Transcript Volume of gas

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.

According to the Newton’s 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.
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.
GAS LAWS
At the end of this lesson, you should be able to:
1.
2.
3.
4.
5.
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.
Property of gases


There is a relationship between pressure,
volume and temperature of a gas.
For a gas in an enclosed container, the
1.
2.
3.
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.
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
-mv
mvx


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.
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.
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.
GAS LAW
BOYLE’S LAW
CHARLES’ LAW
PRESSURE LAW
Gas law
Boyle’s Law
 Boyle’s 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 Boyle’s law is
P
1
V
P
or P 1
V
While temperature kept constant
P1V1 = P2V2
V
Pressure against volume




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
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
Gas law
Charles’ law

Charles’s 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
VαT

While pressure is kept constant
V(cm3)
V = constant
T
or
V1 = V2
T1 T2
T (K)
Volume against temperature

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
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
Gas law
Pressure 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 (Pa)
P
αT
T (K)
Pressure against temperature
That
is P1 = P2 when volume kept constant
T1 T2




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
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
Absolute temperature and the Kelvin
scale

In the experiment to verify
Charles’ Law, the graph of V
α T is a straight line which
cuts the temperature axis (T)
at the value -273°C.

The value -273°C is
equivalent to 0K and known
as the absolute zero because
it is the lowest possible
temperature to be reached.

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

The combined gas law



For Boyle’s 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
P
V
T1
T2
T
Problem solving