Gasses and Pressure
Floating on Air
Bloomfield Chapter 5.1
1. Gases and pressure:
- How tires work
- Why does your sealed Tupperware explode in the microwave?
2. The atmosphere:
- Why is there less O2 on the top of Longs Peak?
3. Balloons
- Helium and Hot air … why do these rise?
Important physics:
Lecture 15:
Gasses and Pressure
Bloomfield 5.1
- Forces: Newton’s Laws (Fnet = mass x acceleration),
- Weight = (mass in kg) x g
- Ideal gas law
- Pressure
- Buoyancy force – Archimedes principle.
Revisit 1010 notes on force and NET force if you need a refresher
Reminders:
HW 7 available. Due Monday 10pm.
Lab 6 today and tomorrow
Reading quiz in a moment
Research topic due this Friday
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Air Pressure
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Need to raise pressure of tire to make it work.
Think about all the different ways to raise pressure of a gas. Work in
group, write down 3 ways and why this would increase pressure.
Air pressure:
- Air contains lots of small molecules zooming around.
- Hit objects and each other … exert a force
1. Add more gas molecules (Increase N (# of molecules)  Increase P, more
collisions with wall/each other every second)
2. Make gas hotter (Increase T (temperature)  Increase P, moving faster, more
collisions, hitting harder)
3. Make box smaller (Decrease V (volume)  Increase P, higher density, more
collisions with wall/each other every second)
Force exerted = pressure of air x area
OR Pressure = Force/Area
(Units: Pa = N/m2)
With a totally flat bike tire (tubeless tire), the air pressure
on the inside of the tire is:
a. less than the air pressure on the outside
b. greater than the air pressure on the outside
c. equal to the air pressure on the outside.
Rim
Looking at behavior of a gas gives “ideal gas law”:
Pressure= k * (number of particles) * (Temperature in K)
Volume
In Pascals (Pa)
Boltzmann’s
Constant (k):
1.38x10-23 Pa m3/(atom K)
Tube
Number Density =
# atoms/m3
Temperature
in absolute scale (Kelvin)
0 C = 273 K
room temp = 293 K
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Ideal gas law
Pressure= k * (number of particles) * (Temperature in K)
Volume
Forces review
P = kNT
V
Does pressure depend on type of gas atom/molecule? (e.g.He vs Air):
a) yes b) no
http://www.colorado.edu/physics/phet/simulations/force1d/force1d.jnlp
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DO NOT(!) BE ALARMED
A loud “boom” sound will occur
between 11:15 and 12:15 pm
on the 1st floor of Duane. This
is a scheduled demo so do not
worry. We apologize for this
brief disturbance in the name of
education.
What will happen if we remove the air from inside the
drum?
a. Nothing
b. The drum will explode
c. The drum will implode
d. Something else
Pressure
Gauge
REMOVE AIR FROM INSIDE
PUMP
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How much force is air pressure putting on the steel drum?
The mighty force of Air Pressure!
Initially:
Air both inside and out
Pressure inside = Pressure outside
No Net Force on walls of barrel
(of course still have force of gravity)
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Force = (Air) Pressure * Area
Top of
Atmosphere
(~50 km)
As Air removed:
Atmospheric pressure is defined as the force per
unit area exerted against a surface by the weight of
air above that surface
So how much does the atmosphere above us
weigh?
Add up weight of every air molecule in column:
Total weight = 10,300 kg* 9.8 m/s2
= 101,000 Newtons
Pressure at sea level = 101,000N/1m2
= 101,000 Pa
(LIKE A BIG BUS ON EVERY m2!)
Column of Air
above ground
(1 m2).
To Pump
?
•Air molecules at near sea level must exert this
force/area upwards to support column of air above.
•But air molecules move randomly so they exert the
same pressure (or force per area) in ALL directions
(not just vertically).
•Pressure is not a vector (does not have a direction)
Sea Level
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What about on Long’s Peak?
What about in Boulder?
Boulder
Elevation 5400 ft
Top of
Atmosphere
Top of
Atmosphere
Boulder
Elevation 5400 ft
Longs peak
Elevation 14,000 ft
(Not to scale!)
• Pressure = Weight/Area of Atmosphere ABOVE
• Atmosphere ~80% above, ~20% below
 Pressure = 20% less than at sea level
Boulder
Sea Level
Runners
at the
Bolder
Boulder
- Pressure = Weight/area of Atmosphere ABOVE
- Atmosphere ~60% above, ~40% below
- Air pressure on LP 40% LESS than at sea level!
Longs Peak
English tourist
Boulder
Sea Level
Boulderite
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Buoyancy and Archimede’s Principle
Consider cube of air
defined by these
imaginary borders:
Also air pressure pushing
against front and back of cube.
What are the forces acting on the
cube of air?
a. just gravity down
b. gravity down, air pressure pushing
equally on all sides.
c. gravity down, air pressure from all
sides but bigger on bottom than top.
Remember back, Phys1010… Fnet = ma.
If air parcel is stationary, then:
a. Fair pressure > Wair in cube
b. Fair pressure < Wair in cube
c. Fair pressure = Wair in cube
d. No way of knowing.
d. gravity down, air pressure from all
sides but bigger on top than bottom.
GROUND
e. only air pressure
GROUND
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Buoyancy Force Question
Buoyancy Force
#1
Air
Buoyancy force
#2
He
Fair pressure called Fbuoyancy
#3
AIR
Fbuoyancy = Wair in cube
= massair × g
= densityair × volumecube × g
How does F buoyancy compare for each balloon?
A. F buoyancy for #1 > #2 > #3
B. F buoyancy for #2 > #1 > #3
C. F buoyancy for #1 = #2; & both larger than #3
D. F buoyancy for #2 > #3 > #1
E. F buoyancy for #1 = #3; & both smaller than # 2.
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Buoyancy Force and Archimede’s Principle
#2
He
How does F buoyancy compare for each balloon?
1. F buoyancy = upward force from pressure of air surrounding object
2. The air surrounding object cannot tell what it is pushing on … could be
a balloon, a person, a table, or just air … hits it the same regardless of
what it is hitting.
3. Archimede’s principle:
F buoyancy upwards equals the weight of the air (or more generally the
weight of the fluid) displaced by the object.
 Depends on volume of object and density of air (fluid) outside.
F buoyancy
?
F buoyancy
Weight
Balloon + He
+ string
Calculating F buoyancy for Balloon #2 :
density of He (in boulder) = 0.17 kg/m3 density of air in boulder = 1 kg/m3
r = 0.3m
Why is #3 true?
Because we know that if our object is just
a pocket (or cube) of air, then Fbuoyancy will
exactly balance it’s weight and the pocket
of air will feel no net force.
a)
b)
c)
d)
e)
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2.3 N
9.8 N
1.1 N
3.2 N
22.8N
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#2
He
a)
b)
c)
d)
e)
800 kg
2g
70 g
400 g
2 kg
F buoyancy = ?
#2
He
Weight balloon + string = 0.2 N
F buoyancy = ?
Weight balloon + string = 0.2 N
Weight He = ?
Weight He = ? N
Max load = ?
Max load = ? N
Calculating F buoyancy for Balloon #2 :
density of He (in boulder) = 0.17 kg/m3 density of air in boulder = 1 kg/m3
r = 0.3m, Fbuoyancy = ?
If the balloon and string have a weight of 0.2 N, what is the maximum mass
I can tie to the string and the balloon still just about lifts off?
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How can we lift stuff with a balloon?
Air vs. Helium Balloon
What if we make a sealed light-weight Aluminum (Al) foil balloon…
remove air inside volume/balloon? Could we carry our selves?
BIG VOLUME
Lots air displaced
BIG F buoyancy?
SAME
VOLUMES
Nope… Squashed
by atmosphere
(just like drum!)
AIR
HELIUM
How does buoyancy force for each balloon compare?
a) Fbuoyancy greater for air filled balloon
b) Fbuoyancy greater for helium filled balloon
c) Fbuoyancy the same for each
d) You can’t tell
What could you do that could make this work?
a. make out of really heavy metal to hold against air
pressure
b. fill with water so would not compress in
c. fill with some other gas that is lighter than air.
d. fill with air
e. something else
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Air vs. Helium Balloon
SAME
VOLUMES
AIR
Air vs. Helium Balloon
HELIUM
SAME
VOLUMES
How does the PRESSURE inside each balloon compare?
a. Pressure greater inside air filled balloon
b. Pressure greater inside He filled balloon
c. Pressure the same in each
d. Can’t tell
AIR
HELIUM
How do the number of particles (He atoms or air molecules) compare in
each balloon?
a. More particles in air filled balloon
b. More particles in He filled balloon
c. Same number of particles in each
d. Can’t tell
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Air vs. Helium Balloon
AIR
What about a hot air balloon?
Why does a hot air balloon rise?
a) Hotter air inside balloon has higher pressure than colder air outside
b) Density of air is smaller inside balloon
c) He is injected inside balloon
d) Mass of air molecule decreases when it gets hotter
HELIUM
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Cold air balloon
Will it sink or will it float?
If I stick a balloon full of air into liquid nitrogen and wait for some time, then ….
(Liquid Nitrogen temp = 77 K)
a.
b.
c.
d.
e.
number of molecules inside balloon will be less
pressure inside the balloon will be lower
volume will decrease and number density of molecules will be higher
b and c
a and b
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It have a plastic ball and a large tub of water. What property of the ball
determines whether it will sink or float in the water?
a) Volume of the ball
b) Mass of the ball
c) Density of the ball
d) Color of the ball
e) Surface roughness of the ball
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I have a plastic ball of density 950 kg/m3
First I drop it in a bucket of water (density = 1000 kg/m 3) and then I drop it in a
bucket of oil (density = 900 kg/m3)
Which statement below is correct:
a)
b)
c)
d)
e)
It sinks in both
It floats in both
Sinks in oil, floats in water
Floats in oil, Sinks in water
Cannot determine without more information.
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