost in a rigid vessel filled with $1 \mathrm{~kg}$ of liquid $\mathrm{R}-134 \mathrm{a}$, whose temperature remains constant at $30^{\circ} \mathrm{C},$ as $\mathrm{R}-134 \mathrm{a}$ vapor is released from the vessel? This vessel may exchange heat with the surrounding atmosphere, which is at $100 \mathrm{kPa}$ and $30^{\circ} \mathrm{C}$. The vapor is released until the last of the liquid inside the vessel disappears.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
08:15

Problem 75

A vertical piston-cylinder device initially contains $0.12 \mathrm{~m}^{3}$ of helium at $20^{\circ} \mathrm{C}$. The mass of the piston is such that it maintains a constant pressure of $200 \mathrm{kPa}$ inside. A valve is now opened, and helium is allowed to escape until the volume inside the cylinder is decreased by one-half. Heat transfer takes place between the helium and its surroundings at $20^{\circ} \mathrm{C}$ and $95 \mathrm{kPa}$ so that the temperature of helium in the cylinder remains constant. Determine $(a)$ the maximum work potential of the helium at the initial state and $(b)$ the exergy destroyed during this process.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
07:14

Problem 76

An insulated vertical piston-cylinder device initially contains $15 \mathrm{~kg}$ of water, $13 \mathrm{~kg}$ of which is in the vapor phase. The mass of the piston is such that it maintains a constant pressure of $300 \mathrm{kPa}$ inside the cylinder. Now steam at $2 \mathrm{MPa}$ and $400^{\circ} \mathrm{C}$ is allowed to enter the cylinder from a supply line until all the liquid in the cylinder is vaporized. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, determine $(a)$ the amount of steam that has entered and $(b)$ the exergy destroyed during this process.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
02:44

Problem 77

Liquid water at $200 \mathrm{kPa}$ and $15^{\circ} \mathrm{C}$ is heated in a chamber by mixing it with superheated steam at $200 \mathrm{kPa}$ and $200^{\circ} \mathrm{C}$. Liquid water enters the mixing chamber at a rate of $4 \mathrm{~kg} / \mathrm{s},$ and the chamber is estimated to lose heat to the surrounding air at $25^{\circ} \mathrm{C}$ at a rate of $600 \mathrm{~kJ} / \mathrm{min}$. If the mixture leaves the mixing chamber at $200 \mathrm{kPa}$ and $80^{\circ} \mathrm{C}$, determine $(a)$ the mass flow rate of the superheated steam and $(b)$ the wasted work potential during this mixing process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:59

Problem 78

Consider a family of four, with each person taking a 6-min shower every morning. The average flow rate through the shower head is $10 \mathrm{~L} / \mathrm{min}$. City water at $15^{\circ} \mathrm{C}$ is heated to $55^{\circ} \mathrm{C}$ in an electric water heater and tempered to $42^{\circ} \mathrm{C}$ by cold water at the T-elbow of the shower before being routed to the shower head. Determine the amount of exergy destroyed by this family per year as a result of taking daily showers. Take $T_{0}=25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:46

Problem 79

Outdoor air $\left(c_{p}=1.005 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ is to be preheated
by hot exhaust gases in a crossflow heat exchanger before it enters the furnace. Air enters the heat exchanger at $101 \mathrm{kPa}$ and $30^{\circ} \mathrm{C}$ at a rate of $0.5 \mathrm{~m}^{3} / \mathrm{s}$. The combustion gases $\left(c_{p}=\right.$ $1.10 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ ) enter at $350^{\circ} \mathrm{C}$ at a rate of $0.85 \mathrm{~kg} / \mathrm{s}$ and leave
at $260^{\circ} \mathrm{C}$. Determine the rate of heat transfer to the air and the rate of exergy destruction in the heat exchanger.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:16

Problem 80

A well-insulated shell-and-tube heat exchanger is used to heat water $\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ in the tubes from 20 to $70^{\circ} \mathrm{C}$
at a rate of $4.5 \mathrm{~kg} / \mathrm{s}$. Heat is supplied by hot oil $\left(c_{p}=2.30 \mathrm{~kJ} /\right.$ $\mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ ) that enters the shell side at $170^{\circ} \mathrm{C}$ at a rate of $10 \mathrm{~kg} / \mathrm{s}$
Disregarding any heat loss from the heat exchanger, determine $(a)$ the exit temperature of oil and $(b)$ the rate of exergy destruction in the heat exchanger. Take $T_{0}=25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:16

Problem 81

Steam is to be condensed on the shell side of a hez exchanger at $120^{\circ} \mathrm{F}$. Cooling water enters the tubes at $60^{\circ}$ at a rate of $115.3 \mathrm{lbm} / \mathrm{s}$ and leaves at $73^{\circ} \mathrm{F}$. Assuming th heat exchanger to be well insulated, determine $(a)$ the rate $\mathrm{c}$ heat transfer in the heat exchanger and $(b)$ the rate of exerg destruction in the heat exchanger. Take $T_{0}=77^{\circ} \mathrm{F}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:30

Problem 82

A $0.1-m^{3}$ rigid tank initially contains refrigerant- $134 a$ at $1.2 \mathrm{MPa}$ and 100 percent quality. The tank is connected by a valve to a supply line that carries refrigerant- $134 \mathrm{a}$ at $1.6 \mathrm{MPa}$ and $30^{\circ} \mathrm{C}$. The valve is now opened, allowing the refrigerant to enter the tank, and it is closed when the tank contains only saturated vapor at 1.4 MPa. The refrigerant exchanges heat with a source at $200^{\circ} \mathrm{C}$ during this process. The surroundings are at $15^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$. Determine $(a)$ the mass of the refrigerant that entered the tank and $(b)$ the exergy destroyed during this process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:45

Problem 83

A $0.2-\mathrm{m}^{3}$ rigid tank initially contains saturated refrigerant- 134 a vapor at 1 MPa. The tank is connected by a valve to a supply line that carries refrigerant- $134 \mathrm{a}$ at $1.4 \mathrm{MPa}$ and $60^{\circ} \mathrm{C}$. The valve is now opened, and the refrigerant is allowed to enter the tank. The valve is closed when one-half of the volume of the tank is filled with liquid and the rest with vapor at 1.2 MPa. The refrigerant exchanges heat during this process with the surroundings at $25^{\circ} \mathrm{C}$. Determine $(a)$ the amount of heat transfer and $(b)$ the exergy destruction associated with this process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:21

Problem 84

Derive an expression for the work potential of the single-phase contents of a rigid adiabatic container when the initially empty container is filled through a single opening from a source of working fluid whose properties remain fixed.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:00

Problem 85

A refrigerator has a second-law efficiency of }\end{array}$ 28 percent, and heat is removed from the refrigerated space at a rate of $800 \mathrm{Btu} / \mathrm{min}$. If the space is maintained at $25^{\circ} \mathrm{F}$ while the surrounding air temperature is $90^{\circ} \mathrm{F}$, determine the power input to the refrigerator.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:12

Problem 86

The inner and outer surfaces of a $0.5-\mathrm{cm}$ -thick, $2-\mathrm{m} \times$ $2-\mathrm{m}$ window glass in winter are $10^{\circ} \mathrm{C}$ and $3^{\circ} \mathrm{C}$, respectively. If the rate of heat loss through the window is $4.4 \mathrm{~kJ} / \mathrm{s}$, determine the amount of heat loss, in $\mathrm{kJ},$ through the glass over a period of $5 \mathrm{~h}$. Also, determine the exergy destruction associated with this process. Take $T_{0}=5^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:53

Problem 87

An aluminum pan has a flat bottom whose diameter is $30 \mathrm{~cm}$. Heat is transferred steadily to boiling water in the pan through its bottom at a rate of $1100 \mathrm{~W}$. If the temperatures of the inner and outer surfaces of the bottom of the pan are $104^{\circ} \mathrm{C}$ and $105^{\circ} \mathrm{C}$, respectively, determine the rate of exergy destruction within the bottom of the pan during this process, in $W$. Take $T_{0}=25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:01

Problem 88

A $5-\mathrm{cm}$ -external-diameter, 10 -m-long hot water pipe at $80^{\circ} \mathrm{C}$ is losing heat to the surrounding air at $5^{\circ} \mathrm{C}$ by natural convection at a rate of $1175 \mathrm{~W}$. Determine the rate at which the work potential is wasted during this process as a result of this heat loss.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
09:06

Problem 89

Steam is condensed in a closed system at a constant pressure of $75 \mathrm{kPa}$ from a saturated vapor to a saturated liquid by rejecting heat to a thermal energy reservoir at $37^{\circ} \mathrm{C}$. Determine the second-law efficiency of this process. Take $T_{0}=25^{\circ} \mathrm{C}$ and $P_{0}=100 \mathrm{kPa}.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
04:30

Problem 90

Refrigerant-134a is converted from a saturated liquid to a saturated vapor in a closed system using a reversible constant-pressure process by transferring heat from a heat reservoir at $6^{\circ} \mathrm{C}$. From a second-law point of view, is it more effective to do this phase change at $100 \mathrm{kPa}$ or $180 \mathrm{kPa}$ ? Take $T_{0}=25^{\circ} \mathrm{C}$ and $P_{0}=100 \mathrm{kPa}.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:34

Problem 91

A well-insulated, thin-walled, counterflow heat }\end{array}$ exchanger is to be used to cool oil $\left(c_{p}=2.20 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ from 150 to $40^{\circ} \mathrm{C}$ at a rate of $2 \mathrm{~kg} / \mathrm{s}$ with water $\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ that enters at $22^{\circ} \mathrm{C}$ at a rate of $1.5 \mathrm{~kg} / \mathrm{s}$. The diameter of the tube is $2.5 \mathrm{~cm},$ and its length is $6 \mathrm{~m}$. Determine $(a)$ the rate of heat transfer and $(b)$ the rate of exergy destruction in the heat exchanger.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:56

Problem 92

A well-insulated heat exchanger is to heat water $\left(c_{p}=4.18 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ from $25^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ at a rate of $0.4 \mathrm{~kg} / \mathrm{s}$ The heating is to be accomplished by geothermal water $\left(c_{p}=4.31 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ available at $140^{\circ} \mathrm{C}$ at a mass flow rate of $0.3 \mathrm{~kg} / \mathrm{s}$. The inner tube is thin-walled and has a diameter of $0.6 \mathrm{~cm}$. Determine $(a)$ the rate of heat transfer and $(b)$ the rate of exergy destruction in the heat exchanger.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
View

Problem 93

Hot exhaust gases leaving an internal combustion engine at $400^{\circ} \mathrm{C}$ and $150 \mathrm{kPa}$ at a rate of $0.8 \mathrm{~kg} / \mathrm{s}$ are to be used to produce saturated steam at $200^{\circ} \mathrm{C}$ in an insulated heat exchanger. Water enters the heat exchanger at the ambient temperature of $20^{\circ} \mathrm{C}$, and the exhaust gases leave the heat exchanger at $350^{\circ} \mathrm{C}$. Determine $(a)$ the rate of steam production, (b) the rate of exergy destruction in the heat exchanger, and $(c)$ the second-law efficiency of the heat exchanger.

Victor Salazar
Victor Salazar
Numerade Educator
01:39

Problem 94

A crater lake has a base area of $20,000 \mathrm{~m}^{2},$ and the water it contains is $12 \mathrm{~m}$ deep. The ground surrounding the crater is nearly flat and is $105 \mathrm{~m}$ below the base of the lake. Determine the maximum amount of electrical work, in $\mathrm{kWh}$, that can be generated by feeding this water to a hydroelectric power plant.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:24

Problem 95

A $30-\mathrm{cm}$ -long, $1500-\mathrm{W}$ electric resistance heating element whose diameter is $1.2 \mathrm{~cm}$ is immersed in $70 \mathrm{~kg}$ of water initially at $20^{\circ} \mathrm{C}$. Assuming the water container is well insulated, determine how long it will take for this heater to raise the water temperature to $80^{\circ} \mathrm{C}$. Also, determine the minimum work input required and the exergy destruction for this process, in kJ. Take $T_{0}=20^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
07:55

Problem 96

Nitrogen gas enters a diffuser at $100 \mathrm{kPa}$ and $110^{\circ} \mathrm{C}$ with a velocity of $205 \mathrm{~m} / \mathrm{s}$ and leaves at $110 \mathrm{kPa}$ and $45 \mathrm{~m} / \mathrm{s}$. It is estimated that $2.5 \mathrm{~kJ} / \mathrm{kg}$ of heat is lost from the diffuser to the surroundings at $100 \mathrm{kPa}$ and $27^{\circ} \mathrm{C}$. The exit area of the diffuser is $0.04 \mathrm{~m}^{2}$. Accounting for the variation of the specific heats with temperature, determine ( $a$ ) the exit temperature, (b) the rate of exergy destruction, and ( $c$ ) the second-law efficiency of the diffuser.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:26

Problem 97

An adiabatic steam nozzle has steam entering at $300 \mathrm{kPa}, 150^{\circ} \mathrm{C},$ and $45 \mathrm{~m} / \mathrm{s},$ and leaving as a saturated vapor at $150 \mathrm{kPa}$. Calculate the actual and maximum outlet velocity. Take $T_{0}=25^{\circ} \mathrm{C}$.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
06:16

Problem 98

Steam enters an adiabatic nozzle at $3.5 \mathrm{MPa}$ and $300^{\circ} \mathrm{C}$ with a low velocity and leaves at $1.6 \mathrm{MPa}$ and $250^{\circ} \mathrm{C}$ at a rate of $0.4 \mathrm{~kg} / \mathrm{s}$. If the ambient state is $100 \mathrm{kPa}$ and $18^{\circ} \mathrm{C}$, determine $(a)$ the exit velocity, $(b)$ the rate of exergy destruction, and $(c)$ the second-law efficiency.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
41:09

Problem 99

Two rigid tanks are connected by a valve. Tank $A$ is insulated and contains $0.2 \mathrm{~m}^{3}$ of steam at $400 \mathrm{kPa}$ and 80 percent quality. Tank $B$ is uninsulated and contains $3 \mathrm{~kg}$ of steam at $200 \mathrm{kPa}$ and $250^{\circ} \mathrm{C}$. The valve is now opened, and steam flows from tank $A$ to tank $B$ until the pressure in tank $A$ drops to $300 \mathrm{kPa}$. During this process $900 \mathrm{~kJ}$ of heat is transferred from tank $B$ to the surroundings at $0^{\circ} \mathrm{C}$. Assuming the steam remaining inside tank $A$ to have undergone a reversible adiabatic process, determine $(a)$ the final temperature in each tank and $(b)$ the work potential wasted during this process.

Prabhat Tyagi
Prabhat Tyagi
Numerade Educator
04:57

Problem 100

A piston-cylinder device initially contains $8 \mathrm{ft}^{3}$ of helium gas at 40 psia and $70^{\circ} \mathrm{F}$. Helium is now compressed in a polytropic process $\left(P U^{n}=\right.$ constant $)$ to 140 psia and $320^{\circ} \mathrm{F}$ Assuming the surroundings to be at 14.7 psia and $70^{\circ} \mathrm{F}$, determine $(a)$ the actual useful work consumed and $(b)$ the minimum useful work input needed for this process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:42

Problem 101

An adiabatic turbine operates with air entering at $550 \mathrm{kPa}$ and $425 \mathrm{~K}$ and leaving at $110 \mathrm{kPa}$ and $325 \mathrm{~K}$. Calculate the second-law efficiency of this turbine. Take $T_{0}=25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
07:39

Problem 102

Steam at $7 \mathrm{MPa}$ and $400^{\circ} \mathrm{C}$ enters a two-stage adiabatic turbine at a rate of $15 \mathrm{~kg} / \mathrm{s}$. Ten percent of the steam is extracted at the end of the first stage at a pressure of $1.8 \mathrm{MPa}$ for other use. The remainder of the steam is further expanded in the second stage and leaves the turbine at $10 \mathrm{kPa}$. If the turbine has an isentropic efficiency of 88 percent, determine the wasted power potential during this process as a result of irreversibilities. Assume the surroundings to be at $25^{\circ} \mathrm{C}$.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:33

Problem 103

Argon gas enters an adiabatic turbine at $1350^{\circ} \mathrm{F}$ and 200 psia at a rate of $40 \mathrm{lbm} / \mathrm{min}$ and exhausts at 20 psia. If the power output of the turbine is $105 \mathrm{hp},$ determine $(a)$ the isentropic efficiency and $(b)$ the second-law efficiency of the turbine. Assume the surroundings to be at $77^{\circ} \mathrm{F}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
05:19

Problem 104

Steam enters a two-stage adiabatic turbine at $8 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$. It expands in the first stage to a state of $2 \mathrm{MPa}$ and $350^{\circ} \mathrm{C}$. Steam is then reheated at constant pressure to a temperature of $500^{\circ} \mathrm{C}$ before it is routed to the second stage, where it exits at $30 \mathrm{kPa}$ and a quality of 97 percent. The work output of the turbine is $5 \mathrm{MW}$. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$, determine the reversible power output and the rate of exergy destruction within this turbine.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
09:24

Problem 105

To control an isentropic steam turbine, a throttle valve is placed in the steam line leading to the turbine inlet. Steam at $6 \mathrm{MPa}$ and $600^{\circ} \mathrm{C}$ is supplied to the throttle inlet, and the turbine exhaust pressure is set at $40 \mathrm{kPa}$. What is the effect on the stream exergy at the turbine inlet when the throttle valve is partially closed such that the pressure at the turbine inlet is 2 MPa? Compare the second-law efficiency of this system when the valve is partially open to when it is fully open. Take $T_{0}=25^{\circ} \mathrm{C}$.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
11:58

Problem 106

Consider a well-insulated horizontal rigid cylinder that is divided into two compartments by a piston that is free to move but does not allow either gas to leak into the other side. Initially, one side of the piston contains $1 \mathrm{~m}^{3}$ of $\mathrm{N}_{2}$ gas at $500 \mathrm{kPa}$ and $80^{\circ} \mathrm{C}$ while the other side contains $1 \mathrm{~m}^{3}$ of He gas at $500 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$. Now thermal equilibrium is established in the cylinder as a result of heat transfer through the piston. Using constant specific heats at room temperature, determine ( $a$ ) the final equilibrium temperature in the cylinder and $(b)$ the wasted work potential during this process. What would your answer be if the piston were not free to move? Take $T_{0}=25^{\circ} \mathrm{C}$.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
06:49

Problem 107

Repeat Prob. $8-106$ by assuming the piston is made of $5 \mathrm{~kg}$ of copper initially at the average temperature of the two gases on both sides.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:12

Problem 108

One ton of liquid water at $65^{\circ} \mathrm{C}$ is brought into a wellinsulated and well-sealed $3-m \times 4-m \times 7-m$ room initially at $16^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$. Assuming constant specific heats for both the air and water at room temperature, determine $(a)$ the final equilibrium temperature in the room, $(b)$ the exergy destruction, $(c)$ the maximum amount of work that can be produced during this process, in $\mathrm{kJ}$. Take $T_{0}=10^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:53

Problem 109

In large steam power plants, the feedwater is often heated in closed feedwater heaters, which are basically heat exchangers, by steam extracted from the turbine at some stage. Steam enters the feedwater heater at $1.6 \mathrm{MPa}$ and $250^{\circ} \mathrm{C}$ and leaves as saturated liquid at the same pressure. Feedwater enters the heater at 4 MPa and $30^{\circ} \mathrm{C}$ and leaves $10^{\circ} \mathrm{C}$ below the exit temperature of the steam. Neglecting any heat losses from the outer surfaces of the heater, determine $(a)$ the ratio of the mass flow rates of the extracted steam and the feedwater heater and $(b)$ the reversible work for this process per unit mass of the feedwater. Assume the surroundings to be at $25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:10

Problem 110

Reconsider Prob. $8-109 .$ Using appropriate software, investigate the effect of the state of the steam at the inlet of the feedwater heater on the ratio of mass flow rates and the reversible power. Vary the extracted steam pressure between 200 and $2000 \mathrm{kPa} .$ Plot both the ratio of the mass flow rates of the extracted steam and the feedwater heater and the reversible work for this process per unit mass of feed. water as functions of the extraction pressure.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:36

Problem 111

One method of passive solar heating is to stack gallons of liquid water inside the buildings and expose them to the sun. The solar energy stored in the water during the day is released at night to the room air, providing some heating. Consider a house that is maintained at $22^{\circ} \mathrm{C}$ and whose heating is assisted by a $270-\mathrm{L}$ water storage system. If the water is heated to $45^{\circ} \mathrm{C}$ during the day, determine the amount of heating this water will provide to the house at night. Assuming an outside temperature of $5^{\circ} \mathrm{C}$, determine the exergy destruction associated with this process. Answers: $25,900 \mathrm{~kJ}, 904 \mathrm{~kJ}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:19

Problem 112

A passive solar house that was losing heat to the outdoors at $5^{\circ} \mathrm{C}$ at an average rate of $50,000 \mathrm{~kJ} / \mathrm{h}$ was maintained at $22^{\circ} \mathrm{C}$ at all times during a winter night for $10 \mathrm{~h}$. The house was heated by 50 glass containers, each containing $20 \mathrm{~L}$ of water that was heated to $80^{\circ} \mathrm{C}$ during the day by absorbing solar energy. A thermostat-controlled $15-\mathrm{kW}$ backup electric resistance heater turned on whenever necessary to keep the house at $22^{\circ} \mathrm{C}$. Determine $(a)$ how long the electric heating system was on that night, (b) the exergy destruction, and (c) the minimum work input required for that night, in $\mathrm{kJ}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
22:13

Problem 113

A $100-\mathrm{L}$ well-insulated rigid tank is initially filled with nitrogen at $1000 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. Now a valve is opened. and one-half of nitrogen's mass is allowed to escape. Determine the change in the exergy content of the tank.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
07:07

Problem 114

A $4-\mathrm{L}$ pressure cooker has an operating pressure of $175 \mathrm{kPa}$. Initially, one-half of the volume is filled with liquid water and the other half by water vapor. The cooker is now placed on top of a $750-\mathrm{W}$ electrical heating unit that is kept on for 20 min. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa},$ determine $(a)$ the amount of water that remained in the cooker and $(b)$ the exergy destruction associated with the entire process. Answers: (a) $1.51 \mathrm{~kg},$ (b) $689 \mathrm{~kJ}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:20

Problem 115

Repeat Prob. $8-114$ if heat were supplied to the pressure cooker from a heat source at $180^{\circ} \mathrm{C}$ instead of the electrical heating unit?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:53

Problem 116

Consider a 20-L evacuated rigid bottle that is surrounded by the atmosphere at $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$. A valve at the neck of the bottle is now opened and the atmospheric air is allowed to flow into the bottle. The air trapped in the bottle eventually reaches thermal equilibrium with the atmosphere as a result of heat transfer through the wall of the bottle. The valve remains open during the process so that the trapped air also reaches mechanical equilibrium with the atmosphere. Determine the net heat transfer through the wall of the bottle and the exergy destroyed during this filling process.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:15

Problem 117

A rigid $50-L$ nitrogen cylinder is equipped with a safety relief valve set at $1200 \mathrm{kPa}$. Initially, this cylinder contains nitrogen at $1200 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. Heat is now transferred to the nitrogen from a thermal energy reservoir at $500^{\circ} \mathrm{C}$, and nitrogen is allowed to escape until the mass of nitrogen becomes one-half of its initial mass. Determine the change in the nitrogen's work potential as a result of this heating. Take $T_{0}=20^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
08:09

Problem 118

A frictionless piston-cylinder device, shown in Fig. $\mathrm{P} 8-118$, initially contains $0.01 \mathrm{~m}^{3}$ of argon gas at $400 \mathrm{~K}$ and $350 \mathrm{kPa}$. Heat is now transferred to the argon from a furnace at $1200 \mathrm{~K},$ and the argon expands isothermally until its volume is doubled. No heat transfer takes place between the argon and the surrounding atmospheric air, which is at $300 \mathrm{~K}$ and $100 \mathrm{kPa}$. Determine $(a)$ the useful work output, $(b)$ the exergy destroyed, and (c) the maximum work that can be produced during this process.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
07:53

Problem 119

A constant-volume tank contains $30 \mathrm{~kg}$ of nitrogen at $900 \mathrm{~K},$ and a constant-pressure device contains $15 \mathrm{~kg}$ of argon at $300 \mathrm{~K}$. A heat engine placed between the tank and device extracts heat from the high-temperature tank, produces work, and rejects heat to the low-temperature device. Determine the maximum work that can be produced by the heat engine and the final temperatures of the nitrogen and argon. Assume constant specific heats at room temperature.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
25:36

Problem 120

The compressed-air storage tank shown in Fig. $\mathrm{P} 8-120$ has a volume of $500,000 \mathrm{~m}^{3},$ and it initially contains air at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. The isentropic compressor proceeds to compress air that enters the compressor at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$ until the tank is filled at $600 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. All heat exchanges are with the surrounding air at $20^{\circ} \mathrm{C}$. Calculate the change in the work potential of the air stored in the tank. How does this compare to the work required to compress the air as the tank is being filled?

Eric Mockensturm
Eric Mockensturm
Numerade Educator
06:59

Problem 121

Reconsider Prob. $8-120 .$ The air stored in the tank is now released through the isentropic turbine until the tank contents are at $100 \mathrm{kPa}$ and $20^{\circ} \mathrm{C}$. The pressure is always $100 \mathrm{kPa}$ at the turbine outlet, and all heat exchanges are with the surrounding air, which is at $20^{\circ} \mathrm{C}$. How does the total work produced by the turbine compare to the change in the work potential of the air in the storage tank?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:59

Problem 122

$\mathrm{E}$ In a production facility, 1.5 -in-thick, $1-\mathrm{ft} \times 3-\mathrm{ft}$
square brass plates $\left(\rho=532.5 \mathrm{lbm} / \mathrm{ft}^{3}\right.$ and $c_{p}=0.091 \mathrm{Btu} /$
Ibm $\cdot{ }^{\circ} \mathrm{F}$ ) that are initially at a uniform temperature of $75^{\circ} \mathrm{F}$ are heated by passing them through an oven at $1300^{\circ} \mathrm{F}$ at a rate of 175 per minute. If the plates remain in the oven until their average temperature rises to $1000^{\circ} \mathrm{F}$, determine the rate of heat transfer to the plates in the furnace and the rate of exergy destruction associated with this heat transfer process.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:23

Problem 123

Long cylindrical steel rods $\left(\rho=7833 \mathrm{~kg} / \mathrm{m}^{3}\right.$ and $\left.c_{p}=0.465 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right)$ of $10-\mathrm{cm}$ diameter are heat-treated by
drawing them at a velocity of $3 \mathrm{~m} / \mathrm{min}$ through a 6 -m-long oven maintained at $900^{\circ} \mathrm{C}$. If the rods enter the oven at $30^{\circ} \mathrm{C}$ and leave at $700^{\circ} \mathrm{C}$, determine $(a)$ the rate of heat transfer to the rods in the oven and $(b)$ the rate of exergy destruction associated with this heat transfer process. Take $T_{0}=25^{\circ} \mathrm{C}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:22

Problem 124

In a dairy plant, milk at $4^{\circ} \mathrm{C}$ is pasteurized continuously at $72^{\circ} \mathrm{C}$ at a rate of $12 \mathrm{~L} / \mathrm{s}$ for $24 \mathrm{~h} /$ day and 365 days/yr. The milk is heated to the pasteurizing temperature by hot water heated in a natural gas-fired boiler having an efficiency of 82 percent. The pasteurized milk is then cooled by cold water at $18^{\circ} \mathrm{C}$ before it is finally refrigerated back to $4^{\circ} \mathrm{C}$. To save energy and money, the plant installs a regenerator that has an effectiveness of 82 percent. If the cost of natural gas is $\$ 1.30 /$ therm $(1$ therm $=105.500 \mathrm{~kJ}),$ deter mine how much energy and money the regenerator will save this company per year and the annual reduction in exergy destruction.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:21

Problem 125

$- \mathrm{E}$ Refrigerant-134a enters an adiabatic compressor as saturated vapor at 30 psia at a rate of $20 \mathrm{ft}^{3} / \mathrm{min}$ and exits at 70 psia pressure. If the isentropic efficiency of the compressor is 80 percent, determine $(a)$ the actual power input and
(b) the second-law efficiency of the compressor. Assume the surroundings to be at $75^{\circ} \mathrm{F}$. Answers: (a) $2.85 \mathrm{hp}$, (b) 79.8 percent.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:31

Problem 126

$-$ Refrigerant- $134 \mathrm{a}$ at $1600 \mathrm{kPa}$ and $80^{\circ} \mathrm{C}$ is expanded adiabatically in a closed system to $100 \mathrm{kPa}$ with an isentropic expansion efficiency of 85 percent. Determine the second-law efficiency of this expansion. Take $T_{0}=25^{\circ} \mathrm{C}$ and $P_{0}=100 \mathrm{kPa}$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:23

Problem 127

$8.$ Combustion gases enter a gas turbine at $627^{\circ} \mathrm{C}$ and $1.2 \mathrm{MPa}$ at a rate of $2.5 \mathrm{~kg} / \mathrm{s}$ and leave at $527^{\circ} \mathrm{C}$ and $500 \mathrm{kPa}$. It is estimated that heat is lost from the turbine at a rate of $20 \mathrm{~kW}$. Using air properties for the combustion gases and assuming the surroundings to be at $25^{\circ} \mathrm{C}$ and $100 \mathrm{kPa}$, determine $(a)$ the actual and reversible power outputs of the turbine, $(b)$ the exergy destroyed within the turbine, and $(c)$ the second-law efficiency of the turbine

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:06

Problem 128

$8$ Water enters a pump at $100 \mathrm{kPa}$ and $30^{\circ} \mathrm{C}$ at a rate of $1.35 \mathrm{~kg} / \mathrm{s}$ and leaves at $4 \mathrm{MPa}$. If the pump has an isentropic efficiency of 70 percent, determine $(a)$ the actual power input,
(b) the rate of frictional heating, (c) the exergy destruction, and
(d) the second-law efficiency for an environment temperature of $20^{\circ} \mathrm{C}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:12

Problem 129

$ Argon gas expands from $3.5 \mathrm{MPa}$ and $100^{\circ} \mathrm{C}$ to $500 \mathrm{kPa}$ in an adiabatic expansion valve. For environment conditions of $100 \mathrm{kPa}$ and $25^{\circ} \mathrm{C}$, determine $(a)$ the exergy of argon at the inlet, $(b)$ the exergy destruction during the process, and
(c) the second-law efficiency.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:30

Problem 130

Can closed-system exergy be negative? How about flow exergy? Explain using an incompressible substance as an example.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:03

Problem 131

$131$ Obtain a relation for the second-law efficiency of a heat engine that receives heat $Q_{H}$ from a source at temperature $T_{H}$ and rejects heat $Q_{L}$ to a sink at $T_{L}$, which is higher than $T_{0}$ (the temperature of the surroundings), while producing work in the amount of $W$.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:44

Problem 132

Writing the first- and second-law relations and simplifying, obtain the reversible work relation for a closed system that exchanges heat with the surrounding medium at $T_{0}$ in the amount of $Q_{0}$ as well as a heat reservoir at $T_{R}$ in the amount of $Q_{B}$ ( Hint: Eliminate $Q_{0}$ between the two equations.).

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:14

Problem 133

Writing the first- and second-law relations and simplifying, obtain the reversible work relation for a steady-flow system that exchanges heat with the surrounding medium at $T_{0}$ at a rate of $Q_{0}$ as well as a thermal reservoir at $T_{R}$ at a rate of $\dot{Q}_{R}$. (Hint: Eliminate $\dot{Q}_{0}$ between the two equations.).

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:15

Problem 134

Keeping the limitations imposed by the second law of thermodynamics in mind, choose the wrong statement below:
(a) A heat engine cannot have a thermal efficiency of 100 percent.
(b) For all reversible processes, the second-law efficiency is 100 percent.
(c) The second-law efficiency of a heat engine cannot be greater than its thermal efficiency.
(d) The second-law efficiency of a process is 100 percent if no entropy is generated during that process.
(e) The coefficient of performance of a refrigerator can be greater than 1

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:49

Problem 135

Heat is lost through a plane wall steadily at a rate of $800 \mathrm{~W}$. If the inner and outer surface temperatures of the wall are $20^{\circ} \mathrm{C}$ and $9^{\circ} \mathrm{C}$, respectively, and the environment temperature is $0^{\circ} \mathrm{C}$, the rate of exergy destruction within the wall is
$(a) 0 \mathrm{~W}$
(b) $11 \mathrm{~W}$
(c) $15 \mathrm{~W}$
$(d) 29 \mathrm{~W}$
(e) $76 \mathrm{~W}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:06

Problem 136

Liquid water enters an adiabatic piping system at $15^{\circ} \mathrm{C}$ at a rate of $3 \mathrm{~kg} / \mathrm{s}$. It is observed that the water temperature rises by $0.3^{\circ} \mathrm{C}$ in the pipe due to friction. If the environment temperature is also $15^{\circ} \mathrm{C},$ the rate of exergy destruction in the pipe is
(a) $3.8 \mathrm{~kW}$
(b) $24 \mathrm{~kW}$
(c) $72 \mathrm{~kW}$
(d) $98 \mathrm{~kW}$
(e) 124 kW

Eric Mockensturm
Eric Mockensturm
Numerade Educator
00:43

Problem 137

A water reservoir contains 100 tons of water at an average elevation of $60 \mathrm{~m}$. The maximum amount of electric power that can be generated from this water is
(a) $8 \mathrm{kWh}$
(b) $16 \mathrm{kWh}$
(c) $1630 \mathrm{kWh}$
(d) $16.300 \mathrm{kWh}$
(e) $58,800 \mathrm{kWh}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
00:29

Problem 138

A house is maintained at $21^{\circ} \mathrm{C}$ in winter by electric resistance heaters. If the outdoor temperature is $3^{\circ} \mathrm{C}$, the second-law efficiency of the resistance heaters is
(a) $0 \%$
(b) $4.1 \%$
(c) $6.1 \%$
(d) $8.6 \%$
(e) $16.3 \%$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:34

Problem 139

A furnace can supply heat steadily at $1300 \mathrm{~K}$ at a rate of $500 \mathrm{~kJ} / \mathrm{s}$. The maximum amount of power that can be produced by using the heat supplied by this furnace in an environment at $300 \mathrm{~K}$ is
(a) $115 \mathrm{~kW}$
(b) $192 \mathrm{~kW}$
(c) $385 \mathrm{~kW}$
(d) $500 \mathrm{~kW}$
(e) $650 \mathrm{~kW}$

Eric Mockensturm
Eric Mockensturm
Numerade Educator
01:21

Problem 140

A heat engine receives heat from a source at $1500 \mathrm{~K}$ at a rate of $600 \mathrm{~kJ} / \mathrm{s}$ and rejects the waste heat to a sink at $300 \mathrm{~K}$. If the power output of the engine is $400 \mathrm{~kW}$, the second-law efficiency of this heat engine is
(a) $42 \%$
(b) $53 \%$
(c) $83 \%$
(d) $67 \%$
(e) $80 \%$

Eric Mockensturm
Eric Mockensturm
Numerade Educator
01:21

Problem 141

A heat engine receives heat from a source at $1500 \mathrm{~K}$ at a rate of $600 \mathrm{~kJ} / \mathrm{s}$ and rejects the waste heat to a sink at $300 \mathrm{~K}$. If the power output of the engine is $400 \mathrm{~kW},$ the second-law efficiency of this heat engine is
(a) $42 \%$
(b) $53 \%$
(c) $83 \%$
(d) $67 \%$
(e) $80 \%$

Eric Mockensturm
Eric Mockensturm
Numerade Educator
00:53

Problem 142

Steam enters a turbine steadily at $4 \mathrm{MPa}$ and $600^{\circ} \mathrm{C}$ and exits at $0.2 \mathrm{MPa}$ and $150^{\circ} \mathrm{C}$ in an environment at $25^{\circ} \mathrm{C}$ The decrease in the exergy of the steam as it flows through the turbine is
(a) $879 \mathrm{~kJ} / \mathrm{kg}$
(b) $1123 \mathrm{~kJ} / \mathrm{kg}$
(c) $1645 \mathrm{~kJ} / \mathrm{kg}$
(d) $1910 \mathrm{~kJ} / \mathrm{kg}$
(e) $4260 \mathrm{~kJ} / \mathrm{kg}$

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
02:18

Problem 143

A $12-\mathrm{kg}$ solid whose specific heat is $2.8 \mathrm{~kJ} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$ is at a uniform temperature of $-10^{\circ} \mathrm{C}$. For an environment temperature of $20^{\circ} \mathrm{C}$, the exergy content of this solid is
(a) Less than zero
(b) $0 \mathrm{~kJ}$
(c) $4.6 \mathrm{~kJ}$
$(d) 55 \mathrm{~kJ}$
(e) $1008 \mathrm{~kJ}$

Eric Mockensturm
Eric Mockensturm
Numerade Educator
01:20

Problem 144

Obtain the following information about a power plant that is closest to your town: the net power output; the type and amount of fuel used; the power consumed by the pumps, fans, and other auxiliary equipment; stack gas losses; temperatures at several locations; and the rate of heat rejection at the condenser. Using these and other relevant data, determine the rate of irreversibility in that power plant.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:46

Problem 145

Human beings are probably the most capable creatures, and they have a high level of physical, intellectual, emotional, and spiritual potentials or exergies. Unfortunately people make little use of their exergies, letting most of their exergies go to waste. Draw four exergy-versus-time charts, and plot your physical, intellectual, emotional, and spiritual exergies on each of these charts for a $24-\mathrm{h}$ period using your best judgment based on your experience. On these four charts, plot your respective exergies that you have utilized during the last $24 \mathrm{~h}$. Compare the two plots on each chart and determine if you are living a "full" life or if you are wasting your life away. Can you think of any ways to reduce the mismatch between your exergies and your utilization of them?

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
03:08

Problem 146

Domestic hot-water systems involve a high level of irreversibility, and thus they have low second-law efficiencies. The water in these systems is heated from about $15^{\circ} \mathrm{C}$ to about $60^{\circ} \mathrm{C}$, and most of the hot water is mixed with cold water to reduce its temperature to $45^{\circ} \mathrm{C}$ or even lower before it is used for any useful purpose such as taking a shower or washing clothes at a warm setting. The water is discarded at about the same temperature at which it was used and replaced by fresh cold water at $15^{\circ} \mathrm{C}$. Redesign a typical residential hot-water system such that the irreversibility is greatly reduced. Draw a sketch of your proposed design.

TP
Tuan Pham
University of Wisconsin - Madison
13:59

Problem 147

Consider natural gas, electric resistance, and heat pump heating systems. For a specified heating load, which one of these systems will do the job with the least irreversibility? Explain.

Paul A.
Paul A.
California State Polytechnic University, Pomona
02:56

Problem 148

The temperature of the air in a building can be maintained at a desirable level during winter by using different methods of heating. Compare heating this air in a heat exchanger unit with condensing steam to heating it with an electric-resistance heater. Perform a second-law analysis to determine the heating method that generates the least entropy and thus causes the least exergy destruction.

Ajay Singhal
Ajay Singhal
Numerade Educator
08:00

Problem 149

A steam boiler may be thought of as a heat exchanger. The combustion gases may be modeled as a stream of air because their thermodynamic properties are close to those of air. Using this model, consider a boiler that is to convert saturated liquid water at 500 psia to a saturated vapor while keeping the water pressure constant. Determine the temperature at which the air (i.e., combustion gases) must enter this unit so that the transfer of exergy from the air to the boiling water is done at the minimum loss.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
01:19

Problem 150

An adiabatic nozzle is designed to accelerate an ideal gas from nearly $0 \mathrm{~m} / \mathrm{s}, P_{1},$ and $T_{1}$ to $\mathrm{V} \mathrm{m} / \mathrm{s}$. As the efficiency of this nozzle decreases, the pressure at the nozzle exit must also be decreased to maintain the speed at $V$. Plot the change in the flow exergy as a function of the nozzle efficiency for an ideal gas (say, air).

Manik Pulyani
Manik Pulyani
Numerade Educator