Download Spring Book Problems - Blue Valley Schools

CHAPTER 11: Vibrations and Waves
Questions
2.
5.
7.
8.
14.
15.
19.
20.
Is the acceleration of a simple harmonic oscillator ever zero? If so, where? [What about velocity? Position? Max/min/zero?]
How could you double the maximum speed of a simple harmonic oscillator (SHO)?
If a pendulum clock is accurate at sea level, will it gain or lose time when taken to high altitude? Why?
A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–48). How could you estimate the height of the branch
using only a stopwatch?
Why do the strings used for the lowest-frequency notes on a piano normally have wire wrapped around them?
What kind of waves do you think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b)
horizontally parallel to its length?
When a sinusoidal wave crosses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change
(although the wavelength and velocity do change). Explain why.
If a string is vibrating in three segments, are there any places you could touch it with a knife blade without disturbing the motion?
1 to 11–3 Simple Harmonic Motion
1.
(I) If a particle undergoes SHM with amplitude 0.18 m, what is the total distance it travels in one period? [T, f, A]
(I) The springs of a 1500-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump,
what will be the frequency of vibrations? [k, T, A, m, Fg]
5. (II) An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.38
kg hangs from it? [f, T ]
9. (II) A 0.60-kg mass at the end of a spring vibrates 3.0 times per second with an amplitude of 0.13 m. Determine (a) the velocity
when it passes the equilibrium point, (b) the velocity when it is 0.10 m from equilibrium, (c) the total energy of the system, and (d)
the equation describing the motion of the mass, assuming that x was a maximum at t  0.
17. (II) At what displacement from equilibrium is the energy of a SHO half KE and half PE?
21. (II) A 300-g mass vibrates according to the equation x  0.38 sin 6.50t, where x is in meters and t is in seconds. Determine (a) the
amplitude, (b) the frequency, (c) the period, (d) the total energy, and (e) the KE and PE when x is 9.0 cm. (f) Draw a careful graph
of x vs. t showing the correct amplitude and period.
22. (II) Figure 11–50 shows two examples of SHM, labeled A and B. For each, what is (a) the amplitude, (b) the frequency, and (c)
the period? (d) Write the equations for both A and B in the form of a sine or cosine.
3.
11–4
Simple Pendulum
28. (I) A pendulum makes 36 vibrations in exactly 60 s. What is its (a) period, and (b) frequency?
29.
(I) How long must a simple pendulum be if it is to make exactly one swing per second? (That is, one
complete vibration takes exactly 2.0 s.)
31. (II) What is the period of a simple pendulum 80 cm long (a) on the Earth, and (b) when it is in a freely
falling elevator?
33. (II) Your grandfather clock’s pendulum has a length of 0.9930 m. If the clock loses half a minute per day, how should you adjust
the length of the pendulum?
11–7 and 11–8
Waves
36. (I) A fisherman notices that wave crests pass the bow of his anchored boat every 3.0 s. He measures the distance between two
crests to be 6.5 m. How fast are the waves traveling? [T, f, v, λ]
37. (I) A sound wave in air has a frequency of 262 Hz and travels with a speed of 343 m s . How far apart are the wave crests
(compressions)? [f, T, v, λ]
41. (II) A cord of mass 0.65 kg is stretched between two supports 28 m apart. If the tension in the cord is 150 N, how long will it take
a pulse to travel from one support to the other? [f, T, λ, v]
*43. (II) A sailor strikes the side of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean
11–9
floor directly below 3.0 s later. How deep is the ocean at this point? [∆x, t, v]
Wave Energy
47. (II) The intensity of an earthquake wave passing through the Earth is measured to be 2.0 10 6 J m . at a distance of 48 km from
the source. (a) What was its intensity when it passed a point only 1.0 km from the source? (b) At what rate did energy pass through
an area of 5.0 m 2 at 1.0 km?
*11–10 Intensity Related to A and f
*49.(I) Two waves traveling along a stretched string have the same frequency, but one transports three times the power of the other.
What is the ratio of the amplitudes of the two waves?
11–12 Interference
2
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
11–13 Standing Waves; Resonance
52. (I) If a violin string vibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics?
53. (I) A violin string vibrates at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down
from the end? (That is, only two-thirds of the string vibrates as a standing wave.)
CHAPTER 12:
Sound
Questions
5. What evidence can you give that the speed of sound in air does not depend significantly on frequency?
6. The voice of a person who has inhaled helium sounds very high-pitched. Why?
11. Standing waves can be said to be due to “interference in space,” whereas beats can be said to be due to “interference in time.”
Explain.
12. In Fig. 12–16, if the frequency of the speakers were lowered, would the points D and C (where destructive and constructive
interference occur) move farther apart or closer together?
13.
Traditional methods of protecting the hearing of people who work in areas with very high noise levels have
consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones
are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it
electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more
noise reduce the sound levels reaching the ears?
14. Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly
different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart?
Explain.
15. Is there a Doppler shift if the source and observer move in the same direction, with the same velocity? Explain.
16. If a wind is blowing, will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the
wavelength or velocity changed?
17. Figure 12–32 shows various positions of a child in motion on a swing. A monitor is blowing a whistle in
front of the child on the ground. At which position, A through E, will the child hear the highest frequency
for the sound of the whistle? Explain your reasoning.
Problems
[Unless stated otherwise, assume T  20 º C and vsound  343 m s
12–1
1.
2.
3.
4.
Characteristics of Sound
(I) A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She
hears the echo 2.0 s after shouting. Estimate the length of the lake.
(I) A sailor strikes the side of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor
directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m s (Table 12–1)
and does not vary significantly with depth.
(I) (a) Calculate the wavelengths in air at 20°C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b)
What is the wavelength of a 10-MHz ultrasonic wave?
(II) An ocean fishing boat is drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on
another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish, and (b) by the
fishermen?
Loudness
A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound
level? (See Fig. 12–6.)
*12–3
*21.(I)
*23. (II) Your auditory system can accommodate a huge range of sound levels. What is the ratio of highest to lowest intensity at (a)
100 Hz, (b) 5000 Hz? (See Fig. 12–6.)
12–4 Sources of Sound: Strings and Air Columns
25. (I) An organ pipe is 112 cm long. What are the fundamental and first three audible overtones if the pipe is (a) closed at one end,
and (b) open at both ends?
27. (I) If you were to build a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would
be the range of the lengths of pipes required?
33. (II) (a) At T  20 º C, how long must an open organ pipe be to have a fundamental frequency of 294 Hz? (b) If this pipe is filled
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
with helium, what is its fundamental frequency?
35. (II) A uniform narrow tube 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and
330 Hz. What is (a) the fundamental frequency, and (b) the speed of sound in the gas in the tube?
37. (II) How many overtones are present within the audible range for a 2.14-m-long organ pipe at 20°C (a) if it is open, and (b) if it is
closed?
12–6 Interference; Beats
39. (I) A piano tuner hears one beat every 2.0 s when trying to adjust two strings, one of which is sounding 440
Hz. How far off in frequency is the other string?
40. (I) What is the beat frequency if middle C (262 Hz) and C # (277 Hz) are played together? What if each is played two octaves
lower (each frequency reduced by a factor of 4)?
41.
(I) A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at an unknown frequency.
If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz
occurs when they are played simultaneously, estimate the operating frequency of brand X.
42. (II) A guitar string produces 4 beats s when sounded with a 350-Hz tuning fork and 9 beats s when sounded
with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.
12–7 Doppler Effect
49. (I) The predominant frequency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move
with a speed of 30 .0 m s (a) toward the fire engine, and (b) away from it?
50. (I) You are standing still. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m s
(a) toward you, or (b) away from you?
*12–8
Shock Waves; Sonic Boom
*59. (I) (a) How fast is an object moving on land if its speed at 20°C is Mach 0.33? (b) A high-flying jet cruising at 3000 km h
displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?
76. A tuning fork is set into vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop
slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from
the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?
CHAPTER 13:
Temperature and Kinetic Theory
Questions
3. Which is larger, 1 C° or 1 F°?
*4. If system A is in thermal equilibrium with system B, but B is not in thermal equilibrium with system C, what can you say about
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
the temperatures of A, B, and C?
A flat bimetallic strip consists of aluminum riveted to a strip of iron. When heated, the strip will bend. Which metal will be on the
outside of the curve? [Hint: See Table 13–1.] Why?
In the relation L  L0 T , should L0 be the initial length, the final length, or does it matter? Explain.
The units for the coefficient of linear expansion  are (Cº ) 1 , and there is no mention of a length unit such as meters. Would
the expansion coefficient change if we used feet or millimeters instead of meters? Explain.
Figure 13–27 shows a diagram of a simple thermostat used to control a furnace (or other heating or cooling system). The
bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing liquid
mercury that conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and
how it can be set at different temperatures.
Long steam pipes that are fixed at the ends often have a section in the shape of a U. Why?
A flat, uniform cylinder of lead floats in mercury at 0°C. Will the lead float higher or lower when the temperature is raised?
Explain.
When a cold mercury-in-glass thermometer is first placed in a hot tub of water, the mercury initially descends a bit and then rises.
Explain.
A glass container may break if one part of it is heated or cooled more rapidly than adjacent parts. Explain.
The principal virtue of Pyrex glass is that its coefficient of linear expansion is much smaller than that for ordinary glass (Table
13–1). Explain why this gives rise to the increased heat resistance of Pyrex.
Will a grandfather clock, accurate at 20ºC, run fast or slow on a hot day (30ºC)? Explain. The clock uses a pendulum supported
on a long, thin brass rod.
Freezing a can of soda will cause its bottom and top to bulge so badly the can will not stand up. What has happened?
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
16. When a gas is rapidly compressed (say, by pushing down a piston), its temperature increases. When a gas expands against a
piston, it cools. Explain these changes in temperature using the kinetic theory, in particular noting what happens to the
momentum of molecules when they strike the moving piston.
18. Explain in words how Charles’s law follows from kinetic theory and the relation between average kinetic energy and the absolute
temperature.
19. Explain in words how Gay-Lussac’s law follows from kinetic theory.
20. As you go higher in the Earth’s atmosphere, the ratio of N 2 molecules to O 2 molecules increases. Why?
*22. Alcohol evaporates more quickly than water at room temperature. What can you infer about the molecular properties of one
relative to the other?
*23. Explain why a hot humid day is far more uncomfortable than a hot dry day at the same temperature.
*24. Is it possible to boil water at room temperature (20°C) without heating it? Explain.
Problems
13–1
1.
Atomic Theory
(I) How many atoms are there in a 3.4-gram copper penny?
13–2 Temperature and Thermometers
3. (I) (a) “Room temperature” is often taken to be 68°F. What is this on the Celsius scale? (b) The temperature of the filament in a
lightbulb is about 1800°C. What is this on the Fahrenheit scale?
5.
(I) (a) 15° below zero on the Celsius scale is what Fahrenheit temperature? (b) 15° below zero on the
Fahrenheit scale is what Celsius temperature?
13–4 Thermal Expansion
7. (I) A concrete highway is built of slabs 12 m long (20°C). How wide should the expansion cracks between the slabs be (at 20°C)
to prevent buckling if the range of temperature is 30 º C to 50 º C?
10.
(II) To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled
(usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed in a hole
1.869 cm in diameter at 20°C. To what temperature must the rivet be cooled if it is to fit in the hole?
13–6 Gas Laws; Absolute Temperature
27. (I) Absolute zero is what temperature on the Fahrenheit scale?
Ideal Gas Law
13–7 and 13–8
3
29. (I) If 3.00 m of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0°C. What is
the volume?
33. (II) A storage tank at STP contains 18.5 kg of nitrogen N 2 . (a) What is the volume of the tank? (b) What is the pressure if an
additional 15.0 kg of nitrogen is added without changing the temperature?
13–9
Ideal Gas Law in Terms of Molecules; Avogadro’s Number
41. (I) Calculate the number of molecules m 3 in an ideal gas at STP.
13–10 Molecular Interpretation of Temperature
47. (I) Calculate the rms speed of helium atoms near the surface of the Sun at a temperature of about 6000 K.
49. (I) A gas is at 20°C. To what temperature must it be raised to double the rms speed of its molecules?
*13–13 Vapor Pressure; Humidity
*63. (I) What is the dew point (approximately) if the humidity is 50% on a day when the temperature is 25°C?
*65.(I)
If the air pressure at a particular place in the mountains is 0.72 atm, estimate the temperature at which
water boils.
*67.(I) What is the partial pressure of water on a day when the temperature is 25°C and the relative humidity is
35%?
General Problems
73. A precise steel tape measure has been calibrated at 20°C. At 34°C, (a) will it read high or low, and (b) what will be the
percentage error?
CHAPTER 14: Heat
Questions
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
1.
2.
3.
4.
6.
7.
8.
9.
17.
18.
19.
21.
24.
26.
29.
30.
What happens to the work done when a jar of orange juice is vigorously shaken?
When a hot object warms a cooler object, does temperature flow between them? Are the temperature changes of the two objects
equal?
(a) If two objects of different temperatures are placed in contact, will heat naturally flow from the object with higher internal
energy to the object with lower internal energy? (b) Is it possible for heat to flow even if the internal energies of the two objects
are the same? Explain.
In warm regions where tropical plants grow but the temperature may drop below freezing a few times in the winter, the
destruction of sensitive plants due to freezing can be reduced by watering them in the evening. Explain.
Why does water in a metal canteen stay cooler if the cloth jacket surrounding the canteen is kept moist?
Explain why burns caused by steam on the skin are often more severe than burns caused by water at 100°C.
Explain why water cools (its temperature drops) when it evaporates, using the concepts of latent heat and internal energy.
Will potatoes cook faster if the water is boiling faster? 17.
Down sleeping bags and parkas are often specified as so many
inches or centimeters of loft, the actual thickness of the garment when it is fluffed up. Explain.
Down sleeping bags and parkas are often specified as so many inches or centimeters of loft, the actual thickness of the garment
when it is fluffed up. Explain.
Microprocessor chips have a “heat sink” glued on top that looks like a series of fins. Why is it shaped like that?
Sea breezes are often encountered on sunny days at the shore of a large body of water. Explain in light of the fact that the
temperature of the land rises more rapidly than that of the nearby water.
A 22°C day is warm, while a swimming pool at 22°C feels cool. Why?
Why is the liner of a thermos bottle silvered (Fig. 14–15), and why does it have a vacuum between its two walls?
Heat loss occurs through windows by the following processes: (1) ventilation around edges; (2) through the frame, particularly if
it is metal; (3) through the glass panes; and (4) radiation. (a) For the first three, what is (are) the mechanism(s): conduction,
convection, or radiation? (b) Heavy curtains reduce which of these heat losses? Explain in detail.
An “emergency blanket” is a thin shiny (metal coated) plastic foil. Explain how it can help to keep an immobile person warm.
Explain why cities situated by the ocean tend to have less extreme temperatures than inland cities at the same latitude.
Problems
14–1
1.
3.
Heat as Energy Transfer
5.
(I) How much heat (in joules) is required to raise the temperature of 30.0 kg of water from 15°C to 95°C?
(II) An average active person consumes about 2500 Cal a day. (a) What is this in joules? (b) What is this in kilowatt-hours? (c)
Your power company charges about a dime per kilowatt-hour. How much would your energy cost per day if you bought it from
the power company? Could you feed yourself on this much money per day?
(II) A water heater can generate 32,000 kJ h. How much water can it heat from 15°C to 50°C per hour?
7.
(II) How many kilocalories are generated when the brakes are used to bring a 1200-kg car to rest from a speed of 95 km h?
14–3 and 14–4
Specific Heat; Calorimetry
9. (I) What is the specific heat of a metal substance if 135 kJ of heat is needed to raise 5.1 kg of the metal from 18.0°C to 31.5°C?
11. (II) A 35-g glass thermometer reads 21.6°C before it is placed in 135 mL of water. When the water and thermometer come to
equilibrium, the thermometer reads 39.2°C. What was the original temperature of the water?
15. (II) How long does it take a 750-W coffeepot to bring to a boil 0.75 L of water initially at 8.0°C? Assume that the part of the pot
which is heated with the water is made of 360 g of aluminum, and that no water boils away.
14–5
Latent Heat
21. (I) How much heat is needed to melt 16.50 kg of silver that is initially at 20°C?
(I) If 2.80  105 J of energy is supplied to a flask of liquid oxygen at 183 º C, how much oxygen can
evaporate?
25. (II) A cube of ice is taken from the freezer at 8.5º C and placed in a 95-g aluminum calorimeter filled with
310 g of water at room temperature of 20.0°C. The final situation is observed to be all water at 17.0°C.
What was the mass of the ice cube?
14–6 to 14–8 Conduction, Convection, Radiation
23.
33. (I) One end of a 33-cm-long aluminum rod with a diameter of 2.0 cm is kept at 460°C, and the other is immersed in water at
22°C. Calculate the heat conduction rate along the rod.
35.
(I) (a) How much power is radiated by a tungsten sphere (emissivity e  0.35 ) of radius 22 cm at a
temperature of 25°C? (b) If the sphere is enclosed in a room whose walls are kept at 5º C, what is the net
flow rate of energy out of the sphere?
41. (II) A 100-W lightbulb generates 95 W of heat, which is dissipated through a glass bulb that has a radius of 3.0 cm and is 1.0 mm
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
thick. What is the difference in temperature between the inner and outer surfaces of the glass?
CHAPTER 15: The Laws of Thermodynamics
Questions
1.
What happens to the internal energy of water vapor in the air that condenses on the outside of a cold glass of water? Is work
done or heat exchanged? Explain.
2. Use the conservation of energy to explain why the temperature of a gas increases when it is quickly compressed — say, by
pushing down on a cylinder — whereas the temperature decreases when the gas expands.
3. In an isothermal process, 3700 J of work is done by an ideal gas. Is this enough information to tell how much heat has been
added to the system? If so, how much?
4. Is it possible for the temperature of a system to remain constant even though heat flows into or out of it? If so, give one or two
examples.
5. Explain why the temperature of a gas increases when it is adiabatically compressed.
6. Can mechanical energy ever be transformed completely into heat or internal energy? Can the reverse happen? In each case, if
your answer is no, explain why not; if yes, give one or two examples.
7. Can you warm a kitchen in winter by leaving the oven door open? Can you cool the kitchen on a hot summer day by leaving the
refrigerator door open? Explain.
8. Would a definition of heat engine efficiency as e  W QL be useful? Explain.
9. What plays the role of high-temperature and low-temperature areas in (a) an internal combustion engine, and (b) a steam
engine?
10. Which will give the greater improvement in the efficiency of a Carnot engine, a 10 C° increase in the high-temperature
reservoir, or a 10 C° decrease in the low-temperature reservoir? Explain.
11. The oceans contain a tremendous amount of thermal (internal) energy. Why, in general, is it not possible to put this energy to
useful work?
12. A gas is allowed to expand (a) adiabatically and (b) isothermally. In each process, does the entropy increase, decrease, or stay
the same? Explain.
13. A gas can expand to twice its original volume either adiabatically or isothermally. Which process would result in a greater
change in entropy? Explain.
14. Give three examples, other than those mentioned in this Chapter, of naturally occurring processes in which order goes to
disorder. Discuss the observability of the reverse process.
15. Which do you think has the greater entropy, 1 kg of solid iron or 1 kg of liquid iron? Why?
16. (a) What happens if you remove the lid of a bottle containing chlorine gas? (b) Does the reverse process ever happen? Why or
why not? (c) Can you think of two other examples of irreversibility?
17. You are asked to test a machine that the inventor calls an “in-room air conditioner”: a big box, standing in the middle of the
room, with a cable that plugs into a power outlet. When the machine is switched on, you feel a stream of cold air coming out of
it. How do you know that this machine cannot cool the room?
18. Think up several processes (other than those already mentioned) that would obey the first law of thermodynamics, but, if they
actually occurred, would violate the second law.
19. Suppose a lot of papers are strewn all over the floor; then you stack them neatly. Does this violate the second law of
thermodynamics? Explain.
20. The first law of thermodynamics is sometimes whimsically stated as, “You can’t get something for nothing,” and the second law
as, “You can’t even break even.” Explain how these statements could be equivalent to the formal statements.
*21. Entropy is often called “time’s arrow” because it tells us in which direction natural processes occur. If a movie were run
backward, name some processes that you might see that would tell you that time was “running backward.”
*22. Living organisms, as they grow, convert relatively simple food molecules into a complex structure. Is this a violation of the
second law of thermodynamics?
Problems
15–1 and 15–2
1.
First Law of Thermodynamics
(I) An ideal gas expands isothermally, performing 3.40 10 3 J of work in the process. Calculate (a) the change in internal
energy of the gas, and (b) the heat absorbed during this expansion.
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2.
3.
4.
5.
10.
(I) A gas is enclosed in a cylinder fitted with a light frictionless piston and maintained at atmospheric
pressure. When 1400 kcal of heat is added to the gas, the volume is observed to increase slowly from
12.0 m 3 to 18.2 m 3 . Calculate (a) the work done by the gas and (b) the change in internal energy of the gas.
(I) One liter of air is cooled at constant pressure until its volume is halved, and then it is allowed to expand
isothermally back to its original volume. Draw the process on a PV diagram.
(I) Sketch a PV diagram of the following process: 2.0 L of ideal gas at atmospheric pressure are cooled at constant pressure to a
volume of 1.0 L, and then expanded isothermally back to 2.0 L, whereupon the pressure is increased at constant volume until the
original pressure is reached.
(II) A 1.0-L volume of air initially at 4.5 atm of (absolute) pressure is allowed to expand isothermally until the pressure is 1.0
atm. It is then compressed at constant pressure to its initial volume, and lastly is brought back to its original pressure by heating
at constant volume. Draw the process on a PV diagram, including numbers and labels for the axes.
(II) Consider the following two-step process. Heat is allowed to flow out of an ideal gas at constant volume
so that its pressure drops from 2.2 atm to 1.4 atm. Then the gas expands at constant pressure, from a
volume of 6.8 L to 9.3 L, where the temperature reaches its original value. See Fig. 15–22. Calculate (a)
the total work done by the gas in the process, (b) the change in internal energy of the gas in the process,
and (c) the total heat flow into or out of the gas.
*15. (I) Calculate the average metabolic rate of a person who sleeps 8.0 h, sits at a desk 8.0 h, engages in light activity 4.0 h, watches
television 2.0 h, plays tennis 1.5 h, and runs 0.5 h daily.
15–5
Heat Engines
17. (I) A heat engine exhausts 8200 J of heat while performing 3200 J of useful work. What is the efficiency of this engine?
19.
(I) What is the maximum efficiency of a heat engine whose operating temperatures are 580°C and 380°C?
15–6 Refrigerators, Air Conditioners, Heat Pumps
29. (I) The low temperature of a freezer cooling coil is 15 º C, and the discharge temperature is 30°C. What is the maximum
theoretical coefficient of performance?
31.
(II) A restaurant refrigerator has a coefficient of performance of 5.0. If the temperature in the kitchen
outside the refrigerator is 29°C, what is the lowest temperature that could be obtained inside the
refrigerator if it were ideal?
15–7 Entropy
35. (I) What is the change in entropy of 250 g of steam at 100°C when it is condensed to water at 100°C?
39. (II) A 10.0-kg box having an initial speed of 3.0 m s slides along a rough table and comes to rest. Estimate the total change in
entropy of the universe. Assume all objects are at room temperature (293 K).
*15–12 Energy Resources
*48. (I) Solar cells (Fig. 15–26) can produce about 40 W of electricity per square meter of surface area if directly facing the Sun.
How large an area is required to supply the needs of a house that requires 22 k Wh day? Would this fit on the roof of an average
house? (Assume the Sun shines about 9 h day. )
General Problems
66. Metabolizing 1.0 kg of fat results in about 3.7 107 J of internal energy in the body. (a) In one day, how much fat does the body
burn to maintain the body temperature of a person staying in bed and metabolizing at an average rate of 95 W? (b) How long
would it take to burn 1.0-kg of fat this way assuming there is no food intake?
68. A dehumidifier is essentially a “refrigerator with an open door.” The humid air is pulled in by a fan and guided to a cold coil,
where the temperature is less than the dew point, and some of the air’s water condenses. After this water is extracted, the air is
warmed back to its original temperature and sent into the room. In a well-designed dehumidifier, the heat is exchanged between
the incoming and outgoing air. This way the heat that is removed by the refrigerator coil mostly comes from the condensation of
water vapor to liquid. Estimate how much water is removed in 1.0 h by an ideal dehumidifier, if the temperature of the room is
25°C, the water condenses at 8°C, and the dehumidifier does work at the rate of 600 W of electrical power.
CHAPTER 16: Electric Charge and Electric Field
Questions
1.
If you charge a pocket comb by rubbing it with a silk scarf, how can you determine if the comb is positively or negatively
charged?
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
4.
A positively charged rod is brought close to a neutral piece of paper, which it attracts. Draw a diagram showing the separation of
charge and explain why attraction occurs.
5. Why does a plastic ruler that has been rubbed with a cloth have the ability to pick up small pieces of paper? Why is this difficult
to do on a humid day?
11. Is the electric force a conservative force? Why or why not? (See Chapter 6.)
14. When determining an electric field, must we use a positive test charge, or would a negative one do as well? Explain.
20. Given two point charges Q and 2Q, a distance l apart, is there a point along the straight line that passes through them where
E  0 when their signs are (a) opposite, (b) the same? If yes, state roughly where this point will be.
21. Consider a small positive test charge located on an electric field line at some point, such as point P in Fig.
16–31a. Is the direction of the velocity and/or acceleration of the test charge along this line? Discuss.
Problems
Coulomb’s Law
16–5 and 16–6
[1 mC  10
3
C, 1 C  10
6
C, 1 nC  10 9 C.]
(I) Calculate the magnitude of the force between two 3.60-C point charges 9.3 cm apart.
3. (I) What is the magnitude of the electric force of attraction between an iron nucleus (q  26e) and its
innermost electron if the distance between them is 1.5 10 12 m?
7. (II) Two charged spheres are 8.45 cm apart. They are moved, and the force on each of them is found to
have been tripled. How far apart are they now?
12. (II) Particles of charge 75,  48, and 85 C are placed in a line (Fig. 16–49). The center one is 0.35 m
from each of the others. Calculate the net force on each charge due to the other two.
16–7 and 16–8 Electric Field, Field Lines
1.
23. (I) What are the magnitude and direction of the electric force on an electron in a uniform electric field of strength 2360 N C
that points due east?
25. (I) A downward force of 8.4 N is exerted on a 8.8 C charge. What are the magnitude and direction of the electric field at this
point?
27. (II) What is the magnitude of the acceleration experienced by an electron in an electric field of 750 N C? How does the
direction of the acceleration depend on the direction of the field at that point?
© 2005 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No
portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.