School Physics notes: Conservation of energy, energy store transfers & Sankey diagrams

Conservation of energy, energy transfers, conversions & efficiency

Examples, calculations, Sankey diagrams, wasted energy

Doc Brown's school physics revision notes: GCSE physics, IGCSE physics, O level physics,  ~US grades 8, 9 and 10 school science courses or equivalent for ~14-16 year old students of physics

Law of conservation of energy and a closed system

See also Types of energy - a comparison with examples explained, energy store calculations gcse physics

This page will answer many questions e.g.  What do we mean by efficiency in energy transfer?   How do you calculate efficiency? What is the formula for efficiency?   What does a Sankey diagram tell you?   How do you draw and interpret a Sankey diagram?

Energy conservation and a closed system

Know and understand that energy can be transferred usefully from one form to another, or stored, or dissipated, but energy cannot be created or destroyed.

This is the law of conservation of energy.

Another way of stating the law is to say the ...

'total energy of a system remains constant no matter what energy conversions take place'.

However, energy is only useful if it can be converted from one form to another.

Examples - from a suitable energy source ==> useful form (plus waste in most cases)

Energy stores have been described in Types of energy store - a comparison with examples explained

Here we are interested in how efficient are energy transfers to produce useful energy.

What do we mean by conservation of energy and a closed system?

A system is an object or objects involved in a particular situation which can be described in its own context without any energy being exchanged with its surroundings - the system does not absorb energy from, or lose energy too, the surroundings.

If energy is gained or lost by the system, it cannot be closed.

However, you can make an existing system into a closed system by including other things as part of it.

e.g. a car and its kinetic energy is limited because energy is being lost by friction (wheel-road) and air resistance (car body-air), but if you include the air around it and the road (the environment) you have 'constructed' a closed system.

Theoretically, irrespective of form, if the total energy at the start of a process doesn't equal the total energy at the end, that process can't happen.

You can use the work (E = Fd) and power (P = E/t) formulae to calculate an energy transfer-conversion from one energy store to another, but the formulae do not explain why the transfer takes place, nor does it tell you how much of the energy involves useful work or wasted energy. E can represent energy or work done - its all the same!

See Types of energy store - a comparison with examples explained, mechanical work done and power calculations

If there are no frictional forces operating, the work done on the object equals the work done = the energy is transferred to a useful energy store.

However, this is rarely the case since resistive forces are often present e.g. surfaces scraping against each other, air resistance etc.

Work must be done against these resistive forces which causes energy to be wasted - dissipated to the surroundings as heat due to friction - increasing the thermal energy store of the surroundings.

Under these circumstances, the energy transferred to the useful energy store as useful work, will be less than that transferred from the original energy store.

If work is done by the object itself, the work done does actually equal the energy transferred from the objects useful energy store.

See Types of energy store - a comparison with examples explained, mechanical work done and power calculations

Reminders:

Law of conservation of energy - energy cannot be created or destroyed.

BUT, not all the energy in a system is useful, there is always some wasted or dissipated energy and their relative values can be quite different.

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Types of energy transfer: What do energy transfers-conversions involve?

You need to be a bit more specific than just saying 'energy transferred' from x energy store to y energy store!

Energy is transferred electrically when a moving electrical charge (the current) is doing work against a resistance.

e.g. a battery providing electrical energy via the circuit to light a torch bulb.

Operating any electrical appliance or device from mains circuit electricity.

Energy is transferred by heating when a hotter object or material transfers heat energy to a colder object or material.

e.g. boiling water in an electric kettle - the hot element transfers heat to the water.

When you first put something to bake in an oven, heat is transferred from the hot air to the colder baking tin and contents.

Using a soldering iron to make an electric circuit link.

Energy is transferred mechanically when a force acts on an object to move it or change its shape e.g. pushing, pulling, stretching-expanding or squashing-compressing.

e.g. kicking a football - the force you exert from your leg accelerates the football and give it kinetic energy.

A car engine moving the wheels of a car.

Cutting a piece of cake!

e.g. The Earth receives visible light, infrared and ultraviolet radiation from the Sun.

Infrared radiation from an electric fire.

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Some 'domestic' examples of energy transfers Cooking 1: Our electricity supply is initially powered from either a fossil fuel chemical energy store, a nuclear energy store or a renewable energy store (hydroelectric, wind or solar etc.).

The initially energy store decreases and the kinetic energy store of the turbine blades and generator increases.

The generator converts the kinetic energy into electrical energy, which becomes thermal energy in a toasted sandwich maker the heat is transferred to the bread by conduction.

The electrical energy is converted into heat/thermal energy by the insulated electrical resistors in the iron cased toaster (iron is a good conductor of heat) - the thermal store of the heating elements is increased.

The thermal energy is transferred by conduction to the iron grill and the sandwich, increasing both their energy stores and cooking the sandwich.

See also The Usefulness of electricity, transferring electrical energy and cost calculations gcse physics revision notes Gas fire appliance: The natural gas (methane) is a chemical energy store.

On combustion the fuel's chemical energy store decreases and the heat/thermal energy store of the waste gases increases.

The hot gases from a gas fire will always rise due to the immediate formation of a rising convection current which carries the heat around the room.

The decrease in the chemical energy store of the fuel gas therefore increases the thermal energy of the contents of the room, mainly by convective heat transfer.

The heat is also transferred by infrared radiation emitted from the hot flame - from the higher temperature flame to the lower temperature room.  A car battery is a potential chemical energy store. When using the car, the chemical energy store of the battery decreases as electrical energy is produced to operate lights (visible EM radiation), ignition systems (heat), wipers (KE) etc.,

In the case of the headlamps the thermal energy store of the metal filament is increased (not LED lamp)

so some of the thermal energy becomes visible light and infrared radiation ...

... hence an early morning case of infrared radiation! Unlike 'modern' LED bulbs, 'old fashioned' filament bulbs emit quite a bit of IR heat radiation (from the increased thermal energy store of the filament). You can detect this with a frosty car where the central portion of the ice has melted on the transparent headlamp cover. Filament bulbs only convert ~10% of the electrical energy into visible light energy, most of the rest is converted into infrared EM radiation. The ice absorbs infrared equivalent to the latent heat of fusion (melting) and changes to liquid water. You can see this (in the above photographs) after the headlamps have been switched on for a few minutes on a frosty morning. The concentrated IR beam increases the thermal energy store of the plastic cover and the ice and the central part of the lamp cover warms up first melting the ice.

Energy store changes: The chemical energy store of the battery decreases as it is converted into electrical energy. The electrical energy increases the thermal energy store of the metal filament of the bulb. The thermal energy store of the filament decreases as it emits visible and infrared EM radiation. The absorbed EM radiation increases the thermal energy store of the headlamp cover and ice - causing the latter to melt. Eventually all the energy involved from the battery increases the thermal energy store of the surroundings.

A 'green' note: If there is, and its happening now in the UK and other countries, a change from very inefficient filament light bulbs to very efficient low energy LED light bulbs, there will be quite a reduction in the domestic demand for electricity. This reduced demand will help, on closure fossil fuel power stations, reduce CO2 emissions, reducing the greenhouse effect, and allow renewable energy resources to take over more of our electricity generation.

From the efficiency of light production old fashioned tungsten filament bulbs used in the home are very inefficient - ~5% of the electrical energy is transferred as visible light energy. The other ~95% of the energy ends up as thermal energy i.e. increase the thermal energy store of the room and its contents.  Cooking 2: The initial energy store to produce electricity has already been described with the toaster (and elsewhere on this page). The electrical current does work on the resistance convert electrical energy into heat energy - increasing its thermal energy store.

The electrical resistance elements of a cooker ring or a toaster become hot enough to emit a strong beam of infrared radiation to heat the contents of a pan or grill the toast.

Electrical energy is converted into heat/thermal energy which increases the thermal energy store of the heating elements and then increases the thermal energy store of the pan and contents or bread being toasted.

Eventually all the heat is wasted/dissipated to the surroundings, slightly heating up the kitchen.

Using a mobile phone

The battery is a chemical energy store (after charging).

The chemical energy is transferred as electrical energy.

The electrical energy is converted into light energy and sound energy.

There is also a little wasted thermal energy from the electrical circuits operating the phone.

A HiFi system

Electrical energy is converted into kinetic energy as the cones in the speakers are made to vibrate - their kinetic energy stores are increased.

The kinetic energy of the vibrating cones causes waves of sound energy to spread into the room.

Sound waves are vibrations in the air - a sort of kinetic energy.

Much of the sound energy is absorbed by objects in the room, so it dissipated-wasted as heat energy.

A small % of the sound energy vibrates your ear drums, increasing their kinetic energy store, and the ear 'system' sends electrical signals to the brain.

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More varied examples of conservation & energy transfers between energy stores

In all these examples you must treat them as far as possible as a closed system (so include the surroundings) and be able to account for all the energy transfers involved.

To put it as simply as possible: Total energy input = Useful energy output + Wasted (dissipated) energy

There is a separate section on EFFICIENCY - calculations and Sankey diagrams which deals with numerical calculations and details of useful input/output data.

1. When a gun fires, chemical energy is converted into heat energy, sound energy, light energy, but mainly into the kinetic energy store of the bullet by way off the rapidly expanding hot gases from the explosion.

When the bullet fires, the thermal energy store of the gases produced is increased.

When the bullet embeds itself into some material the kinetic energy of movement is converted into some sound energy, but mainly increases the thermal energy store of the material it hits.

 Chemical energy store of bullet == heat - hot gases ==> ==  mechanical conversion ==> KE store of bullet (and recoiling gun) == mechanical conversion ==> heat energy - thermal store of material + sound, light, friction and heat losses to surroundings 2. Photovoltaic solar panels convert light energy directly into electrical energy which may be stored in a battery.

The Sun's nuclear energy and thermal energy stores are decreasing and the energy is transferred by radiation to the solar panel.

The chemical potential energy store of the battery is increased by the transfer of energy in the electrical charge of current.

3. TV and mobile phone: We use a large number of electrical devices in the home e.g.

A TV converts electrical energy into useful light and sound, but some waste heat from the electrical circuits is produced. Eventually all the electrical energy is dissipated in some way to the surroundings increasing its thermal energy store. In charging a mobile phone battery you convert mains electrical energy into useful chemical potential energy. The electrical energy store decreases and the chemical potential energy store increases.

When using your mobile phone the useful chemical energy store decreases as it produces electrical energy, which in turn is converted into useful light and sound energy when using the phone. However, there is some wasted thermal energy added directly to the surroundings - you can detect this wasted heat as your phone warms up as you are using it. 4. Wind turbines convert kinetic energy into electrical energy. The kinetic energy store of the wind decreases, the kinetic energy store of the turbine blades increases.

This kinetic energy is converted into electrical energy by a generator.

The turbine does work in turning the generator and this kinetic energy is converted into electrical energy.

Some energy is wasted due to friction of moving parts - energy dissipated to increase the thermal energy store of the surroundings. 5. When you wind up a clock you are converting chemical energy from your body to mechanically create kinetic energy to increase the elastic potential energy store of the clock spring.

The potential energy store of the spring decreases as it moves the hands around giving them kinetic energy.

Suppose instead of a spring you have a falling weight?

In this case the winding up involves using kinetic energy to increase the gravitational potential energy of the clock weight.

As the weight falls the GPE store decreases.

Although using the term 'kinetic energy' seems ok, what you should appreciate that in winding up the clock and when the clock is freely working, a force is acting through a distance.

Since work = force x distance, your bodies chemical energy used = work done in winding up clock = work done in working the clock. 6. In some hydroelectric power schemes, excess 'off-peak' electricity is used to pump water back up into the reservoir.

This is mechanically using electrical energy to increase the kinetic energy of the pumped-water to move it upwards against the force of gravity.

The gravitational potential energy store is initially increased as the water builds up behind the dam and then decreased when the water flows down through the generators.

At peak demand times, extra water is released, accelerated by gravity, and so the dam's GPE energy store decreases and the kinetic energy (KE) store of the water increases.

The KE store of the water then decreases as it is mechanically converted into the kinetic energy of the generator which converts its KE into electrical energy (with some loss in sound and heat from friction).

The 'peak time' energy store changes can be expressed in a simple diagram

 GPE store of water == gravitational acceleration - mechanical conversion ==> KE store of the flowing water == KE of rotating generator - mechanical conversion ==> electrical energy + friction and heat losses to surroundings

7. When you are cooking you are converting electrical energy (electric cooker) or chemical energy (gas cooker) into thermal energy to increase the thermal energy stores of the cooker ring and then the pan and its contents.

There will be heat energy losses due to convection, conduction or radiation to increase the thermal energy store of the surrounding air.

8. When you brake to slow down a moving car and bring it to a halt, the kinetic energy store of the car is decreased and energy is lost as thermal energy (heat), created by the friction between the brake pads and the discs on the wheels.

This is an example of a mechanical transfer between energy stores - resulting in initially increasing the thermal energy store of the brake pads.

Eventually this excess heat increases the thermal energy store of the surrounding air.

You are mechanically using your chemical energy (from food) to create the force of friction and the brakes mechanically convert the KE of the car into thermal energy - work is being done against the forces of friction.

A little sound energy is also involved - adding to the waste energy dissipated to the surroundings.

If you just take your foot of the accelerator, on a level road, the car will eventually come to a halt due to friction between the wheels and the road and the moving parts of the engine, and also, air resistance as the air brushes over the car body. BUT, the KE store of the car still decreases to the same amount as if you were braking and the thermal energy store of the environment increases the same amount too.

If a vehicles crashes into a stationary object, the contact force causes energy to be mechanically transferred from the vehicle's kinetic energy store to elastic potential energy store of the crushed vehicle parts, the thermal energy stores of the vehicle, object crashed into and the surrounding air (including some sound energy too - which also ends up as thermal energy!).

9. When a cricketer hits a cricket ball, there are all sorts of energy changes going on. The bodies chemical energy store is decreased as energy is used in the bodies muscles mechanical motion on swinging the bat.  Therefore the chemical energy is converted into increasing the kinetic energy store of the bat as it is swung at the ball. When the ball is hit the kinetic energy store of the bat decreases and the kinetic energy store of the moving ball is increased. However, some of the kinetic energy of the 'bat and ball' is converted (wasted) into sound and thermal energy - this eventually increases the thermal energy store of the environment.

However, the wasted energy is NOT wasted on the 3rd umpire in test cricket! The Umpire Decision Review System is a technology-based system used in cricket to help the match officials with their decision-making. The two on-field umpires or players can choose to consult with the third umpire to consider a decision of the on-field umpires. The technology used includes microphones to detect small sounds (due to friction, from KE of ball) made as the ball hits bat or pad (or neither), and infra-red thermal imaging to detect temperature changes as the ball hits bat or pad (heat from friction, from KE of ball). If there is no contact between bat/glove & ball or ball & pad, there is no increase above the background sound level and there is no 'hot spot' due to friction, The sound effect is mainly used in the system these days?, so meet ...

... SNICKO the snickometer !!! The sound (if any) of the 'snick' is detected by a sensitive microphone in one of the cricket stumps.

The sound sequence of the movement of the batsman and bat is then portrayed electronically on an oscilloscope or a computer screen linked to a piece of music technology software.

The sound trace is also synchronised with a slow motion replay of the batsman's stroke.

10. Electrical machines that lift objects: When a crane lifts an object, the motor usefully, and mechanically, converts electrical energy into kinetic energy to lift the object. The lifted object has increased its gravitational potential energy store. There will be various losses due to - friction in the moving parts of the machine producing heat and sound, heat losses from the resistance of the electrical circuits (electrical store to thermal energy store).

 input of electrical energy == electric motor - mechanical conversion ==> useful KE of motor lifting object == useful GPE store of object increased - mechanical conversion + heat and sound losses to surroundings

11. As a parachutist is dropped from an aircraft, the person has its maximum gravitational potential energy (GPE) store.

As the person falls, so does their GPE store as the GPE is mechanically converted into kinetic energy.

However, other energy conversions take place to. Some of the GPE is converted into heat and sound by air resistance. This happens both before and after the parachute is opened.

On landing on the ground the parachutist's GPE is reduced to zero and the rest of the kinetic energy is converted to heat and sound.

The energy conversions are:

The descent: GPE ====>  heat + sound + kinetic energy

On landing: kinetic energy ====>  heat + sound

A non-electric car

Fuel (oil, diesel, hydrogen) is a store of chemical potential energy.

The chemical potential energy is converted to thermal energy when its burned in the engines cylinders.

The thermal energy store of the engine expands gas to drive the moving engine parts to increase their kinetic energy store - so the car moves!

There will be thermal energy losses from friction to the thermal energy store of the surrounding air (via air resistance) and moving part and road surface frictions.

Wasted or dissipated thermal energy which cannot be used or reclaimed.

An electric car

When the batteries are charged with electrical energy they become a chemical potential energy store.

When an electric car moves, the chemical energy store is converted into electrical energy.

The electrical energy drives a motor to move the car whose kinetic energy store is increased.

There will be thermal energy losses from friction to the thermal energy store of the surrounding air (via air resistance) and moving part and road surface frictions.

Wasted or dissipated thermal energy which cannot be used or reclaimed.

The electric car has less moving parts than a conventional fossil fuelled car, so the thermal energy loss due to friction should be less.

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Energy transfer and efficiency - useful work output and wasted energy

Introduction- reminders via a 'car' example:

Law of conservation of energy - energy cannot be created or destroyed.

BUT, not all the energy in a system is useful, there is always some wasted or dissipated energy and their relative values can be quite different.

In practical terms: Energy input = Useful output (useful work)  +  wasted (dissipated) energy

e.g. an electric car can have an efficiency of over 80%, that is over 80% of the stored electrical energy actually gets used to move the car. Most energy loss is from friction from moving parts and air resistance.

However, the electricity must be generated - if its from fossil fuels, the efficiency of electricity production drops to ~35%, but from renewable energy resources like wind turbines the overall efficiency is much higher.

However, for a petrol/diesel fuelled car the efficiency is less than 20%, meaning over 80% of the chemical energy store of the fuel is lost as heat from the engine and friction from the moving parts (more so than in an electric car) and air resistance.

In many cases the wasted or dissipated energy increases the thermal energy store of the surroundings.

So, ....

• Know and understand that when energy is transferred only part of it may be usefully transferred, the rest is ‘wasted’.

• BUT there is no change to the total energy of the system.

• Know and understand that wasted energy is eventually transferred to the surroundings, which will become warmer - increasing its thermal energy store.

• Appreciate that the wasted (dissipated) energy becomes increasingly spread out and so becomes less useful.

• Be able to calculate the efficiency of a device using the equations:

• Efficiency can be expressed as a decimal fraction from 0.0 to 1.0, but it is usually quoted as a percentage.

• The equation is quite simple and can be calculated from energy or power data.

• efficiency = useful energy out / total energy in

• efficiency = useful power out / total power in

• So, expressed as a percentage from 0 to 100

• % efficiency = useful energy out x 100 / total energy in

• % efficiency = useful power out x 100 / total power in

• With the x100 the efficiency has a value between 0% and 100%.

• There are other ways to express the efficiency formula e.g.

• efficiency = useful energy transferred to device / total energy supplied to the device

• You must be able to calculate efficiency as a decimal fraction (i.e. omit the x 100) or as a percentage (0-100%).

• • The efficiency formula triangle if you need to rearrange the equation to calculate energy in or energy out.

• It should be pointed out that virtually no device is 100% efficient, there is no such device as a perfect machine.

• Friction is one of the principal ways in which energy is wasted when machines are operating.

• This is because when any work is done mechanically, friction forces must be overcome because moving parts are rubbing against each other.

• Work is done against the resistive force of friction.

• The friction produces thermal energy (things heat up, and often some sound too) which is lost to increase the thermal energy store of the machine and its surroundings.

• This wasted energy, by definition, cannot contribute to the useful work output.

• The heat may be conducted away or radiated away to increase the thermal energy store of the surroundings - the machine itself or surrounding air.

• Wherever possible, lubricants like oil and grease, which flows easily, are used to minimise the friction between moving parts that touch each other - bicycles, cars and locomotives are good examples of the application of lubrication.

• Without the use of lubricants on moving parts, any machine can overheat causing damage - very expensive!

• So, more useful work is done, less wasted energy, efficiency increased and money save on fuel and repairs!  A good example is oiling the gears and axles on a mountain bike.

The same arguments apply to any moving machinery where one surface has contact with another.

• In terms of a working machine or device you can state the efficiency formula as

• % efficiency = 100 x useful energy transferred by device / total energy supplied to the device

• REMINDER - the efficiency is rarely 100%, there are usually energy losses - there is no such thing as a perfect machine!

• e.g. any machine with moving parts will experience friction somewhere and in most cases the wasted energy ends up in a useless thermal energy store e.g. the surroundings.

• However, there are circumstances when you can get an initial 100% efficiency e.g.

• An electric heater will convert all the energy from the electrical energy store into heat, all of which is transferred to the thermal energy store of the room - which is where you want the heat. You may get subsequent loss of heat from the room by conduction or convection etc. BUT they are other thermal energy store transfers!

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Sankey diagrams and efficiency - wasted energy

These are quantitative diagrams to show how the energy is distributed in two or more ways - useful and waste energy. A generalised Sankey diagram

E = the energy input,  U = useful work or energy output, W = wasted (dissipated) energy

From the law of conservation of energy: E = W + U

(Remember W is usually one form of energy, but U could involve several forms of energy.)

Be able to interpret and draw a Sankey diagram.

• You should be able to use a Sankey diagram to calculate the efficiency of an appliance.

• From a Sankey diagram you can see quite clearly in a visual way what happens to the energy input into a device ie what proportion of energy was useful and how much energy was wasted.

• The breadth of the base of each arrow is proportional to the percentage of that energy output.

• The greater the width of the 'arrow' the greater proportion of energy it represents.

• • Sankey diagram for an electric motor e.g. in a domestic appliance.

• An electric motor illustrates the idea of a Sankey diagram.

• You will find an electrical motor in devices such as an electric drill, washing machine, food mixer, electric car etc. etc. A lot of our lives runs on electrical power!

• The Sankey diagram above analyses what happens to every 100 J of electrical energy that is used by the electric motor.

• The total energy input and outputs can be expressed as ...

• total energy in = total energy out = T (J) = K (J) + S (J) + H (J)

• total energy in = total energy out = T% = 100% = K% + S% + H% = 56% + 17% + 27%

• % Efficiency = 56 x 100 / 100 = 56%

• This electric motor only has an efficiency of 56% useful energy out as kinetic energy with losses of 17% sound from friction-vibration and 27% heat energy loss from moving parts friction or warm electrical wiring in the motor.

• In this example the numbers are easy, but whatever the numbers are, from the Sankey diagram, you need to be able to get to the proportion of useful energy and covert it to a percentage of the total energy input.

• Sankey diagram for a cooling fan

• This is a more accurate Sankey diagram drawn to scale on 'graph paper'.

• To interpret it correctly, you need to be able to !

• The Law of conservation of energy states that energy cannot be created but only changes from one form to another.

• Know that appliances transfer energy but they rarely transfer all of the energy to the place we want, but whatever happens to the energy, its neither lost nor gained, but not all of it is usefully transferred.

• The Sankey style diagram above illustrates how you can represent what happens to the energy when some kind of energy consuming device is in operation.

• The input energy quantity indicated by the purple arrow (left) must equal the useful energy output of the blue arrow (right) plus the wasted energy output of the red arrow (down).

• If you can decrease the energy wasted you can increase the efficiency of the device.

• Appreciate that we need to know the efficiency of appliances so that we can choose between them, including how cost effective they are, and how to improve them.

• Devices eg industrial machines, household appliances, light bulbs etc. can only be useful if they can efficiently transform one form of 'source' energy ('total input') into an appreciable percentage of a 'useful' energy ('useful output').

• Such devices should be designed to 'waste' as little energy as possible, the less waste energy, the greater the efficiency of the device.

• See the energy flow diagram and efficiency formula 'triangle' above and the calculation of efficiency and Sankey diagram further down the page.

• It should be pointed out that virtually no device is 100% efficient, there is no such device as a perfect machine.

• One of the most efficient 'energy converters' is an electric heater were nearly all the input electrical energy is converted into useful output heat energy

• It is sometimes stated that an electrical heat is 100% efficient, BUT if the electric bar is glowing and visible, then there must be some energy loss as light.

• Whether of not the energy outputs are useful or waste, most of the energy input in a device ultimately ends up as heat energy.

• The most useful energy sources are in a sense 'highly concentrated' like a battery or a fuel like petrol, but as the energy is used you cannot recover the waste energy - it has been dissipated to the surroundings and become useless heat energy in this 'diluted' form.

•

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Costs, efficiency and pay-back time for a variety of energy strategies

• You can compare the efficiency and cost effectiveness of methods used to reduce ‘energy consumption’,

• You should know what the term ‘pay-back time’ means - the time it takes to recover your energy investment from the savings you make from eg installing insulation, low energy light bulbs, any new-replacement appliance etc.

• A general formula to calculate payback time

•  cost of installation/device etc. (£) payback time (years)   = ------------------------------------------------------- savings per year in energy/fuel costs (£)
• cost of installation (£) ÷ savings per year in fuel costs (£)

• You should be able to make judgements about the cost effectiveness of different methods of reducing energy consumption over a set period of time.

• This is not restricted to a consideration of building insulation but may include:

• low energy light bulbs and LED lighting, these are 4-10 times more efficient than the old filament bulbs in terms of useful output of light energy. They are more expensive but are designed to last a lot longer and these lighting devices are cost effective with a payback time of months. If an LED bulb cost £5 and saved £15 a year on the electricity bill, the payback time is 4 months.

• payback time = £5/£15 = 1/3 year (4 months)

• LED bulbs are more costly than low energy bulbs but can provide even greater savings.

• replacing old appliances with energy efficient ones

• ways in which ‘waste’ energy can be useful, eg heat exchangers. Heat exchanges are a means of using potentially waste heat. To extract the heat from a device or industrial process, a cooler fluid (gas/liquid) is brought into contact with the heat source and so heats up via a heat exchanger. The now hotter fluid can now be passed through another heat exchange system to re-release the heat to some useful purpose.

• Example of heater exchangers

• Some of the heat from a car engine is passed into a heat exchanger and released through the car's interior heating system.

• In some industrial processes which involve an exothermic (heat releasing) reaction eg manufacture of ammonia from hydrogen and nitrogen, some of the heat from the reaction is used to heat the incoming reactant gases to the correct high temperature for the reaction.

• Be able to describe the energy transfers and the main energy wastages that occur with a range of appliances.

• You should be familiar with common electrical appliances found in the home as these will be examined on.

• Examples will not be limited to electrical appliances; however, in this case all the information would be given in the question.

• Modern appliances are much better designed these days to be 'greener' and waste much less energy, but this does come at a price when you come to buy your more expensive replacement.

• You payback time will depend very much on the cost effectiveness of your purchase!

• See Methods of reducing heat transfer eg in a house and investigating insulating properties of materials

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Examples of reducing unwanted energy transfers - friction and air resistance

A system consists of an object or objects and the total energy in a system is constant - one expression of the law of conservation of energy - energy cannot be created or destroyed.

e.g. no mechanical device cannot work perfectly, there are always energy losses.

When anything moves, in most cases there is a friction force operating which causes energy to be lost.

When things rub together, work is done against the resistive force of friction raising the temperature of the system.

This also includes air resistance - so in a moving car you get resistance as it moves through air as well as all the friction associated with the moving parts of the car (engine and wheels) and friction between the tyre and road surfaces.

This work generates thermal energy which is lost and spread out into the surrounding thermal energy store - dissipated, and is therefore not useful energy - waste energy can't be used during the overall energy transfer .

This raises the temperature of the surrounding thermal energy store e.g. air, water or road surface etc. and you cannot extract or reclaim this lost thermal energy

There are several ways you can reduce wasted energy i.e. energy lost from a useful energy store to a useless energy store e.g.

In the case of moving machinery an application of oil and grease considerably reduces the friction and therefore the waste heat energy generated by surfaces rubbing together.

The lubricant smoothes the surfaces so they rub against each other with less friction.

The lubricant must be liquid (e.g. oil) or semi-liquid (eg grease) so that it spreads easily over the contact surfaces so that the two surfaces move smoothly over each other e.g. wheel bearings on a car axle or the pistons in the a engine's cylinder.

lubrication helps anything that moves on wheels to move more slowly - less friction - less energy wasted and lost to the surroundings - heat energy is dissipated to the thermal energy store of the surrounding air.

For examples of reducing energy losses in the home see ...

For examples of reducing water friction and air resistance see ...

Acceleration, friction, drag effects and terminal velocity experiments gcse physics revision notes

and in these examples you are reducing the loss from a kinetic energy store to the surrounding air/water thermal energy store

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Examples of how to solve work out efficiency calculation questions

(see also Types of energy store, mechanical work done and power calculations

You need to use other formulae apart from the equation for efficiency.

e.g. energy transferred = worked done E (J) = force (N) x distance (m)

power (W) = energy transferred (J) / time taken (s)

Exemplar 'efficiency' questions worked out for you

Q1 An electric kettle transfers 50 000 J of electrical energy into an electric kettle in 40 seconds.

Measurements of the temperature rise, mass of water and its specific heat capacity enable you to calculate that 40 000 J of energy were added to the water's thermal energy store.

(a) What was the percentage efficiency of the electric kettle?

% Efficiency = 100 x useful energy output / total energy input

% Efficiency = 100 x 40 000 / 50 000 = 80%

(b) What was the measured power rating of the electric kettle.

power = work done / time taken = energy transferred (J) / time taken (s)

Power in watts = 50 000 / 40 = 1250 W (1.25 kW)

(c) What was the useful power output of the electric kettle?

Efficiency = 100 x useful power output / total power input

useful power output = efficiency x total power input / 100

useful power output = 80 x 1250 / 100 = 0.8 x 1250 = 1000 W

Q2 An electrical appliance includes an electric motor, is found to be 75% efficient.

If the appliance has a maximum power input of 800 W

(a) What is the useful power output?

Efficiency = 100 x useful power output / total power input

useful power output = efficiency x total power input / 100

Efficiency = 100 x useful power output / total power input

useful power output = 75 x 800 / 100 = 0.75 x 800 = 600 W

(b) If the appliance runs for two minutes how many joules of energy are wasted?

power = 800 W = 800 J/s

energy input for 2 minutes = 800 x 2 x 60 = 96,000 J

since the appliance is 75% efficient, then 25% of the energy is wasted

therefore energy wasted = 25 x 96,000 / 100 = 0.25 x 96,000 = 24,000 J 'useless' energy

(c) If the motor of another electrical appliance transfers 120 J of useful energy for every 150 J of electrical energy supplied.

(i) What is the efficiency of the motor?

% Efficiency = 100 x useful energy output / total energy input

% efficiency = 100 x 120 / 150 = 80%

Q3 After winding up, a clockwork toy car stores 400 J of elastic potential energy.

When allowed to run, 320 J of the toy's energy store is released as useful kinetic energy.

(a) What is the % efficiency of the clockwork motor of the toy car?

% efficiency = 100 x useful energy output / total energy input

% efficiency = 100 x 320 / 400 = 80%

(b) If the toy runs for 20 seconds, what is the actual useful working power of the toy?

power = useful work done / time taken

power = 320 / 20 = 16 W

(If you ignore energy loss due to friction, the original maximum power output would be 400 / 20 = 20 W)

Q4 An electrical machine has a useful power output of 3.0 kW from a total power input of 4.0 kW

(a) What is the efficiency of the machine?

% efficiency = 100 x useful energy output / total energy input

% efficiency = 100 x 3.0 / 4.0 = 75% (0.75 as a decimal fraction)

(b) How much electrical energy is transferred to the machine in 5.0 minutes?

P = E / t, E = P x t, P = 4.0 kW = 4000 J/s, t = 5 x 60 = 300 s

therefore E transferred = P x t = 4000 x 300 = 120,000 J = 120 kJ

(c) If, in a given time, 6.0 x 106 J of electrical energy are transferred to the machine, how many joules of useful work are obtained in that same time?

efficiency = useful energy output / total energy input

useful energy output = efficiency x total energy input

useful energy output = 0.75 x 6.0 x 106 = 4.5 x 106 J

Q5 A sprinter's body applies a force of 80 N for a sprint distance of 100 m.

In the process the runner used 50 000 J of chemical energy from the body's food store.

(a) What is the efficiency of the sprinter?

useful work done = applied force x distance

work done = 80 x 100 = 8000 J

% efficiency = 100 x useful energy output / total energy input

% efficiency = 100 x 8000 / 50 000 = 16%

(b) What has happened to the rest of the energy?

When you take exercise, your body becomes temporarily hotter. A lot of the chemical energy being transferred ends up increasing the thermal energy store of your body.

Q6 Suppose (i) an electrical car is 80% efficient in its use of electrical energy and (ii) the electricity is generated from a fossil fuelled power station with an efficiency of 30%.

(a) What is the overall efficiency of the energy transfer of original chemical energy into the kinetic energy store of the car?

The answer is basically 80% of 30%

Overall efficiency is 30 x 100 / 80 = 24%

(b) How much chemical energy from a fossil fuel energy store is needed to provide a car with 450 kJ of kinetic energy?

450 kJ only represents 24% of the energy from the fossil fuel.

You therefore need to scale up by a factor of 100/24.

Therefore energy required from the fossil fuel chemical energy store = 450 x 100 / 24 = 1875 kJ

(just as a check, as in maths lessons!, 24% of 1875 = 24 x 1875 / 100 = 450 kJ)

Q7 An electric motor is supplied with 2000 J of electrical energy per minute.

If 500 J of the electrical energy is lost as thermal energy from the circuits to the surroundings, what is the efficiency of the electric motor?

If 500 J is wasted energy, 2000 - 500 = 1500 J of useful work per minute.

Efficiency = useful work / total energy input = 1500 / 2000 = 0.75  (or 75% efficiency)

Q8  An LED lamp has an efficiency of 0.90.

If the LED lamp is supplied with 500 J of electrical energy, how much energy is converted to light energy?

Efficiency = useful energy output / total energy input

Rearranging gives: Useful light energy output = Efficiency x Total energy input

Light energy output = 0.90 x 500 = 450 J

Q9 Sankey diagram for a cooling fan

Above is the Sankey diagram for the energy input and outputs for a working cooling fan.

Assume 6000 J of electrical energy is supplied to the fan every minute.

(a) How much useful energy is transferred per minute?

From the scale of the Sankey diagram you can see that:

10 squares equals the total input = 100 % ≡ 6000 J/min

On the right the useful kinetic energy driving the fan around is equal to 8 squares.

Therefore useful energy out put = 6000 x 8 /10 = 4800 J/min

(b) What is the % efficiency of the cooling fan?

% efficiency = 100 x useful energy transferred to device / total energy supplied to the device

Therefore the efficiency of this device = 100 x 4800 / 6000 = 80%

In other words 80% of the electrical energy input is transferred to the kinetic energy store of the rotating fan.

(c) (i) What % of the input energy is wasted through a heating effect? (ii) What is this loss in J/min?  (iii) What causes the friction and what happens to the energy?

(i) The energy loss as thermal energy equals 1.5 squares on the Sankey diagram.

The % wasted energy = 100 x 1.5/10 = 15%

(ii) This equates to 6000 x 15 / 100 = 900 J/min

(iii) What causes the friction and what happens to the wasted energy?

There are two sources of friction.

Friction between moving parts in the fan motor.

Friction between the fan and the air it is passing through.

In both cases work is done against the force of friction.

The energy lost from friction increases the thermal energy store of the surrounding air - wasted - dissipated. (Strictly speaking this includes the sound energy too)

(d) What is the rate of energy loss due to sound vibrations in J/s?

The energy loss due to sound is 0.5 of a square on the Sankey diagram.

Therefore the loss of energy = 6000 x 0.5 / 10 = 300 J/min  = 300 / 60 = 5 J/s

(The sound vibrations are caused by friction as the surfaces of moving parts rub against each other. This energy is eventually dissipated as thermal energy.

(e) How can the energy losses be minimised.

Quite simply, a drop of oil on the fan axle.

This allows surfaces to rub over each other more smoothly, reducing the friction effects.

The lubricant reduces friction and increases the output of useful energy, less wasted as heat or sound.

(f) What is the power rating of the fan?

6000 J is supplied per min. time 1 min = 60 s, power of 1 W = 1 J/s

Power = energy transferred (J) / time (s) = 6000 / 60 = 100 W

Q10 An electric motor in a toy train does 0.2 J of work to accelerate it to a speed of 25 cm/s.

(a) If the toy train has a mass of 3500 g, what is the efficiency of the motor?

First calculate the kinetic energy store of the train.

mass = 3500/1000 = 3.50 kg, speed = (25/100) = 0.25 m/s

KE = 1/2mv2  = 0.5 x 3.5 x 0.252 = 0.1094 J

Efficiency = useful energy out / total energy input = 0.1094 / 0.20 = 0.55 (2 s.f.)

Efficiency = 0.55 x 100 = 55% (2 s.f.)

(b) Why is the efficiency much less than 100%?

Apart from a little sound, most energy is lost (dissipated) from the friction of the moving parts of the electric motor and friction between the wheels and the rails - all energy lost ends up increasing the thermal energy store of the surroundings.

Q11

For more power calculations see Types of energy & stores and calculations of mechanical work done and power

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