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BalloonsBalloons

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Introductory QuestionIntroductory Question

A helium balloon has mass, yet it A helium balloon has mass, yet it doesn’t fall to the floor. Is there a doesn’t fall to the floor. Is there a real force pushing up on the helium real force pushing up on the helium balloon?balloon?

A.A. YesYes

B.B. NoNo

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5 Questions about 5 Questions about BalloonsBalloons

How does air “inflate” a rubber How does air “inflate” a rubber balloon?balloon?

Why doesn’t the atmosphere Why doesn’t the atmosphere collapse?collapse?

Does air around a balloon exert a Does air around a balloon exert a force on it?force on it?

Why does a hot air balloon float in Why does a hot air balloon float in cold air?cold air?

Why does a helium balloon float in Why does a helium balloon float in air?air?

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Question 1Question 1

How does air “inflate” a rubber How does air “inflate” a rubber balloon?balloon? How does air occupy space?How does air occupy space? How does it push on the balloon’s How does it push on the balloon’s

elastic skin?elastic skin?

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Air’s CharacteristicsAir’s Characteristics

Air is a gasAir is a gas It consists of individual atoms and It consists of individual atoms and

moleculesmolecules Its particles are kept separate by Its particles are kept separate by

thermal energythermal energy Its particles bounce around in free fallIts particles bounce around in free fall

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Air and PressureAir and Pressure

Air has pressureAir has pressure Air particles transfer momentum when Air particles transfer momentum when

they bouncethey bounce Each momentum transfer/bounce Each momentum transfer/bounce

involves forcesinvolves forces Air particles exerts forces on container Air particles exerts forces on container

wallswalls Average force is proportional to surface Average force is proportional to surface

areaarea Average force per unit ofAverage force per unit of

area is called “pressure”area is called “pressure”

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Air and DensityAir and Density

Air has densityAir has density Air particles have massAir particles have mass Each volume of air has a massEach volume of air has a mass Average mass per unit ofAverage mass per unit of

volume is called “density”volume is called “density”

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Air Pressure and DensityAir Pressure and Density

Air pressure is proportional to Air pressure is proportional to densitydensity Denser particles hit surface more oftenDenser particles hit surface more often Denser air Denser air more pressure more pressure

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Pressure ImbalancesPressure Imbalances

Balanced pressure exerts no overall Balanced pressure exerts no overall forceforce Forces on balloon’s sides cancelForces on balloon’s sides cancel

Unbalanced pressure exerts overall Unbalanced pressure exerts overall forceforce Forces on balloon’s sides don’t cancelForces on balloon’s sides don’t cancel Forces push balloon toward lower Forces push balloon toward lower

pressurepressure Air pressure also pushes on the air Air pressure also pushes on the air

itselfitself Air itself is pushed toward lower Air itself is pushed toward lower

pressurepressure

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Question 2Question 2

Why doesn’t the atmosphere Why doesn’t the atmosphere collapse?collapse? If air has weight, why doesn’t it fall to If air has weight, why doesn’t it fall to

the ground?the ground? Why is the air denser at lower Why is the air denser at lower

altitudes?altitudes?

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The AtmosphereThe Atmosphere Air near the ground supports the air overheadAir near the ground supports the air overhead

The atmosphere is in stable equilibriumThe atmosphere is in stable equilibrium Air pressure decreases with altitudeAir pressure decreases with altitude Each layer of air experiences an upward forceEach layer of air experiences an upward force This upward force balances the layer’s weightThis upward force balances the layer’s weight

Supporting itself structures the atmosphereSupporting itself structures the atmosphere Air pressure is highest near the groundAir pressure is highest near the ground Air density is highest near the groundAir density is highest near the ground

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Question 3Question 3

Does air around a balloon exert a Does air around a balloon exert a force on it?force on it?

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The Buoyant ForceThe Buoyant Force

Because of the atmosphere’s Because of the atmosphere’s structure,structure, air pressure isair pressure is

stronger near the bottom of a balloon,stronger near the bottom of a balloon, weaker near the top of the balloon,weaker near the top of the balloon,

so air pushes up harder than it pushes so air pushes up harder than it pushes down,down,

and this imbalance yields an upward and this imbalance yields an upward buoyant forcebuoyant force

The atmosphere pushes upward on a The atmosphere pushes upward on a balloon!balloon!

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Archimedes’ PrincipleArchimedes’ Principle

A balloon immersed in a fluid A balloon immersed in a fluid experience an upward buoyant force experience an upward buoyant force equal to the weight of the fluid it equal to the weight of the fluid it displacesdisplaces

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Question 4Question 4

Why does a hot air balloon float in Why does a hot air balloon float in cold air?cold air? Why does a cold air balloon sink in cold Why does a cold air balloon sink in cold

air?air? What is the difference between hot air What is the difference between hot air

and cold air?and cold air?

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Room-Air Balloon in AirRoom-Air Balloon in Air A rubber balloon filled with room airA rubber balloon filled with room air

weighs more than the room air it displacesweighs more than the room air it displaces experiences a downward net force in room airexperiences a downward net force in room air sinks in room airsinks in room air

Its average density > density of room airIts average density > density of room air

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Air and TemperatureAir and Temperature

Air pressure is proportional to Air pressure is proportional to temperaturetemperature Faster particles hit surface more and Faster particles hit surface more and

harderharder Hotter air Hotter air more pressure more pressure

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An Aside About An Aside About TemperatureTemperature

Like most things, air has a Like most things, air has a temperaturetemperature Air particles have thermal kinetic Air particles have thermal kinetic

energyenergy Average thermal kinetic energy is Average thermal kinetic energy is

proportional to absolute temperatureproportional to absolute temperature SI absolute temperature: kelvins or SI absolute temperature: kelvins or

KK 0 K is absolute zero — no thermal 0 K is absolute zero — no thermal

energy leftenergy left Step size: 1 K step same as 1 °C stepStep size: 1 K step same as 1 °C step

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Hot-Air Balloon in AirHot-Air Balloon in Air

A rubber balloon filled with hot airA rubber balloon filled with hot air contains fewer air particles than if it contains fewer air particles than if it

were coldwere cold weighs less than the room air it weighs less than the room air it

displacesdisplaces experiences an upward net force in experiences an upward net force in

room airroom air floats in room airfloats in room air

Its average density < density of Its average density < density of room airroom air

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Question 5Question 5

Why does a helium balloon float in Why does a helium balloon float in air?air? How does helium differ from air?How does helium differ from air? Doesn’t helium have mass and weight?Doesn’t helium have mass and weight?

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Helium vs. AirHelium vs. Air

Replacing air particles with helium Replacing air particles with helium atomsatoms leaves particle density unchangedleaves particle density unchanged

all particles contribute equally to pressureall particles contribute equally to pressure reduces the gas’s densityreduces the gas’s density

helium atoms are less massive than air helium atoms are less massive than air particlesparticles

leaves the gas’s pressure unchangedleaves the gas’s pressure unchanged helium atoms travel faster & hit more oftenhelium atoms travel faster & hit more often

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Helium Balloon in AirHelium Balloon in Air

A rubber balloon filled with heliumA rubber balloon filled with helium has same particle density as airhas same particle density as air weighs less than the air it displacesweighs less than the air it displaces experiences an upward net force in airexperiences an upward net force in air floats in airfloats in air

Its average density < density of Its average density < density of room airroom air

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Introductory Question Introductory Question (revisited)(revisited)

A helium balloon has mass, yet it A helium balloon has mass, yet it doesn’t fall to the floor. Is there a doesn’t fall to the floor. Is there a real force pushing up on the helium real force pushing up on the helium balloon?balloon?

A.A. YesYes

B.B. NoNo

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The Ideal Gas LawThe Ideal Gas Law

This law is a summary relationship This law is a summary relationship for gases:for gases:

pressure = Boltzmann constant x pressure = Boltzmann constant x

particle density xparticle density x

absolute temperatureabsolute temperature

Assumes, however, perfectly Assumes, however, perfectly independent particlesindependent particles

Real particles aren’t perfectly Real particles aren’t perfectly independentindependent

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Summary about BalloonsSummary about Balloons

Balloons float when their average Balloons float when their average densities are less than that of airdensities are less than that of air

Helium balloons float because Helium balloons float because helium atoms are lighter than air helium atoms are lighter than air particlesparticles

Hot-air balloons float because hot air Hot-air balloons float because hot air has lower particle density than cold has lower particle density than cold airair