what do you think happens to the particles of air inside the ball as it warms in the sun

Up to this betoken nosotros have been thinking of pressure equally being determined past the weight of the air overhead.  Air force per unit area pushes downwardly against the ground at sea level with 14.7 pounds of force per square inch.  If you imagine the weight of the atmosphere pushing down on a airship sitting on the ground you realize that the air in the balloon pushes back with the aforementioned forcefulness.  Air everywhere in the temper pushes upwards, down, and sideways.

The platonic gas police equation is another way of thinking near air force per unit area, sort of a microscopic scale view.  Nosotros ignore the atmosphere and concentrate on only the air inside a modest volume or airship or packet* of air.  We are going to "derive" an equation that shows how pressure (P) depends on sure properties of the air insidie the balloon.

* the word parcel just ways a pocket-size volume of air.

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Hot air balloons rise (they also sink), so does the relatively warm air in a thunderstorm updraft (its warmer than the air around it).   Conversely cold air sinks.  The surface winds caused past a thunderstorm downdraft (as shown above) tin accomplish speeds of 100 MPH and are a serious weather condition hazard.

Understanding the ideal gas law is the first step in explaining what really causes air to rise or sink.

In the second stride nosotros volition look at Charles' Law, a special situation involving the ideal gas police force (air temperature and density change together in a way that keeps the pressure within a balloon abiding).  And so we'll learn virtually the vertical forces that human activity on air (an upwards and a downward forcefulness) in Pace 3

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The effigy in a higher place makes an important bespeak: the air molecules in a balloon "filled with air" really have up very little space.  A balloon filled with air is really generally empty infinite.  Information technology is the collisions of the air molecules with the inside walls of the balloon that keep the balloon inflated.

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In A

The pressure produced past the air molecules inside a airship will get-go depend on the number of air molecules, Due north, in the balloon.  As yous add more and more air to something like a cycle tire, the pressure increases. If there weren't whatever air molecules at all at that place wouldn't be any pressure. Pressure is directly proportional to N - an increase in N causes an increase in P.  If N doubles, P also doubles (as long as the other variables in the equation don't change). In B
Air pressure within a airship also depends on the size of the airship.  Pressure is inversely proportional to volume, V .  If V were to double, P would drop to 1/2 its original value. Note
It is possible to keep pressure level constant past changing Due north and Five together in just the correct kind of way.  This is what happens in the oxygen concentration experiment described in Week 1.  Oxygen in a graduated cylinder reacts with steel wool to form rust.  Oxygen is removed from the air sample which is a decrease in North.  As oxygen is removed, water rises up into the cylinder decreasing the air sample book.  N and Five both subtract in the same relative amounts and the air sample pressure remains constant. If y'all were to remove 20% of the air molecules, V would decrease to xx% of its original value and pressure level would stay constant.

Part C: Increasing the temperature of the gas in a balloon volition cause the gas molecules to motility more quickly.  They'll collide with the walls of the balloon more ofttimes and rebound with greater force.  Both will increase the pressure.  You shouldn't throw a tin can of spray pigment into a burn because the temperature will cause the pressure level inside the can to increment and the can could explode.  We'll demonstrate the effect of temperature on pressure in class on Friday. Surprisingly, as explained in Part D, the force per unit area does not depend on the mass of the molecules.  Force per unit area doesn't depend on the composition of the gas.  Gas molecules with a lot of mass will move slowly, the less massive molecules will move more quickly.  They both will collide with the walls of the container with the aforementioned force. The figure below shows two forms of the ideal gas law.  The tiptop equation is the i we just derived and the bottom is a second slightly different version. You can ignore the constants thou and R if you are just trying to empathise how a change in i of the variables would touch the pressure.  You simply need the constants when you are doing a calculation involving numbers (which we won't be doing).

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Charles' Law is a special case involving the ideal gas law.  Charles Law requires that the pressure in a book of air remain abiding.  T, V, and density tin change but they must do so in a way that keeps P constant.  This is what happens in the temper.  Volumes of air in the atmosphere are free to expand or compress.  They do so to keep the pressure within the air volume abiding (the pressure within the volume is staying equal to the pressure of the air exterior the volume).

Air in the atmosphere behaves like air in a balloon.  A airship can grow or shrink in size depending on the force per unit area of the air inside.  When a airship isn't getting bigger or smaller it ways the force within that is pushing out is counterbalanced by the force outside that is pushing in.

We start in the peak figure with air inside a balloon that is exactly the aforementioned as the air exterior.  The air inside and outside have been colored green.  The arrows show that the pressure level of the air  inside pushing outward and the force per unit area of the air surrounding the balloon pushing inward are nevertheless strength.

Next we warm the air in the balloon (Fig. 2).  The ideal gas law equation tells united states that the pressure of the air in the balloon will increase.  The increment is momentary though.

Considering the force per unit area inside is now greater (the big yellowish arrows) than the pressure exterior, the balloon will expand.  As book begins to increase, the pressure of the air inside the balloon will decrease.  Eventually the airship volition expand just plenty that the pressures inside and outside are again in balance.  You lot end up with a balloon of warm depression density air that has the same force per unit area as the air surrounding it (Fig. three)

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You can apply the same reasoning to understand what happens when yous cool the air in a balloon.

The air within and exterior are the aforementioned in Fig. 1.  Cooling the air inside the balloon in Fig. 2 causes a momentary drop in the inside pressure level (pocket-size yellow colored arrows) and creates a pressure level imbalance.  The stronger outside air pressure level compresses the airship.

As the balloon volume decreases, force per unit area inside the balloon increases.  It eventually is able to residue the outside air force per unit area.   You lot end upwardly with a airship filled with cold high density air.

If you warm air it will expand and density will decrease until the pressure within and outside the parcel are equal.
If you absurd air the parcel will shrink and the density volition increase until the pressures balance.

These two associations:

(i)   warm air = low density air
(ii)  cold air = loftier density air

are important and will come upwards a lot during the balance of the semester.

Hither's a visual summary of Charles' Law

If you warm a parcel of air the book volition increase and the density volition subtract.  Pressure inside the parcel remains abiding.  If you cool the bundle of air it's volume decreases and its density increases.  Pressure within the parcel remains constant.

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Charles Law is demonstrated in the classroom version of this class by dipping a balloon in liquid nitrogen.

The airship shrinks down to practically zero volume when pulled from the liquid nitrogen.  It is filled with very cold high density air at that point.  Equally the balloon warms the airship expands and the density of the air inside the balloon decreases.  The volume and temperature kept irresolute in a fashion that kept pressure abiding.  Eventually the balloon ends up back at room temperature (unless it pops).

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Now nosotros are in a position to have a quick expect at the forces that tin cause parcels of air to rise or sink.

Basically information technology comes down to this - there are two forces acting on a bundle of air in the atmosphere:
ane. Gravity pulls downward.  The strength of the gravity force depends on the mass of the air inside the parcel.  This forcefulness is just the weight of the bundle
2. There is an upward pointing pressure deviation force.  This strength is caused by the air exterior the packet (air surrounding the parcel).  Pressure decreases with increasing altitude.  The pressure level of the air at the bottom of a parcel pushing upward is slightly stronger than the pressure of the air at the peak of the balloon that is pushing downwards.  The overall consequence is an upward pointing force. When the air inside a parcel is exactly the aforementioned as the air exterior, the 2 forces are equal in strength and cancel out.  The parcel is neutrally bouyant and doesn't rise or sink. If y'all replace the air inside the airship with warm low density air, information technology won't counterbalance as much.  The gravity force is weaker.  The up pressure difference strength doesn't modify, because it is determined by the air outside the balloon which hasn't changed, and ends up stronger than the gravity strength.  The balloon will rising. Conversely if the air within is cold high density air, it weighs more.  Gravity is stronger than the upward pressure divergence force and the balloon sinks.

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We can modify the sit-in that nosotros did before to demonstrate Charles' Law.  In this case nosotros use balloons filled with helium (or hydrogen).  Helium is less dense than air even when the helium has the same temperature every bit the surrounding air.  A helium-filled balloon doesn't demand to warmed up in society to ascension.

Nosotros dunk the helium-filled balloon into some liquid nitrogen to absurd it and to cause the density of the helium to increase.  When removed from the liquid nitrogen the balloon doesn't rise, the cold helium gas is denser than the surrounding air (the purple and blueish balloons in the figure above).  Every bit the balloon warms and expands its density of the helium decreases.  The balloon at some point has the same density as the air effectually it (green in a higher place) and is neutrally bouyant.  Somewhen the balloon becomes less dumbo that the surrounding air (xanthous) and floats upward to the ceiling. Something like this happens in the atmosphere.

At (i) sunlight reaching the ground is absorbed and warms the ground.  This in turns warms air in contact with the basis (2)  Once this air becomes warm and its density is low enough, small-scale "blobs" of air split from the air layer at the basis and begin to ascension.  These are called "thermals."  (3) Ascent air expands and cools (this is something we oasis't covered even so).  If it cools enough (to the dew bespeak) a cloud will get visible as shown at Indicate four.  This whole procedure is called free convection.  Many of southern Arizona's summer thunderstorms start this style.

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The relative strengths of the downward graviational force and the up pressure departure force determine whether a package of air will rising or sink.  Archimedes Law is another way of trying to empathise this topic.

A gallon of h2o weighs most viii pounds (lbs). If y'all submerge a i gallon jug of water in a swimming puddle, the jug becomes, for all intents and purposes, weightless.  Archimedes' Police (see figure below, from p. 53a in the photocopied ClassNotes) explains why this is true.

The upward bouyant strength is actually just another name for the force per unit area departure force covered before today (higher force per unit area pushing up on the bottle and low pressure at the tiptop pushing downwards, resulting in a net upward force).  A one gallon bottle will displace 1 gallon of puddle water.  1 gallon of puddle water weighs eight pounds.  The upward bouyant forcefulness volition be 8 pounds, the same every bit the downward force on the jug due to gravity.  The ii forces are equal and contrary. Now nosotros imagine pouring out all the water and filling the 1 gallon jug with air.  Air is nearly 1000 times less dense than water;compared to water,  the jug will weigh practically cypher.

If y'all submerge the jug in a pool it will readapt 1 gallon of h2o and experience an eight pound upward bouyant force once more.  Since in that location is no downwardly force the jug volition float. One gallon of sand (which is about 1.v times denser than water) jug will weigh 12 pounds.

The jug of sand volition sink because the downwardly force is greater than the upward forcefulness. You lot tin sum all of this upward by proverb annihilation that is less dense than water will bladder in water, annihilation that is more dense than water will float in water. The aforementioned reasoning applies to air in the atmosphere.

Air that is less dense (warmer) than the air around it volition rise.  Air that is more dense (colder) than the air around it volition sink.

At that place's a colorful demonstration of how pocket-size differences in density can decide whether an object floats or sinks.

Cans of both regular and Diet Pepsi are placed in beakers filled with water (Coke and Diet Coke tin besides be used).

Both cans are made of aluminum which has a density almost three times college than water.  The beverage itself is largely water.  The regular Pepsi as well has a lot of high-fructose corn syrup, the Nutrition Pepsi doesn't.  The mixture of h2o and corn syrup has a density greater than plain h2o.  There is besides a little air (or perhaps carbon dioxide gas) in each can.

The average density of the can of regular Pepsi (water & corn syrup + aluminum + air) ends up existence slightly greater than the density of water.  The boilerplate density of the tin can of nutrition Pepsi (water + aluminum + air) is slightly less than the density of water.

In some respects people in swimming pools are similar cans of regular and nutrition soda.  Some people float (they're a little less dense than water), other people sink (slightly more than dense than water).

Many people tin can fill their lungs with air and make themselves float, or they can empty their lungs and brand themselves sink.  People must have a density that is about the same as water.

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Source: http://www.atmo.arizona.edu/students/courselinks/fall12/atmo170a1s1/coming_up/week_2/lect6_ideal_gas_law.html

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