Lesson 2.5 Gases
Overview
This lesson deals with gases, atmospheric pressure,
Boyles law and Bernoulli’s principle. On completion
of the lesson, you should be able to discuss the behavior
of gases in terms of the kinetic theory. You should also
be able to explain variations in atmospheric pressure
with altitude, explain the relationship between pressure
and and volume and pressure and velocity in venturis and
aircraft wings.
MINI
LAB
CHOICE OF ACTIVITIES
- Crush can: Boil some
water inside a soda can and quickly invert it
into a container with cold water in it.
- Barometer: Make a
barometer with a glass jar and a thin sheet of
rubber sealed around the edge of the opening.
Attach a pointer to the surface of the sheet.
- Make a hot air
balloon
- Venturi: Cut a
drinking straw in half. Place the end of one
piece in some water. Use the other half of the
straw to direct a jet if air over the open end of
the straw. This should create a spray as the air
"draws" the water up towards the stream
of air.
Kinetic Theory
Gas molecules fill whatever container they are in. They
move around rapidly, collide with each other and collide
with the surface of the container. The pressure of the
gas is caused by the rate at which the molecules collide
with the container’s surface. When molecules collide
with the surface of a container at a higher rate, the
pressure increases
Gases Have Weight
We move about in a sea of gas. This gas occupies space
and has mass.
We can demonstrate this by comparing the mass of a sample
of compressed gas with a similar sample at normal
atmospheric pressure.
Gases And Buoyancy
The air around us has pressure and this pressure can
cause buoyancy.
The lifting power of a balloon depends on the difference
in density between the gas in the balloon and the air
outside the balloon.
For example, helium atoms have four times the mass of
hydrogen atoms but the lifting power of a hydrogen
balloon is only marginally better than that of a helium
balloon. The lifting power of a balloon is equal to the
mass of air displaced less the mass of the balloon.
(See Example 2.5.2 below)
Air Pressure
The amount of pressure that the air around us can exert
is quite large.
The force that air exerts at sea level, relative to a
vacuum, is 101,300 N per square meter.
It can support a column of water 10 meters high. On 1
square meter, this is equivalent to the weight of 10 tons
of water. We have seen how air pressure can crush a can
and how air pressure holds things in place. In the famous
Magdenberg experiment, the mayor of Magdenberg, Otto von
Guericke used two teams of horses to try to pull two
hemispheres apart after the air between them was
evacuated.
Barometers
We use barometers to measure changes in air pressure.
A mercury barometer consists of a tube that is closed at
one end. It is filled with mercury and tipped upside down
with its open end below the surface of the mercury in a
small reservoir. The pressure on the liquid in the
reservoir keeps the liquid in the tube. (Or we could say
that the vacuum above the liquid keeps it in place but a
vacuum is just the absence of pressure.) Normal
atmospheric pressure at sea level will keep the top of
the column of mercury at a level of 760 mm above the
level of the mercury in the reservoir. The level of the
mercury in the column changes as the atmospheric pressure
changes.
Theoretically, we could
use water in a similar type of barometer but the lower
density of water would require the tube to be that over
10 meters high. The main problem is however that water
boils when the pressure gets too low and the closed end
of the tube will contain a lot of water vapor that will
affect the reading quite considerably.
A type of water barometer
consists of a sealed container with water and air in it.
The level of water in a side tube changes as the air
pressure changes and this can be used to give an
indication of the atmospheric pressure.
Aneroid Barometer
Changes in atmospheric pressure help us to predict
changes in the weather. It’s useful to have a
barometer but water barometers or mercury barometers are
not practical for household use.
Mercury is very dangerous and water barometers are bulky
and inaccurate. The most practical barometer is the
aneroid barometer.
This is just a closed container that changes its shape as
the air pressure around it changes. A system of levers
and a pointer are used to amplify the movement of the
surface of the container and give an indication of the
change in pressure.
Altimeters
We can also us a barometer to measure the height above
sea level. Airplanes have altimeters which have the same
structure as an aneroid barometer. The scale on the
altimeter is graduated to show the height above sea level.
The air expands as its pressure decreases. This means
that the density of the air decreases as it gets further
away from the earth. Because of this, the relationship
between altitude and pressure is not simply proportional.
Pressure at a certain depth of fluid depends on the
density of the fluid. In liquids, the density is the same
at all depths but with gases, the density changes with
depth.
Bernoulli & Venturi
Speed affects pressure. Aircraft stay in the sky because
air speeds up as it goes over the top of the aircraft’s
wing. The increase causes a drop in pressure on the top
of the wing. When the kinetic energy of the air
increases, its pressure energy must decrease and visa
versa.
The wing is also shaped so that the air slows down
slightly as it passes under the wing and this causes a
slight increase in pressure below the wing. This
difference in pressure acting over a large area, provides
the lift needed to keep the aircraft in the air.
Stalling
Its important that the air flows smoothly over the wing
of an aircraft for the lift forces to work.
If the speed drops too much or if the angle of the wing
is too large, we get turbulence on the wing that messes
up the flow patterns, stops the lift and the airplane
stalls.
Boyles Law:
P1V1
= P2V2 The pressure of a sample of
an ideal gas multiplied by its volume is constant if the
temperature remains constant.
P1 = Initial
pressure (Pa)
V1 = Initial volume (m3)
P2 = Final pressure (Pa)
V2 = Final volume (m3)
Example
2.5.1 Boyle’s Law
If a 5-liter container filled with air at 101300 Pa. is
squashed until the volume of the air 2 liters, what will
be pressure inside the container?
Solution
P1V1 = P2V2 P2
= 5/2 x 101300 Pa
P2
= 253250 Pa
Example
2.5.2 Buoyancy
Calculate the lifting power of a 20 m3 helium-filled
bag in air that has a density of 1.2 kg.m-3.
The density of the helium may be taken as 0.19 kg.m-3.
Assume that the mass of
the empty bag is 5 kg.
Solution
The mass of air displaced by the helium bag is = 20 x 1.2
= 24 kg.
The mass of helium in the
bag = 20 x 0.19 = 3.8 kg
The mass of the bag is = 5
kg
The lift created by the
balloon is therefore equivalent to the weight of:
24 kg – 3.8 kg –
5 kg = 15.2 kg
This is equivalent to 15.2
kg x 9.81 N/kg = 149 N
Questions
- How is the rate at
which gas molecules collide with the inner
surface of a container related to the pressure of
the gas in the container?
- Why does the rate of
collision between gas molecules and the inner
surface of a container increase if the amount of
gas in the container is increased?
- Why does the rate of
collision between gas molecules and the inner
surface of a container increase if the
temperature of the gas in the container is
increased?
- If the atmosphere
exerts a pressure of 101300 N on a square meter
of surface at the earth’s surface, what is
the mass of a column of air with a base of 1 m2
that extends all the way to the top of the
atmosphere?
- What is the
difference between a mercury barometer and an
aneroid barometer?
- How could a barometer
be used to estimate the height of a very tall
building?
- If we assume that 99%
of the atmosphere is in a 30-kilometer deep layer
around the earth, what is the average density of
the earth’s atmosphere?
- If 50% of the earth’s
atmosphere is below 5600 meters, what is the
average density of the air at elevations between
0 and 5600 meters?
- How does Boyle’s
law describe the relationship between the
pressure and volume of a fixed amount of gas?
- If a 2-liter bottle
filled with air at 101300 Pa. is squashed until
the volume of the air in the bottle is 1 liter,
what will be pressure inside the bottle?
- If treasure hunters
use a large bag filled with air to lift a bronze
cannon from the ocean floor to the surface, why
is this potentially dangerous?
- If a dirigible is
filled with hydrogen that has roughly half the
density of helium, why does it not have twice the
lifting power?
- If the air in a large
warehouse has a density of 1.18 kg/m3,
what mass of air in the building is displaced by
a bag of helium with a volume of 10 m3?
If the bag has a mass of 1 kg and the helium in
the bag has a density of 0.185 kg/m3,
what is its lifting power?
- A fluid flowing
through a pipe speeds up as it flows into a
narrower section of pipe. Why does the pressure
of the fluid decrease as its speed increases?
- Will the pressure
increase if the fluid moves into a pipe with a
larger diameter?
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