Gases

1
Chapter 20

• Gases

2
Gases

• Similar to liquids
• They both flow
• Difference
• The distance between the molecules
• In a liquid the molecules are close together and
  constantly experience forces from surrounding
  molecules
• In a gas the molecules are far apart allowing
  them to move freely between collisions
• When 2 molecules in a gas collide one gains speed
  and the other loses speed? total KE is conserved
• Gases expand to fill all space available and take
  the shape of its container
• Gravitation determines the shape gas only when
  the quantity is very largeatmosphere, a star

3
The Atmosphere

• Molecules in the air extend many kilometers above
  the earths surface
• Energized by sunlight and are always moving
• Without suns energy they would form matter on
  the ground
• Would fly off into outer space if there was not
  gravity
• Without the sun and gravity the earth would not
  have an atmosphere
• What determines the thickness of our atmosphere?
• Balance between
• kinetic energy of molecules vs gravity
• spreads molecules apart

4
The Atmosphere

• Density decreases with altitude
• More compressed at sea level than at higher
  altitudes
• 99 of the atmosphere is below an altitude of 30
  km
• Meteorologists study the state of the atmosphere
  at any given time to predict the weather

5
Atmospheric Pressure

• Air, like water, has weight
• At sea level, 1 m3 of air has a mass of about 1.2
  kg and weighs about 11.7 N
• Suppose this room has a 300 square meter floor
  area and a 5 meter high ceiling, about how many
  kilograms of air occupy this classroom?
• We are at the bottom of an ocean of air
• We dont feel the weight of this air because we
  are use to itjust like a fish is used to the
  water
• The atmosphere exerts pressure
• This pressure varies with altitude
• At sea level it is 1.013 x 105 Pa (N/m2)
• If there is so much pressure from the atmosphere,
  why dont windows and other materials made of
  glass break?
• These common objects dont normally break because
  the pressure acts on both sides of the glass.
  The net force of the atmosphere on the windows is
  zero

6
Atmospheric Pressure

• Recall Pressure Force/area weight/area.
• So to find pressure at sea level, need to
  calculate weight of a column of air rising up to
  top of atmosphere, say about 30 km.
• Find that a 1m2 area cylinder, 30 km high, has
  mass of 10 000kg.
• i.e. weight of 100 000 N.
• So pressure 100 000 N/ (1 m)2
• 100 000 Pa 100 kPa

Precisely, sea-level atmospheric pressure 101.3
kPa
7
The Simple Barometer

• Barometeran instrument used for measuring the
  pressure of the atmosphere
• Barometers balance when the weight of the liquid
  in the tube exerts the same pressure as the
  atmosphere outside
• In a mercury barometer at atmospheric pressure,
  the liquid will rise 760 mm however the barometer
  is oriented
• If atmospheric pressure increases, then air
  pushes down harder on the mercury , so column
  pushed up higher than 76 cm.
• Water could be used to make a barometer, but the
  tube would have to be 13.6 times as long as a
  mercury barometer (mercury is 13.6 times more
  dense than water). The height of a water
  barometer would have to be 10.3 meters!

8
The Simple Barometer

• Barometers are similar to drinking straws
• Sucking on a straw reduces the atmospheric
  pressure in the straw
• The atmospheric pressure on the surface of the
  liquid pushes the liquid up into the reduced
  pressure region
• The liquid is pushed up by the pressure of the
  atmosphere, not sucked up
• If the atmosphere cannot push on the surface of
  the drink, you cannot use a straw
• Water can only be lifted 10.3 meters using a
  vacuum pump
• Think of an old farm water pump. It uses the
  same concept of the straw to pump out the water.
  Air pressure is reduced in the pipe as the air
  expands to fill a larger volume. The greater
  atmospheric pressure surrounding the surface of
  the well water pushes the water out of the pipe.
• The atmospheric pressure can only reach 101.3
  kPa, therefore a vacuum pump can only raise water
  10.3 m
• P?g?h
• 101.3 kPa 1.013 x 105 Pa (1000 kg/m3)(9.8
  m/s2)(?h) 10.3 m

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The Simple Barometer

• Why is it hardly possible to drink sodas on the
  moon with straws?
• Because what makes the drink go up the straw the
  atmospheric pressure and this is essentially zero
  on the moon. Its this that pushes the drink up
  the straw, in which your sucking has created much
  less pressure.

10
The Aneroid Barometer

• A barometer that does not use liquid
• A small metal box that is partially exhausted of
  air with a flexible lid that bends as the
  atmospheric pressure changes
• Motion of the lid is indicated by a spring and
  lever system
• These can be used to determine changes in
  elevation

11
Boyles Law

• Pressure is proportional to density
• When the volume of a gas is decreased, the
  density and therefore pressure are increased

If you halve the volume of container, the
pressure is doubled, since more collisions
(bouncing) between molecules and with
walls. Effectively, the density is doubled.
pressure density (at fixed temp)
12
Boyles Law

• Snorkeling uses Boyles Law
• You cannot snorkel at a depth greater than 1 m
• The air will not move from a region of lesser
  pressure (the air at the surface) to a region of
  greater pressure, the compressed air in a your
  lungs
• If you squeeze a balloon to ½ its volume, by how
  much will the pressure inside increase?
• The pressure doubles!

13
Boyles Law

• To capture its prey, a whale will create a
  cylindrical wall of bubbles beneath the surface
  of the water, trapping a confused fish inside.
  If an air bubble has a volume of 5.0 cm3 at a
  depth where the water pressure is 2.00 x 105 Pa,
  what is the volume of the bubble just before it
  breaks at the surface of the water (assume that
  temperature remains the same)?

14
Ideal Gas Law

• Boyles Law only works for a constant temperature
• The ideal gas law expresses the relationship
  between the pressure, volume and temperature of a
  gas
• Temperature is measured in kelvins (K), pressure
  is measured in pascals (Pa), and volume is
  measured in cubic meters (m3)
• ideal gasesneglect any sticky forces between
  molecules and treat them as point particles.
• At normal temps and pressures, air is
  well-approximated to be an ideal gas

15
Ideal Gas Law

• Tootie, a clown, carries a 2.00 x 10-3 m3 helium
  filled mylar balloon from 295 K heated circus
  tent to the cold outdoors, where the temperature
  is 273 K. How much does the volume of the
  balloon decrease? Assume pressure remains
  constant.
• Taylor is cooking a pot roast for dinner in a
  pressure cooker. Water will normally boil at a
  temperature of 373 K and at an atmospheric
  pressure of 1.10 x 105 Pa. What is the boiling
  temperature inside the pot, when the pressure is
  increased to 1.28 x 105 Pa? The pot maintains a
  constant volume.

16
Buoyancy of Air

• An object surrounded by air is buoyed up by a
  force equal to the weight of the air displaced
• A cubic meter of air has a mass of about 1.2 kg
  so it has a weight of 12 N
• If the weight of the 1 cubic meter object is more
  than 12 N, it will fall to the ground.
• If the weight of the 1 cubic meter object is less
  than 12 N, it will rise.
• Hot air balloons rise because heated air is less
  dense than normal air
• The buoyancy would be greater if the air were
  evacuated, but this would not work since the
  balloon sides would collapse

17
Differences in Liquid and Air Buoyancy

• Important differences
• due to the air density becoming less as you go
  higher (liquid density remains about the same).
  So buoyant force decreases as you rise in
  atmosphere (but stays same while rise in water).
• there is no top to the atmosphere (it just
  keeps thinning out), unlike liquid surface.
• Consequence a light balloon released from bottom
  of ocean will rise all the way to waters
  surface whereas if released from surface of
  earth, will stop rising at a certain height.
• Why, and how high will a helium balloon rise?
• When buoyant force on balloon equals its weight,
  it will stop accelerating upwards.
• Buoyant force displaced-weight-of-air, so for
  same volume of balloon, this decreases because
  air is less dense.
• May continue to rise at the constant speed it
  reached
• but will slow due to air resistance
• If balloon material is able to expand, then it
  will as it rises, as theres less pressure
  outside, so will displace a greater volume of air
  net effect is that buoyant force remains same.
  If it continues to expand, it will eventually
  pop

18
Principles of Fluid (liquid) Flow

• Speed of a fluid flow depends on cross sectional
  area
• This results from mass conservationliquids are
  incompressible, therefore mass flowing through
  any portion of a pipe (regardless of
  cross-sectional area) must be equal for any given
  time interval
• Continuity Equation?A1v1 A2v2
• This explains the effect you have experienced by
  placing your thumb over the end of a hose.
• Your thumb blocks some of the area of water flow,
  therefore the speed of the water must make up for
  this loss of area (so mass is conserved)!
• Pressure is also affected when the area and
  velocity change
• Water travels through a 9.6 cm diameter fire hose
  with a speed of 1.3 m/s. At the end of the hose,
  the water flows out through the nozzle whose
  diameter is 2.5 cm. What is the speed of the
  water coming out of the nozzle?

19
Bernoullis Principle

• When the speed of a fluid increases, the pressure
  drops
• Due to conservation of energy
• ½ mv2 PV mgh constant
• KE (due to motion) work (associated with
  pressure forces) gravitational potential energy
  (due to elevation) constant
• If h does not change, then a decrease in P
  (pressure) requires and increase in v (velocity)
  for the energy to be conserved

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Bernoullis Principle

• Streamlines (thin lines above) represent paths
  (trajectories) of parts of fluid. So are closer
  together in narrower regions where flow is
  faster.
• Bernouilis principle holds when
• the temperature, density, and elevation of fluid
  remains about constant.
• when flow is laminar (i.e. smooth, steady), and
  not turbulent (i.e chaotic)
• If the flow speed is too great, the flow becomes
  turbulent and Bernoullis principle no longer
  holds
• The flow will then follow a curling pathan eddy

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Applications of Bernoullis Principle

• Why during storm might a roof blow off?
• Fast moving air above (bunched up streamlines),
  so less air pressure above than inside.
• Design of airplane wings, make air flow faster
  over the top surface, by a tilt in the wing,
  called angle of attack.

Increased lift for larger wing surface area and
larger speeds
22
Applications of Bernoullis Principle

• A spinning ball produces crowding of
  streamlines. This crowding of streamlines causes
  the ball to be pushed to one sidecurve ball!
• Curving may be increased by threads or fuzzthese
  help drag the air producing more crowding

spinning air pressure greater at B than A, so
ball curves up
non-spinning symmetric streamlines
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Applications of Bernoullis Principle

• A small jeep has a soft, ragtop roof. When the
  jeep is at rest the roof is flay. When the jeep
  is cruising at highway speeds with its windows
  rolled up, does the roof
• Bow upward
• Remain flat
• Bow downward
• A. The roof bows upward
• When the jeep is in motion air flows over the top
  of the roof, while the air inside the jeep is at
  restsince the windows are closed. Thus, there
  is less pressure over the roof than under it. As
  a result the roof bows upward.