Explanation

1
Explanation

• Gas pressure is caused by collisions of gas
  molecules on the wall of the container.
• The molecule collide with one other , with the
  walls of the container and with the surface of
  the piston in elastic collisions.
• The collisions of air molecules with the walls of
  the syringe and with the surface of thumb or the
  piston resulting in force acting on them.
• When the gas molecule hits the surface of the
  wall of syringe with a velocity, v and bounces
  back with velocity ,-v there is a change of
  momentum.

2

• According to the Newtons Second Law of motion,
  force equals to rate of change of momentum.
  Hence, there is a force, F acting on the wall of
  the syringe.
• P F / A
• Therefore, there is a pressure exerted on the
  wall of the container.

3

Existence of Gas Pressure

• The plastic bottle expands after it has been
  exposed to sunlight. Why?
• This is due to the volume of air in the bottle
  increases when the temperature increase.
• The lid of the tin will bursts open when the heat
  energy is supplied to it. Why?
• This is because the air pressure in the tin
  increases when the temperature increases.
• When a balloon is compressed, the balloon is not
  flattened and a resistance is felt. Why?
• This due to the air pressure in the balloon
  increases when volume is decreased.

4
GAS LAWS

• At the end of this lesson, you should be able to
• Explain gas pressure, temperature and volume in
  terms of the behaviour of gas molecules.
• Determine the relationship between
• Pressure and volume
• Volume and temperature
• Pressure and temperature
• For a fixed mass of gas.
• Explain absolute zero
• Explain the absolute/kelvin scale of temperature
• Solve problems involving pressure, temperature
  and volume of a fixed mass of gas.

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Property of gases

• There is a relationship between pressure, volume
  and temperature of a gas.
• For a gas in an enclosed container, the
• Number of molecules is constant
• Mass of the gas is constant
• Behaviour of the gas depends on the volume,
  temperature and pressure of the gas.

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Pressure of a gas

• According to the kinetic theory, a gas consists
  of a large number of molecules that are
  constantly moving at random with high speeds.
• During collisions, a molecule exerts force on the
  wall. The momentum change during a collision dp
  mvx- (-mvx)
• 2mvx
• Thus, the pressure of a gas is due to the
  collisions of the gas molecules with the walls of
  the container.
• Gas pressure can be increased by
• Increasing the temperature
• Reducing the volume
• Increasing the number of molecules.

mvx
-mvx
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Volume of gas

• The volume of gas is the space occupied by its
  molecules.
• Therefore, the average distance between the gas
  molecules determines its volume.
• The volume of the gas is equal to the volume of
  the container.

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Temperature of gas

• Gas molecules are in constant random motion and
  have kinetic energy.
• When gas is at higher temperature, the gas
  molecules move with a greater velocity and will
  have more kinetic energy.
• The temperature of the gas is related to the
  average kinetic energy of the gas molecules.

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GAS LAW
BOYLES LAW
CHARLES LAW
PRESSURE LAW
10
Boyles Law
Gas law

• Boyles law states that the pressure of a fixed
  mass of gas is inversely proportional to its
  volume if the temperature is kept constant.
• The mathematical expression for Boyles law is
• or
• While temperature kept constant
• P1V1 P2V2

P
V
Pressure against volume
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• When the volume of a gas is decreased, the number
  of molecules per unit volume increases
• The same number of molecules moves in a smaller
  space
• The molecules collide more frequently with the
  walls of the container
• The increase in the rate of collisions results in
  an increase in the pressure exerted by the gas

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Example

• The air in the cylinder of hand pump has a
  initial volume of 800 cm3 and pessure 102 kPa.
  The air is then slowly compressed to a volume of
  160 cm3. What is the pressure of the compressed
  air in the pump?
• Answer
• P2 510 kPa

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Charles law
Gas law

• Charless law states that the volume of a fixed
  mass of gas is directly proportional to its
  absolute temperature if the pressure is kept
  constant.
• The mathematical expression for Charles law is
• V a T
• While pressure is kept constant
• V constant
• T
• or
• V1 V2
• T1 T2

V(cm3)
T (K)
Volume against temperature
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• When the temperature of a gas is increased, the
  speed of its molecules increases
• Since the speed of the molecules increase with
  temperature, the force that acts on the walls of
  the container will be greater if its volume
  remained unchanged
• As a result, the volume of a fixed mass of gas
  will increase when its temperature is increased,
  provided that the pressure remains constant

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Example

• 2.4 m3 of air at 27 C in an expandable cylinder
  is heated to a temperature of 87 C at constant
  pressure. What is the new volume of air?
• Answer
• V2 2.88 m3

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Pressure law
Gas law

• The pressure law states that the pressure of a
  fixed mass of gas is directly proportional to its
  absolute temperature if the volume is kept
  constant
• The mathematical expression for the pressure law
  is
• P a T
• That is P1 P2 when volume kept constant
• T1 T2

P (Pa)
T (K)
Pressure against temperature
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• When a gas is heated, the average kinetic energy
  of the molecules increases. The temperature of
  the gas increases
• The faster moving molecules strike the walls of
  the container more frequently
• The molecules also experience a larger change of
  momentum when the bounce back from the walls
• A larger force is exerted on the walls resulting
  in a higher pressure

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Example

• The initial pressure and temperature of the air
  in a car tyre was 200 kPa and 27 C respectively.
  After a journey, the pressure of the air was
  found to be 230 kPa. Calculate the temperature of
  the air in the tyre.
• Answer
• T2 345 K
• 345 273 72 C

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Absolute temperature and the Kelvin scale

• In the experiment to verify Charles Law, the
  graph of V a T is a straight line which cuts the
  temperature axis (T) at the value -273C.
• The value -273C is equivalent to 0K and known as
  the absolute zero because it is the lowest
  possible temperature to be reached.

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• If the absolute zero is taken as the origin, the
  temperature scale is known as the absolute scale
  or Kelvin scale. The temperature in this scale is
  known as the absolute temperature and its unit is
  the Kelvin (K).
• The relationship between the temperature in the
  Celcius scale and Kelvin scale is as follow
• t C (Ø 273 ) K
• Ø K (t 273 ) C
• Where t temperature in the Kelvin scale.
• Ø temperature in the Celcius scale

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The combined gas law

• For Boyles Law , PV constant
• For Charles Law, V / T constant
• For Pressure Law, P / T constant
• When combine all the equation, PV / T constant
• P1V1 P2V2
• T1 T2

P V T
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Problem solving