ExplanationExplanationGas pressure is caused by collisions of gas Gas pressure is caused by collisions of gas molecules on the wall of the container.molecules on the wall of the container.

The molecule collide with one other , with the The molecule collide with one other , with the walls of the container and with the surface of walls of the container and with the surface of the piston in the piston in elastic collisionselastic collisions..

The collisions of air molecules with the walls The collisions of air molecules with the walls of the syringe and with the surface of thumb of the syringe and with the surface of thumb or the piston resulting in force acting on or the piston resulting in force acting on them.them.

When the gas molecule hits the surface of the When the gas molecule hits the surface of the wall of syringe with a velocity, v and bounces wall of syringe with a velocity, v and bounces back with velocity ,-v there is a change of back with velocity ,-v there is a change of momentummomentum..

According to the Newton’s Second According to the Newton’s Second Law of motion, force equals to rate Law of motion, force equals to rate of change of momentum. Hence, of change of momentum. Hence, there is a force, F acting on the wall there is a force, F acting on the wall of the syringe.of the syringe.

P = F / AP = F / A

Therefore, there is a pressure Therefore, there is a pressure exerted on the wall of the container.exerted on the wall of the container.

The plastic bottle expands after it has been The plastic bottle expands after it has been

exposed to sunlight. Why?exposed to sunlight. Why?This is due to the This is due to the volume of air in the bottle volume of air in the bottle increasesincreases when when the temperature increasethe temperature increase..

The lid of the tin will bursts open when the The lid of the tin will bursts open when the heat energy is supplied to it. Why?heat energy is supplied to it. Why?This is because the This is because the air pressure in the tin air pressure in the tin increasesincreases when the when the temperature increasestemperature increases..

When a balloon is compressed, the balloon is When a balloon is compressed, the balloon is not flattened and a resistance is felt. Why?not flattened and a resistance is felt. Why?This due to the This due to the air pressure in the balloon air pressure in the balloon increasesincreases when when volume is decreasedvolume is decreased..

Existence of Gas Existence of Gas PressurePressure

At the end of this lesson, you should be able to:At the end of this lesson, you should be able to:

1.1. Explain gas pressure, temperature and volume in Explain gas pressure, temperature and volume in terms of the behaviour of gas molecules.terms of the behaviour of gas molecules.

2.2. Determine the relationship betweenDetermine the relationship between• Pressure and volumePressure and volume• Volume and temperatureVolume and temperature• Pressure and temperaturePressure and temperatureFor a fixed mass of gas.For a fixed mass of gas.

3.3. Explain absolute zeroExplain absolute zero4.4. Explain the absolute/kelvin scale of temperatureExplain the absolute/kelvin scale of temperature5.5. Solve problems involving pressure, temperature Solve problems involving pressure, temperature

and volume of a fixed mass of gas.and volume of a fixed mass of gas.

GAS LAWSGAS LAWS

Property of gases Property of gases

There is a relationship between There is a relationship between pressure, volume and temperature of pressure, volume and temperature of a gas.a gas.

For a gas in an enclosed container, For a gas in an enclosed container, the the

1.1. Number of moleculesNumber of molecules is constant is constant

2.2. Mass of the gasMass of the gas is constant is constant

3.3. Behaviour of the gasBehaviour of the gas depends on the depends on the volume, temperature and pressure of the volume, temperature and pressure of the gas.gas.

Pressure of a gasPressure of a gas According to the kinetic theory, a gas consists of a large According to the kinetic theory, a gas consists of a large

number of molecules that are constantly moving at random number of molecules that are constantly moving at random with high speeds.with high speeds.

During collisions, a molecule exerts force on the wall. The During collisions, a molecule exerts force on the wall. The momentum change during a collision dp = mvmomentum change during a collision dp = mvxx- (-mv- (-mvxx))

= 2mv= 2mvxx

Thus, the pressure of a gas is due to the collisions of the Thus, the pressure of a gas is due to the collisions of the gas molecules with the walls of the container. gas molecules with the walls of the container.

Gas pressure can be increased by:Gas pressure can be increased by: Increasing the temperatureIncreasing the temperature Reducing the volumeReducing the volume Increasing the number of molecules.Increasing the number of molecules.

mvx-mvx

Volume of gasVolume of gas

The volume of gas is the space The volume of gas is the space occupied by its molecules.occupied by its molecules.

Therefore, the average distance Therefore, the average distance between the gas molecules between the gas molecules determines its volume.determines its volume.

The volume of the gas is equal to the The volume of the gas is equal to the volume of the container.volume of the container.

Temperature of gasTemperature of gas Gas molecules are in constant random Gas molecules are in constant random

motion and have kinetic energy.motion and have kinetic energy.

When gas is at higher temperature, the When gas is at higher temperature, the gas molecules move with a greater gas molecules move with a greater velocity and will have more kinetic velocity and will have more kinetic energy.energy.

The temperature of the gas is related to The temperature of the gas is related to the average kinetic energy of the gas the average kinetic energy of the gas molecules.molecules.

GAS LAW

CHARLES’ LAW

PRESSURE LAW

BOYLE’S LAW

Boyle’s LawBoyle’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

or

While temperature kept constant

P1V1 = P2V2

PV

1V

P1

Gas law

P

V Pressure against volume

When the volume of a gas is decreased, the When the volume of a gas is decreased, the number of molecules per unit volume number of molecules per unit volume increasesincreases

The same number of molecules moves in a The same number of molecules moves in a smaller spacesmaller space

The molecules collide more frequently with The molecules collide more frequently with the walls of the containerthe walls of the container

The increase in the rate of collisions results The increase in the rate of collisions results in an increase in the pressure exerted by in an increase in the pressure exerted by the gasthe gas

Example Example

The air in the cylinder of hand pump The air in the cylinder of hand pump has a initial volume of 800 cmhas a initial volume of 800 cm33 and and pessure 102 kPa. The air is then pessure 102 kPa. The air is then slowly compressed to a volume of slowly compressed to a volume of 160 cm160 cm33. What is the pressure of the . What is the pressure of the compressed air in the pump?compressed air in the pump?

Answer Answer PP22 = 510 kPa = 510 kPa

Charles’ lawCharles’ law Charles’s law states that the volume of a fixed Charles’s law states that the volume of a fixed

mass of gas is directly proportional to its mass of gas is directly proportional to its absolute temperature if the pressure is kept absolute temperature if the pressure is kept constant.constant.

The mathematical expression for Charles’ law isThe mathematical expression for Charles’ law isV V αα T T

While pressure is kept constantWhile pressure is kept constant

VV = constant= constantTToror

VV11 = = VV22

TT1 1 TT22

Gas law

V(cm3)

T (K)Volume against temperature

When the temperature of a gas is increased, the speed When the temperature of a gas is increased, the speed of its molecules increasesof its molecules increases

Since the speed of the molecules increase with Since the speed of the molecules increase with temperature, the force that acts on the walls of the temperature, the force that acts on the walls of the container will be greater if its volume remained container will be greater if its volume remained unchangedunchanged

As a result, the volume of a fixed mass of gas will As a result, the volume of a fixed mass of gas will increase when its temperature is increased, provided increase when its temperature is increased, provided that the pressure remains constantthat the pressure remains constant

Example Example

2.4 m2.4 m33 of air at 27 °C in an of air at 27 °C in an expandable cylinder is heated to a expandable cylinder is heated to a temperature of 87 °C at constant temperature of 87 °C at constant pressure. What is the new volume of pressure. What is the new volume of air?air?

Answer Answer VV22 = 2.88 m = 2.88 m33

Pressure lawPressure law The pressure law states that the The pressure law states that the pressure of a fixed mass of gas is directly pressure of a fixed mass of gas is directly proportional to its absolute temperature proportional to its absolute temperature if the volume is kept constantif the volume is kept constant

The mathematical expression for the The mathematical expression for the pressure law ispressure law is

P P αα T T

That isThat is PP11 = = PP2 2 when volume kept when volume kept constantconstant

TT1 1 TT2 2

Gas law

P (Pa)

T (K)Pressure against temperature

When a gas is heated, the average kinetic When a gas is heated, the average kinetic energy of the molecules increases. The energy of the molecules increases. The temperature of the gas increasestemperature of the gas increases

The faster moving molecules strike the The faster moving molecules strike the walls of the container more frequentlywalls of the container more frequently

The molecules also experience a larger The molecules also experience a larger change of momentum when the bounce change of momentum when the bounce back from the wallsback from the walls

A larger force is exerted on the walls A larger force is exerted on the walls resulting in a higher pressureresulting in a higher pressure

Example Example

The initial pressure and temperature of the The initial pressure and temperature of the air in a car tyre was 200 kPa and 27° C air in a car tyre was 200 kPa and 27° C respectively. After a journey, the pressure respectively. After a journey, the pressure of the air was found to be 230 kPa. of the air was found to be 230 kPa. Calculate the temperature of the air in the Calculate the temperature of the air in the tyre.tyre.

Answer Answer T2 = 345 KT2 = 345 K

= 345 – 273 = 72 °C= 345 – 273 = 72 °C

Absolute temperature and Absolute temperature and the Kelvin scale the Kelvin scale

In the experiment to In the experiment to verify Charles’ Law, the verify Charles’ Law, the graph of V graph of V αα T is a T is a straight line which cuts straight line which cuts the temperature axis (T) the temperature axis (T) at the value -273°C.at the value -273°C.

The value The value -273°C -273°C is is equivalent to equivalent to 0K 0K and and known as the known as the absolute absolute zerozero because it is the because it is the lowest possible lowest possible temperature to be temperature to be reached.reached.

If the absolute zero is taken If the absolute zero is taken as the origin, the as the origin, the temperature scale is known temperature scale is known as as the absolute scale or the absolute scale or Kelvin scale. Kelvin scale. The The temperature in this scale is temperature in this scale is known as the absolute known as the absolute temperature and its unit is temperature and its unit is the Kelvin (K).the Kelvin (K).

The relationship between The relationship between the temperature in the the temperature in the Celcius scale and Kelvin Celcius scale and Kelvin scale is as follow:scale is as follow:

t °C = (Ø + 273 ) Kt °C = (Ø + 273 ) K

Ø K = (t – 273 ) °CØ K = (t – 273 ) °C

Where t = temperature in the Where t = temperature in the Kelvin scale. Kelvin scale.

Ø= temperature in the Ø= temperature in the Celcius scale Celcius scale

The combined gas lawThe combined gas law

For Boyle’s Law , PV = constantFor Boyle’s Law , PV = constant For Charles’ Law, V / T = constantFor Charles’ Law, V / T = constant For Pressure Law, P / T = constant For Pressure Law, P / T = constant

When combine all the equation, PV / When combine all the equation, PV / T = constantT = constant

PP11VV11 = P = P22VV22

TT11 T T22

P V

T

Problem solvingProblem solving