CIS 9 Physics Revision

Speed & Velocity

Speed

Speed is defined as a measure of the distance an object travels in a given length of time.

The average speed of an object can be determined from the equation below:

Thus, if a car travels 100 meters in 5 seconds its average speed can be calculated as;

Average speed = 100/5 = 20 meters per second

Average speed is used to give the speed of an object over a given interval of time, if however the speed of an object is required for a particular moment then the instantaneous speed is used.

Instantaneous speed is the speed of an object at a given moment. In this case the equation is similar to that of average speed but the time taken is a much smaller interval. A speedometer in the car gives an instantaneous speed as it gives the speed of the moving car at that specific time, whereas the average speed would be used as a measure of speed for the whole journey.

Velocity

Velocity is defined as a measure of the distance an object travels in a stated direction in a given length of time.

Thus velocity is speed in a stated direction. Velocity is referred to as a vector quantity because it possesses both size and direction, the size being speed. Where speed only tells us how fast or slow an object is moving it gives no reference of direction velocity is used as a more complete measure as it not only gives speed but also the direction.

Two cars could be travelling with the same speed of 100 km/h on a motorway. However, by stating one car is travelling 100 km/h north and the other 100 km/h south do we realise they are travelling in opposite directions, thus the velocity gives a better indication of the motion.

The average velocity of an object can be determined from the equation below:

Acceleration

For an object moving in a straight line where there is no change of direction the acceleration is defined as the rate of change of velocity with time.

It is given by the following equation.

Two cars could be travelling with the same speed of 100 km/h on a motorway. However, by stating one car is travelling 100 km/h north and the other 100 km/h south do we realise they are travelling in opposite directions, thus the velocity gives a better indication of the motion.

The average speed of an object can be determined from the equation below:

In the case where an object is slowing down (decreasing velocity) the acceleration is in the opposite direction to the moving object. This is referred to as negative acceleration or retardation or deceleration.

Distance-Time Graphs

Constructing graphs of an objects motion gives a better idea of the behaviour of the moving object.

A distance-time graph is constructed by having the distance as the vertical axis and the time as the horizontal axis. By recording the distance travelled over different intervals of time and plotting these values a distance-time graph can be plotted. From this plot information about the moving object can easily be extracted.

The animation below shows a distance-time graph:

Points to remember

In a distance-time graph;

• The average speed can be determined from the slope/gradient of the graph.
• The steeper the gradient the higher the average speed.
• A horizontal line indicates the object is stationary (not moving).
  

Velocity-Time Graphs

A velocity-time graph is constructed by having the velocity as the vertical axis and the time as the horizontal axis. By recording the velocity over different intervals of time and plotting these values a velocity-time graph can be plotted. From this plot information about the moving object can easily be extracted.

The animation below shows a velocity-time graph.

Points to remember

In a velocity-time graph:

• The acceleration can be determined from the slope/gradient of the graph. The steeper the gradient the higher the average speed.
• A horizontal line indicates the object is moving at constant velocity.
• The area under the graph gives the total distance travelled.

Forces & Motion

What are Forces?

A force results from the interaction between two objects. A force can be defined as a push or a pull which acts upon an object as a result of its interaction with another object.

When one object exerts a force on another object it always experiences an equal opposing force in return from the object it exerted the force on. Or in other words when two objects interact, the forces they exert on one another are equal and opposite. These forces are referred to as the action and reaction forces.

Forces are measured in units called newtons (N). The unit is named after the famous physicists Sir Isaac Newton (1642-1727) who Laws of Motion are instrumental in understanding the effects of forces.

Examples of forces

Weight

Weight is the force of gravity, which is the pull of the Earth on an object. To understand the force of gravity the concept of mass needs to be understood as well.

The mass of an object is the amount of matter it contains. Thus mass is a measure of how much stuff is in an object. Mass is measured in kilograms (kg) and is the same no matter where the object is located in the universe. For example and object of mass 10kg on the Earth will have the same mass of 10kg on the moon or anywhere else in the universe. Weight on the other hand is a measure of the pull of a planet i.e. Earth on the stuff contained in the object. The direction of the force of gravity is downwards towards the centre of the Earth.

As mentioned earlier when two objects interact they exert equal and opposite forces. The force that opposes the force of gravity in called the Normal Force. This is equal to the force of gravity and acts in an upwards direction (opposite to the downwards direction of the force of gravity). This is exerted by the surface upon which the object is positioned on. Therefore the force of gravity is the action force and the normal force is the reaction force.

FREE BODY FORCE DIAGRAMSFree-body force diagrams are used to give a clear and simple indication of the effect of the forces acting on an object. In a free-body force diagram only the forces acting directly on the object are shown. The forces are represented by arrows, the direction of the arrow gives the direction of the force and the size of the arrow represents the size of the force. This assists the reader in determining the net force acting on the object.

Friction

Frictional forces are the forces that oppose or prevent motion. These forces are a result of the interaction between the surfaces of two objects (more precisely due to the attractions between the molecules of the surfaces in contact). The reason why a football that is kicked eventually comes to rest is due to the friction forces between the surface of the rolling ball and the grass and air it is in contact with.

Magnetic Forces

This is the force produced by magnetic materials which pulls or repels other materials. For example the magnetic strip on a refrigerator door catch pulls the door to the refrigerator frame to keep the door closed.

Newton’s Laws of Motion

The relationship between forces and motion were first fully explained by Sir Isaac Newton in the sixteenth century. Before explaining Newton’s laws of Motion it is important the term resultant force is understood.

Resultant Force

The resultant force on an object is the sum of all the individual forces acting on the object taking into account the direction in which they are acting. Therefore all the forces acting on an object may be replaced by a single force which has the same effect as all the original forces acting together.

Newton’s First Law of Motion

Newton’s first law deals with objects at rest or those moving at constant speed.

Newton stated that if the resultant force on an object is zero then an object at rest will remain at rest and an object in motion will continue its motion in the same direction at constant speed.

This means that all objects have a natural tendency to keep on doing what they are doing. All objects have a reluctance to change their state of motion and require an unbalanced force to bring about a change.

The reluctance or resistance for a mass to change its state of motion is referred to as inertia. This is why it is critical for drivers and passengers to wear seat belts. Passengers in cars possess a lot of inertia; if the car is forced to stop suddenly the passengers in the car will still move forward, the seatbelts however exert large forces on the passengers to stop them.

The animation below explains Newton’s first law of motion:

Newton’s Second Law of Motion

Newton’s first law deals with objects at rest or objects moving at constant velocity. His second law deals with the motion of accelerating and decelerating objects.

We know from everyday life examples such as pushing a car that if two people push a car on a flat road it will accelerate faster than if one person was pushing it. Thus, there is a relationship between the size of the force and the acceleration. We also know that it is easier for two people to push a small car than a large truck and for the same applied force the small car will accelerate faster than a large truck. Therefore there is also a relationship between mass and acceleration.

Experimentation proves that acceleration of a body is proportional to the force applied. This means that acceleration doubles when the force doubles or acceleration trebles when the force trebles, thus the greater the force the greater the acceleration. This relationship is represented as:

(where α represents "directly proportional to")

Experiments also show us if you keep the force constant and double the mass, the acceleration will halve. This means the acceleration is inversely proportional to the mass i.e. the greater the mass the less the acceleration.

It is important to note that the acceleration is parallel to the force applied.

Combing these two results we get:

Rearranging the above equation:

This equation gives the mathematical form of Newton’s second law of motion,

which states:

The acceleration of an object is inversely proportional to the mass of the object and directly proportion to the force acting on the object

Provided the force is measured in newtons the second law can be written mathematically as:

The unit for measuring force is the newton. One newton is defined as:

The force which gives a mass of 1kg an acceleration of 1 m/s²

The animation below explains Newton’s second law of motion:

Force Acting in Free Fall

The force acting on an object in free fall is called its weight. The acceleration of the object is due to the force of gravity, therefore from Newton’s second law of motion we know;

F = m x a

Acceleration due to gravity is represented by “g” and is equal to 9.8m/s2.

Therefore,

F = m x g(where “g” is acceleration due to gravity)

We know that force acting due to gravity is weight so,

W = m x g

Newton’s Third Law of Motion

Newton noticed that forces always come in pairs as a result of the interaction between two bodies and that the two forces were always equal in size and opposite in direction.

In his third law Newton states:

If body A exerts a force on body B, then body B exerts a force on body A that is equal in size but opposite in direction.

Newton’s third law can be explained by the example of the space shuttle shown in the animation below:

 Tip

This is an important point to remember. The two forces in an action-reaction force pair always act on two different objects. Therefore, the two forces can never cancel each other out. The forces acting on the shuttle are the weight and thrust (although their will also be a drag force caused by friction in the atmosphere). The thrust is the reaction force from the exhaust gases. The action force i.e. the exhaust gases from the rear of the shuttle are not acting on the rocket rather the rocket pushes on the exhaust gases. 

Friction

Friction is defined as a force that opposes motion.

When two objects are brought into contact the molecules from the surface of one object get very close to the molecules on the surface of the other object. This results in forces of attraction between the molecules and this must be overcome so that one surface can move over the other.

Objects moving through fluids such as air or water also encounter frictional forces which reduce their motion. This is known as drag.

Friction prevents objects from moving or slows them down. It also causes wear on surfaces as they rub against each other and generates heat. Thus energy is wasted in overcoming friction.

Reducing friction

Lubrication

Oil is used as a lubricant and provides a thin layer of liquid which separates the moving surfaces.

Bearings

Ball bearings reduce frictions by making the moving surface roll rather than slide.

Streamlining

By designing the object to allow the easy flow of fluid around it (streamlining) as is done for rockets and racing cars the drag can be reduced considerably.

Uses of friction

Although in a lot of cases friction is a hindrance but it is also very essential. In order to walk we depend on the friction between the soles of our feet or shoes and the ground. The tyres and brakes on vehicles depend on friction to stop, slow down and start moving. It is the air resistance or drag that slows down a parachute.

Stopping Distance

Cars rely on friction at the brakes and tyres in order to stop.

The total distance a car requires to stop is called the total stopping distance. This is the sum of the distance covered in the time it takes for the driver to react known as the thinking distance and the distance the car travels before coming to rest after the brakes are pressed called the braking distance.

Total stopping distance = thinking distance + braking distance

The diagram below gives the shortest stopping distances for a car on a dry road with good brakes and tyres.

From the diagram a clear pattern can be seen between the velocity of the car and the total stopping distance.The average reaction time of a driver is about 0.7s as the velocity of the car increases so will the thinking distance from the relationship;

Distance travelled = velocity x reaction time

The braking distances increases because at a faster velocity the car possesses more kinetic energy. This energy has to be transferred to the brakes; this is transferred as heat and is the reason why brakes become hot. The relationship between velocity and kinetic energy is,

Kinetic Energy (Joules) = ½ x mass x velocity²

Therefore if the car travels three times the velocity it has 9 times the kinetic energy which means the braking distance will be nine times longer.

Factors affecting the total stopping distance

The driver’s reaction time

The thinking distance depends on the driver’s reaction time. Reactions are strongly influenced by the state of the mind. Thus, a driver under the influence of a drug such as alcohol will have a much reduced reaction time which will increase the thinking distance. Tiredness and fatigue also influence reaction time. A tired driver will react a lot slower than an alert driver.

Velocity

As illustrated in the chart above the braking distance increases with velocity. This is explained by the relationship between kinetic energy and velocity. The greater the velocity the greater the kinetic energy the brakes have to transfer.

Mass

The mass of the vehicle is also related to kinetic energy in the relationship;

Kinetic Energy (Joules) = ½ x mass x velocity²

The greater the mass the greater the kinetic energy, thus a heavier car will require a longer braking distance.

Road Surface

Friction between the car tyres and the road surface stop it from skidding and sliding. On a wet or icy road surface the contact between the tyres and the road is considerably reduced. If the driver brakes hard the car will skid therefore the driver needs to apply a reduced force on the brakes increasing the braking distance.

Tyre Condition

Tyres are designed with grooves which channel the water away on wet roads in order to ensure contact of the tyre is made with the road. If the tyres are worn the friction between the road and tyres is reduced increasing braking distance.

Brake Condition

Worn brakes will take longer to transfer the kinetic energy of the car increasing the braking distance.

Air Resistance

The force that resists the motion of an object through a gas and liquid is called drag.

For objects moving through air sometimes instead of drag the term air resistance is used. As an object moves through air, the gas molecules in the air push against the surface of the moving object resulting in friction between the gas molecules in the air and the surface of the moving object.

The amount of drag encountered depends on the following:

Shape

An object with smooth lines will allow the air to flow over it more easily reducing the drag. This is known as streamlining and is why objects built for speed such as racing cars have smooth bodies.

Speed

Drag increases with speed.

Area

The larger the area of contact the more drag it will experience.

The type of fluid

There will be more drag in a liquid compared to a gas as the molecules are a lot closer together. A stone will fall much faster in air than in water.

Terminal Velocity

When an object falls it accelerates due to its weight (the downward force of gravity acting on the objects mass). As it accelerates its velocity increases. The increase in velocity is accompanied by an increase in air resistance (drag). Eventually the air resistance acting upwards on the objects equals the weight acting downwards. The overall force on the object is balance or zero; it therefore cannot accelerate and continues to fall at constant velocity. This is referred to as the terminal velocity.

The animation below shows the terminal velocity of a skydiver:

Moment

The turning effect of a force is known as the moment. It is the product of the force multiplied by the perpendicular distance from the line of action of the force to the pivot or point where the object will turn.

When undoing a nut fastened to a screw by hand one realises that the amount of force required is a lot greater than when undoing the same nut using a spanner. The spanner increases the distance between the fulcrum and the line of action of the force, thus for the same force a greater moment is obtained.

SMALL MOMENT The distance from the fulcrum to the line of action of force is very small	LARGE MOMENT The distance from the fulcrum to the line of action of force is large

Principle of Moments

The principle of moments states that when in equilibrium the total sum of the anti clockwise moment is equal to the total sum of the clockwise moment.

When a system is stable or balance it is said to be in equilibrium as all the forces acting on the system cancel each other out.

 In equilibrium

Total Anticlockwise Moment = Total Clockwise Moment

This principle can be explained by considering two people on a seesaw.

Moments Acting On A Seesaw Both people exert a downward force on the seesaw due to their weights. Person A’s weight is trying to turn the seesaw anticlockwise whilst person B’s weight is trying to turn the seesaw clockwise. Person A’s Moment = Force x perpendicular distance from fulcrum 1000  x 1  = 1000 Nm Person B’s Moment = Force x perpendicular distance from fulcrum 500   x 2   = 1000 Nm Persons A’s moment  = Persons B’s Moment Anticlockwise moment = Clockwise moment Therefore seesaw is in equilibrium.

Circular Motion & Centripetal Force

From Newton’s first law of motion it is known that an object will remain stationary, or keep moving at constant velocity in a straight line unless acted upon by an unbalanced force. When an object moves in a circular path its direction is changing all the time therefore according to Newton’s first law there must be an unbalanced force acting upon it all the time.

When an object moves in a circle although its speed is constant the direction is continuously changing. Therefore its velocity is continuously changing as velocity is speed in a particular direction. The changing velocity in time means the object is accelerating all the time.

The resultant force which causes this acceleration is the centripetal force.

The centripetal force always acts toward the centre of the circle.

The centripetal force is determined from the following equation:

If a ball is tied to the end of a strong string and swung in a circle, the ball accelerates towards the centre of the circle. The centripetal force which causes the inwards acceleration is from the tension in the string caused by the person’s hand pulling the string. If the string breaks there is no longer a resultant force acting on the ball, so it will continue its motion in a straight line at constant speed.

The centripetal force required to make an object perform circular motion increases in the following cases:

• If the mass of the object increases.
• If the velocity of the object increases.
• If the radius of the circle decreases.

The above points are evident when considering the equation for centripetal force.

Energy:

Work

When a force acts on an object and causes it to move through a distance, energy is transferred and work is done.

Work is only done when there is movement against an opposing force. For e.g. lifting a book off the floor to put on a table, here the movement is from the floor to the table and the opposing force is the weight of the book.

The amount of work done can be calculated by the equation:

The unit for work is Joules (J). One joule of work is done when a force of 1 Newton moves an object through a distance of 1 metre.

Start	End
In order to lift the barbell above his head the weight lifter need to apply a force which opposes the downward acting force of gravity on the mass of the barbell. The distance from the floor to above the lifters head is 2 metres.	Mass of barbell = 25 + 25 = 50kg Weight of barbell = mass x acceleration due to gravity W = m x g W = 50 x 9.8 = 490 Newtons Work done = force x distance Work done = 490 x 2 = 980 Joules

In the example above the work done by the weight lifter in lifting the weights was 980 joules. In order to do this work energy had to be transferred. 980 joules of chemical energy from food eaten by the weight lifter was transferred to 980 joules of gravitational potential energy to the barbell. Thus the amount of work done is equal to the energy transferred from one form to another.

Forms of Energy

Energy is the ability to do work.

The table below describes some of the different forms of energy.

Kinetic Energy

Energy by virtue of its motion. This is the energy that moving objects possess. Can be made to work when they strike another object. Examples, moving car, moving person, flowing water.

Gravitational Potential Energy

Energy by virtue of its position. Any object lifted above the ground gains gravitational potential energy. The height the object attains gives it the potential to do work when it falls. Examples, water in a high level reservoir, a skier on the top of a ski slope, a ski diver before jumping from a plane.

Elastic Potential Energy (Strain Energy)

The energy a material possesses when it is stretched and is put under strain. The stored energy from the stretched material can be made to do work when released. Examples, a stretched bow, the stretched elastic in a catapult, the tightened strings on a guitar or violin.

Thermal Energy (Heat Energy)

The energy due to the movement of atoms and molecules in a substance. When a substance is heated up the atoms and molecules move faster and possess kinetic energy which can be used to do work. For example heating water to produce steam to drive a turbine in electricity generation.

Chemical Energy

The energy stored in the bonds of atoms and molecules. When the atoms and molecules undergo reactions bonds are broken and energy is released in the form of heat or kinetic energy. Examples, digesting food, burning fuels, fuel is burnt by a rocket to do work against gravity.

Electrical Energy

Energy due to the flow of electrons. Work can be done by the flowing electrons in an electrical circuit. Examples, electrical appliances such as lights, ovens, motor.

Nuclear Energy

Energy stored in the nuclei of atoms. This is the energy that holds the nucleus together. Large amounts of energy are released when the nuclei are split or combined during nuclear reactions. For example, radioactive uranium nuclei are split in nuclear reactors and the heat energy released is used to generate steam to drive turbines for electricity generation.

Wave Energy

Waves carry energy. Sound is the result of the energy transferred through waves. Radiant energy from the sun travels through electromagnetic waves. Examples, light waves from the sun, sound waves from a talking person.

Conservation of Energy & Energy Transfer

A very important and useful fact about energy is that it can change from one form to another. When a machine does work the energy is not used up rather it is transferred – converted from one form to another. The amount of energy stays the same or is said to be conserved.

This fact is known as the Principle of Conservation of Energy.

Principle of Conservation of Energy:
Energy can neither be created nor destroyed, but can be changed from one form to another.

The principle of conservation of energy can be explained by considering the energy changes in a simple pendulum.

CONSERVATION OF ENERGY

Example of Energy Transfer

A cement work uses a conveyor to transport 25kg cement bags from the ground floor to the pallet sorting machine situated on the first floor. The conveyor uses an electric motor with a voltage of 220V and current of 3 A. The time taken for the cement bag to reach the first floor is 5 s.

Calculate the work done in lifting one bag of cement from the ground floor to the first floor and the electrical energy transferred by the motor in 5 seconds?

Answer:

Work done in lifting one bag
Work done = energy transferred
Cement is lifted to a height of 6m so it will gain gravitational potential energy.
GPE = mass x acceleration due to gravity x height
GPE = 25 x 9.8 x 6 = 1470 Joules
Tip: If we look closely at the gravitational potential energy equation it is the same as that for Work done = force x distance
Force = mass x acceleration, here the acceleration is due to gravity therefore,
Force = m x g, substituting this value in the work done equation gives:
Work done = m x g x distance, here the distance is height thus
Work done = m x g x h
Electrical energy transferred in 4 seconds
Electrical Energy = V x I x t
Electrical Energy = 220 x 3 x 5 = 3300 Joules
Not all the electrical energy is transferred to gravitational potential energy but is loss as heat via friction to the moving parts of the motor and conveyor and also as noise energy as the moving parts contact each other.

Energy Transfer Diagrams

Most of the machines or devices we use transfer energy from one form to another. Input energy is taken in by the device in one form and transformed to output energy in another form.
An energy transfer diagram or a Sankey diagram is used to show the transfer of energy across a process or a device. It is a flow diagram in which the widths of the arrows show the relative amounts of each type of energy.
An energy transfer diagram for a power station along with a Sankey diagram is shown below:

Efficiency

The efficiency of a device is calculated using the following formula:

Device	Light Bulb	Energy Saving Light Bulb
Energy Transfer Diagram	Electrical Energy  Heat and Light Energy	Electrical Energy  Heat and Light Energy
Sankey Diagram
Efficiency	Efficiency = 5/100 x 100 Efficiency = 5%	Efficiency = 15/60 x 100 Efficiency = 25%
Explanation	Energy cannot be created nor destroyed. It can only be transformed from one form to another. Thus the 100J of electrical energy is transformed to 5 J of light energy and 95J of heat energy. In the case of the light bulb the 95J of energy transferred as heat is wasted energy as it is not useful because the purpose of the device is to produce light. An ordinary light bulb works on the principle of a thin wire (filament) being heated by the resistance to the electrical current. At a temperature of about 1100°C it glows with a bright white light. As the electrical energy is required in heating the wire hence this is why most of the energy is given off as heat. Lamps which give of light when hot are called incandescent.	Energy saving light bulbs work on the principle of fluorescence. Here the electrical energy is supplied to electrodes which generate fast moving electrons that pass through a tube containing mercury gas. On collision with the mercury atoms ultraviolet light is produced which then collides with the phosphor atoms coated around the tube converting the ultraviolet to visible light. Here a greater proportion of the electrical energy is converted to useful light, thus the energy saving light bulb is a more efficient device.

 Tip

Energy cannot be created nor destroyed. It can only be transformed from one form to another (the law of conservation of energy).
When energy is transformed or transferred only part of it can be usefully transformed or transferred. The energy which is not usefully transformed or transferred is referred to as wasted energy.
Both the useful energy and the wasted energy which is transformed or transferred are eventually transferred to their surroundings which become warmer. As the energy spreads out it becomes more difficult to use for further energy transformations.
The greater the percentage of the energy that can be usefully transformed by a device the higher its efficiency.

Heat (Thermal) Energy and Heat Transfer

Heat (thermal) energy is due to the movement of atoms and molecules in a substance. The faster the atoms/molecules move the higher the temperature of the substance. Therefore heat energy is really the kinetic energy of the atoms and molecules of a substance.

Heat energy can be used to do work. When a liquid is heated the liquid will eventually boil and change to a gas. The gas takes up more space (volume) then the liquid and can exert a great force. This can be used to drive turbines that can generate electricity.

Heat is the transfer or flow of energy from a hot object to a cold object. It is important to understand that heat only travels from a hot object to a colder object. Thus an object gets warm by receiving heat energy and cold by loosing heat energy.

Heat energy can be transferred in three ways:

1. Conduction

2. Convection

3. Radiation

Conduction

Conduction is the transfer of energy from one atom or molecule to another atom or molecule.

The atoms in a substance are always vibrating. When heat is applied to a substance the heat energy is given to the atoms and they vibrate and move faster and so their kinetic energy increases. The vibrating atoms bump into neighbouring atoms and pass on their kinetic energy. These atoms then pass on their kinetic energy to atoms close to them and so on. In this way the heat energy moves through the substance.

Conduction takes place in solids, liquids and gases, but works best in solids as their atoms/molecules are located closer together.  Metals are the best solids for conducting heat. Metals have tightly packed atoms which can easily pass on their kinetic energy and also have free moving electrons. These electrons can move from the hot part of the metal to the colder part transferring the energy more quickly.

Poor conductors or insulators do not possess free moving electrons.
The animation below shows heat transfer in a metal by conduction.

CONDUCTION
The heat from the flame is given to the atoms and they begin to vibrate faster. The atoms collide with the atoms close to them and in this way the heat flows from the hot end to the cold end. As the distance from the flame increases the temperature decreases by a proportional amount.

Convection

Convection is the movement of heat in liquids and gases. The particles in liquids and gases are not tightly packed together and so free to move around. When the particles in a liquid or gas with a lot of heat energy move to take the place of the particles with less heat energy convection is said to take place and the heat energy is transferred from the hot areas to the cold areas.

When liquids and gases are heated their atoms/molecules gain kinetic energy and move faster. As a result the particles move further apart and so take up more volume.  As more volume is taken up the density (mass per unit volume) decreases i.e. it becomes lighter in weight. Thus the area of hotter less dense liquid or gas will rise into the area of colder denser liquid or gas. The denser colder liquid or gas will then sink into the warm areas till it is warm enough to rise and so convection currents are set up and heat is transferred.

The animation below shows heat transfer by convection in a kettle.

CONVECTION
The water molecules at the bottom of the kettle gain heat energy from the flame and vibrate faster and move further apart. Their density decreases and the hotter particle rise to the top of the kettle. The colder less dense molecules move into replace the hotter particles. This continues until all the water is the same temperature.

Radiation

Radiation is the transfer of heat energy by electromagnetic radiation and specifically speaking that by infra red radiation. All objects whether hot or cold radiate heat energy (infra red radiations). The hotter the object the more heat energy it radiates. All objects also receive radiation and the exchange of radiant energy is a continuous process. Therefore a body at constant temperature is receiving and radiating energy at the same rate.

Infra red radiation is an electromagnetic radiation and so can travel through a vacuum, thus radiation unlike conduction and convection does not require particles for its propagation. It is for this reason we can receive heat energy from the sun.

RADIATION
The heating lamp transfers heat energy directly via infra red radiation.

The amount of radiation given out by objects depends on their temperature and their surface. The hotter the object the more energy it radiates and the bigger the heat difference between the hot object and the surroundings the faster the heat transfer.

Dull dark matt surfaces are good absorbers and good emitters of radiation. For example the cooling fins on the back of a refrigerator.

Light, shiny surfaces are poor absorbers and poor emitters of radiation.  This is why it is best to wear bright white clothes on a hot day as they reflect the heat and reduce absorption of the heat energy.

Absolute zero and the Kelvin scale of temperature

Absolute zero

Temperature is the measure of the hotness or coldness of an object. It is a property that allows us to quantify heat and determine which way the heat will flow from one object to another. When an object is cold, we say it has a low temperature and when it is hot, we say it has a high temperature. If we place our hands in water and the heat energy flows from the water to our hands then the water is at a higher temperature than our hands. If the heat energy was to flow from our hands to the water then the water would be at a lower temperature than our hands.
The temperature of a substance is a measure of the motion of all the atoms and molecules in the substance. When a substance is heated the speed of the particles increase as do their kinetic energies and the temperature rises. When a substance is cooled the speed of the particles decrease and so do their kinetic energies and the temperature drops. If the substance is cooled further the motion of the particles continues to slow down and their vibrations become less and less. Eventuallya temperature can be reached at which point the atoms and molecules in the substance are at their lowest energy state and their movement virtually ceases. This is reached at a temperature of -273°C and is called absolute zero. This is the lowest possible temperature because the atoms and molecules are at their lowest energy state and therefore there is no energy for transfer.

Kelvin scale

The Kelvin temperature scale takes its name after Lord Kelvin who developed it in the mid 1800s. It takes absolute zero as the starting point and temperature measurements are given the symbol K (which stands for "Kelvin"). Temperature differences on the Kelvin scale are no different to those on the Celsius (°C) scale. The two scales differ in their starting points. Thus, 0°C is 273K.

Converting from Celsius to Kelvin
Temperature in °C + 273 = Temperature in KConverting from Kelvin to Celsius
Temperature in K – 273 = Temperature in °C

Pressure and volume relationship of a gas – Boyle's law

Boyle's law

All the particles (atoms and molecules) of a substance are continually moving and so possess kinetic energy. In gases the movement of the particles is highly energetic and this is the reason why gases form, the particles have enough energy to overcome the attractive forces holding the particles together. In gases the particles are moving very quickly and freely in a random manner constantly bumping into each other and their surroundings. It is these collisions between the particles of the gas and the walls of the container it is confined to that creates gas pressure. The gas pressure is the overall force of all these collisions divided by the area of the walls of the container it is confined in.
The relationship of a gas with pressure and volume was developed by the scientist Robert Boyle at around 1660 and is known as Boyle’s Law.
Boyle’s law states:

"For a fixed mass of gas, at a constant temperature, the product (pressure x volume) is a constant."

Pressure x Volume = constant

p x V = constant

The animation below gives and explanation of Boyle's law:

BOYLE'S LAW

A sealed cylinder with no leaks contains a fixed mass of a gas kept at a constant temperature. The gas pressure is created by the collision of the moving gas particles with each other and against the walls of the cylinder.

The above set up is used to investigate the relationship between pressure and volume for a gas. A force is exerted on the piston to compress the gas. The corresponding pressure and volume values are recorded for different applied forces.

By plotting the recorded values of pressure (p) against volume (V) a curve is produced. We can see from the values that when the pressure is doubled the volume is halved. If the pressure was to increase by 3 the volume would decrease to a third. Thus, the volume is inversely proportional to the pressure. By plotting pressure (p) against the reciprocal of the volume (1/V) a straight line is obtained the gradient of which is the constant in Boyle’s Law.

A decrease in volume increases the number of gas particles per unit volume. This results in an increase in the number of gas particles close to the cylinder walls and therefore an increase in the number of collisions with the wall. As the number of collisions per unit area increases so does the force per unit area thereby giving an increase in pressure.

Volume and temperature relationship of a gas – Charles' law

Charles' law

The relationship between the volume and temperature of a gas was first put forward by the French scientist Jacques-Alexandre-César Charles at around 1787 and is known as Charles’ Law.
Charles’ law states:

"For a fixed mass of gas, at a constant pressure, the volume (V) is directly proportional to the absolute temperature (T)."

Volume α Temperature

Volume	= constant
Temperature

The animation below gives and explanation of Charles' law:

CHARLES' LAW

A sealed cylinder with no leaks contains a fixed mass. In order to keep the gas pressure constant the piston is allowed to move freely so that the internal pressure created by the gas particles can equal the constant external pressure. If the internal pressure increases the piston will move up to allow the pressure to equalise.

The above set up is used to investigate the relationship between temperature and volume for a gas. Heat energy is applied to the cylinder and the temperature of the gas increases. The average velocity of the gas particles increases resulting in an increase in the rate of collisions and the average force per collision. This produces an increase in pressure inside the cylinder, the cylinder pressure becomes greater than the external pressure and the piston moves up increasing the volume.

By plotting the recorded values of volume (V) against temperature (T) a straight line is produced. We can see from the values that the gas expands uniformly with temperature.  We can extrapolate the straight line and see the relationship between cooling the gas and the volume. Further extrapolation gives the temperature at which the volume of gas would become zero. This temperature is at -273°C and is called the absolute zero of temperature.

Converting the recorded temperatures into the Kelvin scale and plotting the volume (V) against the absolute temperature (T) gives a straight line which when extrapolated passes through the origin. This shows the volume of the gas is directly proportional to the absolute temperature of the gas. Doubling the temperature will double the volume. The gradient of the slope is the constant in Charles’ Law.

Pressure and temperature relationship of a gas – The Pressure Law

The pressure law states:

"For a fixed mass of gas, at a constant volume, the pressure (p) is directly proportional to the absolute temperature (T)."

Pressure α Temperature

Pressure	= constant
Temperature

The animation below gives and explanation of the Pressure law:

THE PRESSURE LAW

A sealed cylinder with no leaks contains a fixed mass. The volume of the gas is kept constant by using a cylinder with a fixed roof capable of withstanding high pressures.The gas pressure is created by the collision of the moving gas particles with each other and against the walls of the cylinder.

The following set up is used to investigate the relationship between temperature and pressure for a gas. Heat energy is applied to the cylinder and the temperature of the gas increases. The average velocity of the gas particles increases resulting in an increase in the rate of collisions and the average force per collision. Because the areas of the walls are kept constant, the force per unit area increases resulting in an increase in pressure.

Plotting the pressure (p) against the absolute temperature (T) gives a straight line which when extrapolated passes through the origin. This shows the pressure of the gas is directly proportional to the absolute temperature of the gas. Doubling the temperature will double the volume. The gradient of the slope is the constant in Charles’ Law. It also shows that if the gas is cooled to absolute zero then the energy of the molecules is at the lowest energy state and therefore cannot generate any pressure.



The three gas laws give the following equations:

pV = constant (when T is kept constant)	Boyle’s Law
V = constant (when p is kept constant) T	Charles’ Law
p = constant (when V is kept constant) T	Pressure Law

These 3 equations are combined to give the ideal gas equation:

pV	= constant
T

Where,

p = the pressure of the gas
V = the volume the gas occupies
T = the gas temperature on the Kelvin scale