Conceptual Physics

Paul G. Hewitt

Chapter 14

Gases - all with Video Answers

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Chapter Questions

Problem 1

What is the energy source for the motion of gas in the atmosphere? What prevents atmospheric gases from flying off into space?

Shital Rijal

Shital Rijal

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Problem 2

What percentage of the atmosphere is below an altitude of 11 km? How will the percentage change if the altitude is 18 km?

Keshav Singh

Numerade Educator

Problem 3

Why do we not feel atmospheric pressure?

Shital Rijal

Numerade Educator

Problem 4

What would be the approximate mass of 1 $\mathrm{m}^{3}$ of air at an altitude of 10 $\mathrm{km}$ ?

Supratim Pal

Numerade Educator

Problem 5

What is the approximate mass of a column of air 1 ${cm}^{2}$ in area that extends from sea level to the upper atmosphere? What is the weight of this amount of air?

Shital Rijal

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Problem 6

What is the pressure at the bottom of the column of air referred to in the preceding question?

Abhishek Jana

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Problem 7

How does the pressure at the bottom of a 76-cm column of mercury in a barometer compare with the air pressure at the bottom of the atmosphere?

Shital Rijal

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Problem 8

How does the weight of mercury in a barometer compare with the weight of an equal cross-section of air from sea level to the top of the atmosphere?

Abhishek Jana

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Problem 9

Why would a barometer, constructed using water, be too tall to be practical for use?

Shital Rijal

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Problem 10

Why do we have to suck on a straw if atmospheric pressure is responsible for the rising liquid? Give an example to prove that sucking on a straw alone will not always result in a rising column of liquid.

Abhishek Jana

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Problem 11

Why won’t a vacuum pump operate for a well that is deeper than 10.3 m?

Shital Rijal

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Problem 12

How does an aneroid barometer respond to any change in atmospheric pressure? What is an altimeter?

Abhishek Jana

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Problem 13

How much should the volume of a given amount of air be reduced to increase its density by a factor of 3?

Shital Rijal

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Problem 14

What happens to the air pressure inside a balloon when it is squeezed to half its volume at constant temperature?

Abhishek Jana

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Problem 15

Does a flat tire have any pressure?

Shital Rijal

Numerade Educator

Problem 16

A balloon that weighs 1 N is suspended in air, drifting neither up nor down. (a) How much buoyant force acts on it? (b) What happens if the buoyant force decreases? (c) If it increases?

Abhishek Jana

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Problem 17

What is the buoyant force experienced in air by an object of $1-m^{3}$ volume? What happens if the object weighs more than the buoyant force?

Shital Rijal

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Problem 18

Why are balloons filled with a gas less dense than ordinary air?

Abhishek Jana

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Problem 19

What do close-together streamlines indicate?

Shital Rijal

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Problem 20

Is pressure greater or less in regions where streamlines are crowded?

Abhishek Jana

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Problem 21

What happens to the internal pressure in a fluid flowing in a horizontal pipe when its speed increases?

Shital Rijal

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Problem 22

How does the size of air bubbles vary when the speed of the flowing water—containing the bubbles— is
increased?

Sheh Lit Chang

University of Washington

Problem 23

Does Bernoulli’s principle refer to changes in the internal pressure of a fluid or to pressures the fluid may exert on objects?

Shital Rijal

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Problem 24

Why does a fighter plane need to move at high speeds to generate sufficient lift?

Abhishek Jana

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Problem 25

How does faster-moving water between two ships affect the water pressure against the sides of the ships?

Shital Rijal

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Problem 26

Are the ships in the preceding question sucked together or pushed together? Explain.

Abhishek Jana

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Problem 27

Is the fluid that goes up the inside tube in a hand sprayer pushed up the tube or sucked up the tube? Explain.

Shital Rijal

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Problem 28

How does a plasma differ from a gas?

Abhishek Jana

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Problem 29

Cite at least three examples of plasma in your daily environment.

Shital Rijal

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Problem 30

What can be produced when a plasma beam is directed into the field of a strong magnet?

Keshav Singh

Numerade Educator

Problem 31

Compare the pressure exerted by the tires of your car on the road with the air pressure in the tires. For this project, you need to know the weight of your car, which you can get from a manual or a dealer. You divide the weight by 4 to get the approximate weight held up by one tire. You can closely approximate the area of contact of a tire with the road by tracing the edges of the tire contact on a sheet of paper marked with 1-inch squares beneath the tire. After you calculate the pressure of the tire against the road, compare it with the air pressure in the tire. Are they nearly equal? If not, which is greater?

Shital Rijal

Numerade Educator

Problem 32

You ordinarily pour water from a full glass into an empty glass simply by placing the full glass above the empty glass and tipping. Have you ever poured air from one glass into another? The procedure is similar. Lower two glasses in water, mouths downward. Let one fill with water by tilting its mouth upward. Then hold the water-filled glass mouth downward above the air-filled glass. Slowly tilt the lower glass and let the air escape, filling the upper glass. You will be pouring air from one glass into another!

Abhishek Jana

Numerade Educator

Problem 33

Raise a submerged upside-down glass that is full of water above the waterline, but with its mouth beneath the surface. Why doesn’t the water run out? How tall would a glass have to be before water began to run out? (You won’t be able to do this indoors unless you have a ceiling that is at least 10.3 m higher than the waterline.)

Shital Rijal

Numerade Educator

Problem 34

Place a card over the open top of a glass filled to the brim with water and invert it. Why does the card stay in place? Try it sideways.

Abhishek Jana

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Problem 35

Invert a water-filled pop bottle or a small-necked jar. Notice that the water doesn’t simply fall out but
gurgles out of the container. Air pressure won’t let it escape until some air has pushed its way up inside
the bottle to occupy the space above the liquid. How would an inverted, water-filled bottle empty on the
Moon?

Shital Rijal

Numerade Educator

Problem 36

Heat a small amount of water to boiling in an aluminum soda-pop can and invert it quickly into a dish of cooler water. Surprisingly dramatic!

Abhishek Jana

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Problem 37

Lower a narrow glass tube or drinking straw into water and place your finger over the top of the tube. Lift the tube from the water and then lift your finger from the top of the tube. What happens? (You’ll do this often if you enroll in a chemistry lab.)

Shital Rijal

Numerade Educator

Problem 38

Push a pin through a small card and place it in the hole of a thread spool. Try to blow the card from the
spool by blowing through the hole, as Evan Jones does in one of the chapter-opening photos. Try it in all
directions.

Abhishek Jana

Numerade Educator

Problem 39

Hold a spoon in a stream of water as shown and feel the effect of the differences in pressure.

Shital Rijal

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Problem 40

Estimate the buoyant force that air exerts on you. (To do this, you can estimate your volume by knowing your weight and by assuming that your weight density is a bit less than that of water.)

Abhishek Jana

Numerade Educator

Problem 41

A mountain-climber friend with a mass of 80 kg ponders the idea of attaching a helium-filled balloon to himself to effectively reduce his weight by 25% when he climbs. He wonders what the approximate size of such a balloon would be. Hearing of your physics skills, he asks you. Share with him your calculations that show the volume of the balloon to be about 17 ${m}^{3}$ (slightly more than 3 ${m}$ in diameter for a spherical balloon).

Shital Rijal

Numerade Educator

Problem 42

On a perfect fall day, you are hovering at low altitude in a hot-air balloon, accelerated neither upward nor downward. The total weight of the balloon, including its load and the hot air in it, is 20,000 N.
a. Show that the weight of the displaced air is 20,000 N.
b. Show that the volume of the displaced air is 1700 $\mathrm{m}^{3} .$

Abhishek Jana

Numerade Educator

Problem 43

An airplane has a total wing surface of 200 square meters. The airplane requires a lift of 500,000 N to
take off. What should be the difference in the air pressure between the bottom and top surface of the wings to produce this lift?

Shital Rijal

Numerade Educator

Problem 44

The weight of the atmosphere above 1 square meter of Earth's surface is about $100,000 \mathrm{N}$ . Density, of course, decreases with altitude. But suppose the density of air were a constant 1.2 $\mathrm{kg} / \mathrm{m}^{3}$ . Calculate where the top of the atmosphere would be.

Abhishek Jana

Numerade Educator

Problem 45

Rank the volumes of air in the glass, from greatest to least, when it is held
a. near the surface as shown.
b. 1 m beneath the surface.
c. 2 m beneath the surface.

Shital Rijal

Numerade Educator

Problem 46

Rank the buoyant forces supplied by the atmosphere on the following, from greatest to least:
a. An elephant
b. A helium-filled party balloon
c. A skydiver at terminal velocity

Abhishek Jana

Numerade Educator

Problem 47

Rank from most to least, the amounts of lift on the fol- lowing airplane wings:
a) Area 1000 $\mathrm{m}^{2}$ with an atmospheric pressure difference of 2.0 $\mathrm{N} / \mathrm{m}^{2}$
b) Area 800 $\mathrm{m}^{2}$ with an atmospheric pressure difference
of 2.4 $\mathrm{N} / \mathrm{m}^{2}$
c) Area 600 $\mathrm{m}^{2}$ with an atmospheric pressure difference
of 3.8 $\mathrm{N} / \mathrm{m}^{2}$

Shital Rijal

Numerade Educator

Problem 48

What are the two competing factors that go to determine the thickness of the atmosphere on any planet?

Abhishek Jana

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Problem 49

Would there be an atmosphere if gravity was ‘turned off’?

Shital Rijal

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Problem 50

Why is the pressure in an automobile’s tires slightly greater after the car has been driven several kilometers?

Abhishek Jana

Numerade Educator

Problem 51

The valve stem on a tire must exert a certain force on the air within to prevent any of that air from leaking out. If the diameter of the valve stem were doubled, by how much would the force exerted by the valve stem increase?

Shital Rijal

Numerade Educator

Problem 52

Why is a soft, underinflated football at sea level much firmer when it is taken to a high elevation in the
mountains?

Abhishek Jana

Numerade Educator

Problem 53

What is the purpose of the ridges that prevent the funnel from fitting tightly in the mouth of a
bottle?

Shital Rijal

Numerade Educator

Problem 54

How does the density of air in a deep mine compare with the air density at Earth’s surface?

Abhishek Jana

Numerade Educator

Problem 55

When an air bubble rises in water, what happens to its mass, volume, and density?

Surendra Kumar

Numerade Educator

Problem 56

Why do you suppose that airplane windows are smaller than bus windows?

Abhishek Jana

Numerade Educator

Problem 57

We can understand how pressure in water depends on depth by considering a stack of bricks. The pressure below the bottom brick is determined by the weight of the entire stack. Halfway up the stack, the pressure is half because the weight of the bricks above is half. To explain atmospheric pressure, we should consider compressible bricks, like those made of foam rubber. Why is this so?

Shital Rijal

Numerade Educator

Problem 58

The “pump” in a vacuum cleaner is merely a high-speed fan. Would a vacuum cleaner pick up dust from a rug on the Moon? Explain.

Abhishek Jana

Numerade Educator

Problem 59

Suppose that the pump shown in Figure 14.9 operated with a perfect vacuum. From how deep a well could water be pumped?

Shital Rijal

Numerade Educator

Problem 60

If a liquid only half as dense as mercury were used in a barometer, how high would its level be on a day of normal atmospheric pressure?

Abhishek Jana

Numerade Educator

Problem 61

Why doesn’t the size of the cross-sectional area of a mercury barometer affect the height of the enclosed mercury column?

Shital Rijal

Numerade Educator

Problem 62

Why does plasma conduct electric current if it is electrically neutral?

Abhishek Jana

Numerade Educator

Problem 63

If you could somehow replace the mercury in a mercury barometer with a denser liquid, would the height of the liquid column be greater than or less than the height of the mercury? Why?

Shital Rijal

Numerade Educator

Problem 64

Would it be slightly more difficult to draw soda through a straw at sea level or on top of a very high mountain? Explain.

Abhishek Jana

Numerade Educator

Problem 65

Why is it so difficult to breathe when snorkeling at a depth of 1 m and practically impossible at a 2-m depth? Why can’t a diver simply breathe through a hose that extends to the surface?

Shital Rijal

Numerade Educator

Problem 66

A little girl sits in a car at a traffic light holding a helium- filled balloon. The windows are closed and the car is relatively airtight. When the light turns green and the car accelerates forward, her head pitches backward but the balloon pitches forward. Explain why.

Abhishek Jana

Numerade Educator

Problem 67

How does the concept of buoyancy complicate the old question “Which weighs more: a pound of lead or a pound of feathers?"

Shital Rijal

Numerade Educator

Problem 68

Why does a precision scale give different readings for the weight of an object in air and in a vacuum (remembering that weight is the force exerted against a supporting surface)? Cite an example in which this would be an important consideration.

Abhishek Jana

Numerade Educator

Problem 69

Would a bottle of helium gas weigh more or less than an identical bottle filled with air at the same pressure? Than an identical bottle with the air pumped out?

Shital Rijal

Numerade Educator

Problem 70

When you replace helium in a balloon with less-dense hydrogen, does the buoyant force on the balloon change if the balloon remains the same size? Explain.

Abhishek Jana

Numerade Educator

Problem 71

A steel tank filled with helium gas doesn’t rise in air, but a balloon containing the same helium rises easily. Why?

Shital Rijal

Numerade Educator

Problem 72

If the number of gas atoms in a container is doubled, the pressure of the gas doubles (assuming constant temperature and volume). Explain this pressure increase in terms of the molecular motion of the gas.

Abhishek Jana

Numerade Educator

Problem 73

What change in pressure occurs in a party balloon that is squeezed to one-third its volume with no change in temperature?

Shital Rijal

Numerade Educator

Problem 74

What, if anything, happens to the volume of gas in an atmospheric research-type balloon when it is heated?

Abhishek Jana

Numerade Educator

Problem 75

What, if anything, happens to the pressure of the gas in a rubber balloon when the balloon is squeezed smaller?

Shital Rijal

Numerade Educator

Problem 76

What happens to the size of the air bubbles released by a diver as they rise?

Abhishek Jana

Numerade Educator

Problem 77

You and your friendly car dealer float a long string of closely spaced helium-filled balloons over his used-car lot. You secure the two ends of the long string of balloons to different points on the ground so that the balloons float over the lot in an arc. What is the name of this arc? (Why could this exercise have been included in Chapter 12?)

Shital Rijal

Numerade Educator

Problem 78

The gas pressure inside an inflated rubber balloon is always greater than the air pressure outside. Explain.

Abhishek Jana

Numerade Educator

Problem 79

The force of the atmosphere at sea level against the out- side of a $10-{m}^{2}$ store window is about a million N. Why doesn't this shatter the window? Why might the window shatter in a strong wind blowing past the window?

Shital Rijal

Numerade Educator

Problem 80

Why does the fire in a fireplace burn more briskly on a windy day?

Abhishek Jana

Numerade Educator

Problem 81

What happens to the pressure in water as it speeds up when it is ejected by the nozzle of a garden hose?

Shital Rijal

Numerade Educator

Problem 82

Why do airplanes normally take off facing the wind?

Keshav Singh

Numerade Educator

Problem 83

What provides the lift to keep a Frisbee in flight?

Shital Rijal

Numerade Educator

Problem 84

When a steadily flowing gas flows from a larger-diameter pipe to a smaller-diameter pipe, what happens to (a) its speed, (b) its pressure, and (c) the spacing between its streamlines?

Abhishek Jana

Numerade Educator

Problem 85

Compare the spacing of streamlines around a tossed baseball that doesn’t spin in flight with the spacing of streamlines around a ball that does. Why does the spinning baseball veer from the course of a nonspinning one?

Shital Rijal

Numerade Educator

Problem 86

Why is it easier to throw a curve with a tennis ball than a baseball?

Abhishek Jana

Numerade Educator

Problem 87

Why do airplanes extend wing flaps that increase the area and the angle of attack of the wing during takeoffs and landings? Why are these flaps pulled in when the airplane has reached cruising speed?

Shital Rijal

Numerade Educator

Problem 88

How is an airplane able to fly upside down?

Abhishek Jana

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Problem 89

Why are runways longer for takeoffs and landings at high- altitude airports, such as those in Denver and Mexico City?

Shital Rijal

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Problem 90

How will two dangling vertical sheets of paper move when you blow between them? Try it and see.

Abhishek Jana

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Problem 91

What physics principle underlies these three observations? When passing an oncoming truck on the highway, your car tends to sway toward the truck. The canvas roof of a convertible car bulges upward when the car is traveling at high speeds. The windows of older trains sometimes break when a high-speed train passes by on the next track.

Shital Rijal

Numerade Educator

Problem 92

Wharves are made with pilings that permit the free passage of water. Why would a solid-walled wharf
be disadvantageous to ships attempting to pull alongside?

Abhishek Jana

Numerade Educator

Problem 93

If you count the tires on a large tractor-trailer that is unloading food at your local supermarket, you may be surprised to count 18 tires. Why so many tires? (Hint: Consider Think and Do #31.)

Shital Rijal

Numerade Educator

Problem 94

Two teams of eight horses each were unable to pull the Magdeburg hemispheres apart (shown on the opening page of this chapter). Suppose that two teams of nine horses each could pull them apart. Then would one team of nine horses succeed if the other team were replaced with a strong tree? Discuss this and defend your answer.

Abhishek Jana

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Problem 95

When boarding an airplane, you bring a bag of chips (or any other item packaged in an airtight foil package) and, while you are in flight, you notice that the bag puffs up. Discuss why this happens.

Shital Rijal

Numerade Educator

Problem 96

The pressure exerted against the ground by an elephant’s weight distributed evenly over its four feet is less than 1 atmosphere. Discuss why it is that you’d be crushed beneath the foot of an elephant, while you’re unharmed by the pressure of the atmosphere?

Abhishek Jana

Numerade Educator

Problem 97

Your friend says that the buoyant force of the atmosphere on an elephant is significantly greater than the buoyant force of the atmosphere on a small helium-filled balloon. Discuss your response.

Shital Rijal

Numerade Educator

Problem 98

Discuss which will register the greater weight: an empty flattened balloon or the same balloon filled with air. Defend your answer: then try it and see.

Abhishek Jana

Numerade Educator

Problem 99

On a sensitive balance, weigh an empty, flat, thin plastic bag. Then weigh the bag filled with air. Discuss whether or not the readings differ.

Shital Rijal

Numerade Educator

Problem 100

Two identical balloons of the same volume are pumped up with air to more than atmospheric pressure and suspended on the ends of a stick that is horizontally balanced. One of the balloons is then punctured. Discuss whether or not the balance of the stick is upset. If so, which way does it tip?

Abhishek Jana

Numerade Educator

Problem 101

Two balloons that have the same weight and volume are filled with equal amounts of helium. One is rigid and the other is free to expand as the pressure outside decreases. When released, discuss which will rise higher.

Darshan Maheshwari

Darshan Maheshwari

Numerade Educator

Problem 102

A helium-filled balloon and a basketball have the same volume. Upon which is the buoyant force of the surrounding air greater? Discuss why the balloon is at the ceiling of a room whereas the basketball is on the floor.

Abhishek Jana

Numerade Educator

Problem 103

Imagine a huge space colony that consists of a rotating air-filled cylinder. Discuss how the density of the
air at “ground level” would compare to the air densities “above.”

Shital Rijal

Numerade Educator

Problem 104

Discuss whether or not a helium-filled balloon could “rise” in the atmosphere of a rotating space habitat.

Abhishek Jana

Numerade Educator

Problem 105

Discuss whether or not lower pressure is the result of fast-moving air, or fast-moving air is the result of lower pressure. Give one example supporting each point of view. (In physics, when two things are related—such as force and acceleration or speed and pressure—it is usu- ally arbitrary which one we call cause and which one we call effect.)

Shital Rijal

Numerade Educator