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- Energy Stores and Transfers
Energy: Stores, Transfers, and Conservation
Grade 6, Grade 8Lesson 1 of 2 in Physics for Ages 11 to 14 Course
What you will learn
- Name the stores that energy can be held in, measure energy in joules, and compare how much energy different stores hold.
- Name the energy stores and measure energy in joulesUse the joule, choose a system, and name the store energy is held in for everyday objects, linking store names to the "forms of energy" names many books use.
- Compare how much energy a store holdsExplain what makes each store hold more or less energy, read graphs of kinetic energy against mass and speed, and describe how stores change when objects move or change arrangement.
- Name the energy stores and measure energy in joules
- Name the ways energy moves between stores and describe the energy changes in everyday events, devices and living things.
- Identify the ways energy is transferredDescribe transfers by forces (mechanically), by electric current, by heating and by radiation, and tell apart electricity, temperature and the energy they transfer.
- Describe energy changes in events and devicesFollow energy from store to store in everyday events, devices and living things, draw simple energy transfer diagrams, and use evidence to argue that energy was transferred.
- Identify the ways energy is transferred
- Apply the law of conservation of energy, explain why some energy is always wasted, and show energy transfers to scale with Sankey diagrams.
- Use the law of conservation of energyState that energy cannot be created or destroyed, balance energy accounts with numbers, and use conservation to explain pendulums, bouncing balls and roller coasters.
- Explain why some energy is wasted and how to reduce itTell useful from wasted energy, explain dissipation and why spread-out energy is less useful, and describe ways to cut wasted transfers.
- Draw and read Sankey diagramsShow energy transfers to scale with Sankey diagrams, read values from them, and use simple energy transfer diagrams when amounts are not known.
- Use the law of conservation of energy
- Calculate how much of the energy put into a device is transferred usefully, and use efficiency to compare devices and choose ways to waste less energy.
- Calculate efficiencyUse the efficiency equation in energy and power form, give answers as decimals or percentages, rearrange it to find useful or input energy, and spot impossible results.
- Compare devices and choose ways to improve efficiencyUse efficiency to compare lamps, motors, engines and heaters, tell efficiency apart from power, and explain why more efficient devices save energy and money.
- Calculate efficiency
- Use power ratings to calculate energy transferred in joules and kilowatt-hours, read electricity meters, and work out what it costs to run appliances.
- Use power ratings to find energy transferredExplain what a power rating in watts means and calculate energy transferred from power and time.
- Measure energy in kilowatt-hoursUse the kilowatt-hour as a unit of energy, convert between kilowatt-hours and joules, and find energy used from power and time or from meter readings.
- Work out the cost of using appliancesCalculate running costs and electricity bills from kilowatt-hours and price per kilowatt-hour, compare appliances, and plan a simple home energy audit.
- Use power ratings to find energy transferred
- Read and compare the energy values on food labels, explain how the body transfers energy from food, and measure the energy in food by burning it.
- Read food labels and link food energy to the bodyConvert between food Calories and kilojoules, compare foods fairly, and describe how the body transfers the energy from food.
- Measure the energy in food by burning itCarry out and analyze a simple experiment that compares the energy released by burning foods or fuels, and explain why the result is lower than the label value.
- Read food labels and link food energy to the body
Energy Stores and Transfers study guide
1Describe where energy is stored
A moving bicycle, a stretched bow, and a battery all have energy. Their stores differ, so we need names that tell us where to look. You will learn those names and the units used to measure energy. Then you will compare stores by changing mass, speed, height, temperature, or the arrangement of objects. These comparisons help explain why speeding up can matter much more than adding a little mass.
1.1 Energy stores and joules
A parked bicycle and a moving bicycle both have energy. Motion is only one way energy can be stored. Energy is a quantity we track when things change; it is not a material we can pour or hold.
Choose what you are studying
A system is the object or group of objects you choose to study. Everything outside it is the surroundings. You could study just the water in a kettle. You could also study the kettle and water together. The choice changes which transfers count as energy entering or leaving your system.
Name the store
| Store | Where to find it |
|---|---|
| Kinetic | A moving object, such as a rolling bicycle |
| Gravitational potential | An object and Earth, with the object raised above a chosen level |
| Elastic potential | A spring, bow, or band that is stretched, bent, twisted, or squashed |
| Thermal | Every object, including cold objects |
| Chemical | Food, fuel, muscles, and batteries |
| Magnetic | Magnets that attract or repel each other |
| Electrostatic | Charged objects that attract or repel each other |
| Nuclear | The centers of atoms, called nuclei |
One object can be part of several stores. A hot car driving uphill has kinetic energy and thermal energy. Its arrangement with Earth also gives it gravitational potential energy. A rock resting on a cliff has no kinetic energy, but its other stores remain.
Measure an amount
The energy unit is the joule, written J. Lifting an apple about 1 meter takes roughly 1 J. Large amounts are easier to write in kilojoules or megajoules:
For example, 2.5 kJ means 2.5 groups of 1,000 J:
Changing the unit changes the number, but not the amount of energy.
Connect stores with forms of energy
Some books use forms of energy and energy transformations. “Kinetic energy” means energy in a kinetic store. “Chemical energy” and “thermal energy” match chemical and thermal stores. Light, sound, and electrical energy describe energy being transferred between stores.
Potential energy comes from the position or arrangement of things that interact. These include an object and Earth, parts of a spring, magnets, charges, and particles in substances. Kinetic energy is energy of motion. Thermal energy is often grouped with motion because particles move randomly inside materials.
A force is a push or pull, measured in newtons (N). Energy is measured in joules. Say, “The moving ball has kinetic energy,” not “The ball contains force.” A force can transfer energy as it moves something.
Key Takeaways
- A system is the object or group you choose to study.
- Energy is measured in J; 1 kJ = 1,000 J and 1 MJ = 1,000,000 J.
- An object can have energy in several stores at once.
- Potential stores depend on arrangements of interacting objects.
- Forces are pushes or pulls; they are not energy stores.
1.2 What makes a store larger?
A store name tells you the kind of energy. To compare amounts, you must also know what changes and what stays the same.
Mass and speed
At the same speed, a heavier object has more kinetic energy. Doubling its mass doubles the kinetic energy. At the same mass, doubling speed gives four times the kinetic energy.
These cart data show the difference:
| Cart mass | Speed | Kinetic energy |
|---|---|---|
| 1 kg | 2 m/s | 2 J |
| 1 kg | 4 m/s | 8 J |
| 1 kg | 6 m/s | 18 J |
| 2 kg | 2 m/s | 4 J |
Compare the first two rows: speed doubles, and energy rises from 2 J to 8 J. Compare the first and last: mass doubles, and energy rises from 2 J to 4 J. A bicycle moving at 20 km/h has four times its kinetic energy at 10 km/h. This helps explain why higher-speed crashes can cause much more damage.
At fixed speed, a graph of kinetic energy against mass is a straight line through zero. At fixed mass, a graph against speed curves upward and gets steeper. Equal increases in speed bring larger and larger energy increases.
Height and stretch
The gravitational store depends on mass, height, and gravity strength. Lifting a heavier object or lifting it higher increases the store. Near Earth's surface, doubling the height lifted doubles the energy added. The same lift stores less energy on the Moon, where gravity is weaker.
Choose a reference level, such as the floor. A book's gravitational energy changes when its height above that level changes. The store belongs to the book and Earth together because they attract each other.
Stretching, squashing, bending, or twisting an object increases its elastic store while it can spring back. At the same stretch, a stiffer spring stores more energy than a softer spring.
Magnets and charges
Separating attracting magnets takes a pull and increases their magnetic store. Letting them come together decreases it. Pushing repelling magnets closer increases their store. The direction depends on whether the objects attract or repel.
Charged objects behave in a similar way. Pulling an attracting charged balloon away from your hair increases the electrostatic store of that arrangement.
Temperature, material, and amount
The thermal store depends on temperature, mass, and material. Warming the same object increases its thermal store. More water at the same temperature has a larger store. A warm bathtub can hold far more thermal energy than a small cup of hotter tea. Temperature alone cannot tell you the total.
Chemical energy depends on the substance and its amount. More fuel holds more energy; fat holds more per gram than sugar. A running flashlight decreases its battery's chemical store.
Nuclear energy depends on the types and numbers of nuclei. Splitting very heavy nuclei, such as uranium, releases energy. Joining very light nuclei, such as hydrogen in the Sun, also releases energy.
Key Takeaways
- At fixed speed, doubling mass doubles kinetic energy.
- At fixed mass, doubling speed gives four times the kinetic energy.
- Gravitational energy depends on mass, height, and gravity strength.
- Elastic energy increases with deformation while the object can spring back.
- Magnetic and electrostatic stores depend on the arrangement of interacting objects.
- Temperature, mass, and material all affect a thermal store.
- Chemical and nuclear stores depend on both type and amount.
2Explain how energy is transferred
Energy moves when a ball falls, a lamp lights, or water warms. A store tells you where energy is held. A pathway tells you how it moves between stores. Forces, currents, temperature differences, and waves each have a part to play. Following these transfers lets you explain a whole event, from its starting store to its final stores, and connect your explanation to changes you can observe.
2.1 Four ways energy moves
A store describes where energy is held. A transfer pathway describes how energy moves from one store to another. Four main pathways are mechanical, electrical, heating, and radiation.
Transfers by forces
A force transfers energy mechanically when it moves something. This is called doing work. Pushing a cart, lifting a bag, and stretching a bow all involve mechanical transfers. When a bow launches an arrow, the string pushes the arrow. The bow's elastic store decreases as the arrow's kinetic store increases.
A push alone does not tell you how much energy has moved. You also need to consider the movement it causes. A force and an amount of energy are different quantities.
Transfers in circuits
An electric current transfers energy electrically. A battery can supply energy to a lamp, motor, or heater through a circuit. The battery's chemical store decreases. The receiving stores depend on what the circuit does: a turning motor can increase a load's kinetic store.
In circuit talk, electricity usually means flowing electric charge. Electrical energy is the energy being transferred. Charge goes around a complete circuit and is not used up in the lamp. As much charge returns to the battery as leaves it. A battery runs down because its chemical energy store decreases.
Transfers from hotter to cooler
Heating transfers energy from a hotter object to a cooler one. A hot pan heats a cooler hand. Warmer room air transfers energy to a cold drink. Without further heating or cooling from elsewhere, the temperatures move toward the same value.
Heating can happen through touching materials, called conduction, or through moving liquids and gases, called convection. The temperature difference sets the direction. When ice cools your hand, energy leaves the warmer hand and enters the colder ice. “Cold” is not flowing into your skin.
Keep these three ideas separate:
| Idea | What it tells you |
|---|---|
| Temperature | How hot something is |
| Thermal store | Energy held in an object |
| Heating | Energy transferred because of a temperature difference |
Transfers by waves
Light and infrared are electromagnetic radiation. They carry energy and can cross empty space. Sunlight reaches Earth this way. Light absorbed by a wall can increase the wall's thermal store.
Sound also carries energy, but it needs matter, such as air, water, or a solid. It cannot cross empty space. Sound involves particles vibrating and pushing on nearby particles, so it is linked to mechanical transfer. A fading sound spreads energy through its surroundings, warming them slightly.
Light, sound, and current describe ways energy travels. They are not extra stores to add to an object alongside its chemical or thermal store.
Key Takeaways
- A pathway tells how energy moves between stores.
- Mechanical transfer happens when a force moves something.
- Current transfers energy electrically; charge is not used up.
- Heating transfers energy from hotter to cooler.
- Electromagnetic radiation can cross empty space; sound needs matter.
2.2 Follow an energy change
Start by comparing the beginning and end of an event. Look for a store that decreases and one that increases. Then explain the physical process linking them.
Build the account
- Choose your system.
- Describe what changes: speed, height, stretch, temperature, or chemical state.
- Name the stores that decrease and increase.
- Name the transfer pathways.
- Include every transfer so the energy totals balance.
A ball thrown upward
After the ball leaves the hand, it rises and slows. Its kinetic store decreases while the gravitational store of the ball and Earth increases. Gravity transfers energy mechanically.
At the highest point, the ball stops for an instant. Its kinetic energy is zero, but its gravitational energy is not. As it falls, the gravitational store decreases and the kinetic store increases. Air resistance also transfers some energy to thermal stores of the ball and air.
A flashlight diagram
A stores diagram uses boxes for stores and arrows for pathways. For a filament flashlight, the chain is:
Chemical store of battery → electrically → thermal store of filament → by radiation and by heating → thermal store of surroundings.
The filament becomes hot and gives out light. The room absorbs the light and warms slightly. “Lamp” alone is a device name, so a box should name the store in that lamp. The arrows show how energy reaches the next store. This diagram is also called an energy chain or energy flow diagram.
Other devices have different destinations. A charging phone increases its battery's chemical store. A kettle increases the water's thermal store electrically and also warms the kettle and air. A plant absorbs sunlight and increases its chemical store. A solar panel receives radiation and transfers energy electrically. Burning wax decreases a candle's chemical store, with transfers by heating and radiation.
Explain what causes the change
When a car brakes, friction slows it down. Its kinetic store decreases and the brakes' thermal store increases. The hot brakes then transfer energy to cooler surroundings by heating.
For a car speeding up, the engine turns the wheels. The tires push backward on the road, and the road pushes forward on the tires. That forward force speeds up the car as energy from the fuel's chemical store reaches its kinetic store. Naming energy alone does not explain the force or process involved.
Use evidence
Suppose a rolling ball hits a box. The ball slows and the box starts sliding. A clear argument has three parts:
- Claim: Energy was transferred from the ball to the box.
- Evidence: The ball slowed while the box began moving.
- Reasoning: The ball's kinetic store decreased and the box's increased. The box's new kinetic energy came from a transfer during the collision.
Sound or warming can show that some energy reached other places too. The moving box need not receive all the energy the ball lost.
Key Takeaways
- Compare start and end before naming store changes.
- Label boxes with stores and arrows with pathways.
- At the top of a vertical throw, the ball has zero kinetic energy but still has gravitational energy.
- Link a transfer claim to observations and store changes.
3Account for energy with conservation and dissipation
A bouncing ball reaches a lower height each time. Its energy has spread into the ball, floor, and air. The total energy still balances, even when the useful part shrinks. You will follow this balance with numbers and learn how friction, sound, and heating spread energy out. Sankey diagrams make the amounts visible: their arrow widths show how the input divides among useful and wasted transfers.
3.1 Keep the energy account balanced
Energy cannot be created or destroyed. This is the law of conservation of energy. An object can lose energy, but that energy must reach another store or leave the chosen system.
Choose the boundary
When no energy enters or leaves a system, its total energy stays the same. A cooling drink alone loses energy. Include the drink and everything it warms, and the decrease in one store matches increases elsewhere.
A device can also keep some incoming energy in its own stores. A charging battery does this. For a device whose own stores do not change overall, the account is:
Find a missing amount
A kettle receives 240,000 J. The water gains 216,000 J. The remaining energy warms the kettle and air:
Check by adding the two gains. They total 240,000 J. For a motor receiving 500 J and lifting a load with 350 J, the wasted part is:
The 150 J still exists, mainly in thermal stores after heating and sound have spread it out.
Follow a swing
At the highest point, a pendulum bob stops briefly. Its kinetic store is empty and its gravitational store is largest for that swing. At the lowest point, the bob moves fastest and its kinetic store is largest.
Air resistance and friction at the pivot transfer energy to the surroundings. Each swing rises a little less. The pendulum's moving-and-raised stores shrink, while thermal stores elsewhere grow.
Compare bounce heights
A ball is dropped from rest at 2.0 m and returns to 1.5 m. For the same ball near Earth's surface, gravitational energy follows height. Compare its energy at the two points where it is briefly at rest:
The rebound has 75% of the original gravitational energy. The remaining 25% reached thermal stores and traveled away as sound during the fall, impact, and rebound. The ball's squashing also temporarily stored energy elastically during impact.
Explain a height limit
A roller-coaster car released from rest cannot rise above its starting height without more energy input. Reaching a greater height would need more gravitational energy than it started with. Friction and air resistance reduce the energy left for climbing, so a real car reaches less than the ideal height.
An engine or another push can add energy and change this limit. Always include that input when following a powered ride.
People say energy is “used up” when a battery runs down. Its chemical store has decreased; energy has spread elsewhere. “Saving energy” means needing less from fuel stores or paid electrical supplies. Real machines dissipate energy as they operate, so a machine cannot keep delivering work forever without a fresh supply.
Key Takeaways
- Energy cannot be created or destroyed.
- With no energy crossing the boundary, total energy stays constant.
- Input equals useful plus wasted output when the device stores do not change overall.
- Lower swings and bounces result from transfers to other stores.
- A freely rolling coaster released from rest needs extra input to climb above its starting height.
3.2 Useful energy and wasted transfers
A speaker is meant to make sound. A toaster is meant to warm bread. Whether a transfer is useful depends on the job you want done.
Decide what serves the purpose
Light from a lamp is useful. Warming the lamp and room is usually wasted for that lighting job. Heating from a room heater is useful because warming the room is its purpose. Sound is useful from a speaker but usually wasted from a vacuum cleaner.
Wasted energy has not vanished. It has been transferred in a way that does not serve the intended purpose. It often ends up warming the surroundings.
What dissipation means
Dissipation is energy spreading out into the surroundings. Each part of a large room may warm by a tiny amount. The energy is still present, but gathering it back for another useful job is very difficult.
For example, light from a lamp is absorbed by walls and objects. Their thermal stores increase. Sound spreads and warms its surroundings slightly. A bicycle's motion eventually warms brakes, tires, road, and air. Conservation describes the unchanged total; dissipation describes the spreading out.
Match the improvement to the waste
| Unwanted transfer | A way to reduce it |
|---|---|
| Moving machine parts warm through friction | Add suitable oil or grease: lubrication |
| A vehicle pushes through air or water | Use a smooth, streamlined shape to reduce drag |
| A hot tank warms the room | Add thermal insulation to slow outward heating |
| Loose parts shake and make noise | Tighten the parts to reduce vibration |
| A filament lamp produces much unwanted warming | Choose an LED that gives the required light with less input |
An explanation should connect the change to its effect. “Oil makes the machine better” gives little detail. “Oil reduces friction between the moving parts, so less energy warms them” identifies the wasted transfer.
Keep useful friction
Friction has useful jobs too. Tires need grip to turn and stop. Brake friction deliberately removes a vehicle's kinetic energy. Reducing all friction would make the car harder to control.
Choose the place where the unwanted transfer happens. Lubricating an engine's moving parts can reduce waste. Making tire-road grip vanish would remove a force the driver needs.
Key Takeaways
- Useful output depends on the intended job.
- Dissipated energy still exists but is spread out and harder to reuse.
- Name the unwanted transfer when suggesting an improvement.
- Lubrication reduces friction; streamlining reduces drag.
- Friction can be useful, as in tires and brakes.
3.3 Show amounts with Sankey arrows
A stores diagram shows where energy goes. A Sankey diagram adds amounts: the width of each arrow represents energy or power. Wider arrows stand for larger amounts.
Read the branches
The input arrow enters from the left. The useful branch continues straight ahead. Wasted branches turn away, usually downward. Labels name each transfer and give its amount and unit.
The output widths must add to the input width. This shows conservation of energy. Arrow length does not measure energy. A long, thin arrow can represent less energy than a short, wide one.
Draw a motor's energy account
A motor receives 200 J. It transfers 140 J usefully to a load's kinetic store, 50 J by heating, and 10 J by sound. Use squared paper with a scale of one square of width for 10 J.
- Draw the input shaft 20 squares wide.
- Continue a useful shaft 14 squares wide straight ahead.
- Branch off a heating shaft 5 squares wide.
- Add a sound branch 1 square wide.
- Label the input and every output with their amounts and pathways.
Check the values:
Check the widths:
The widths are measured across each arrow shaft, at right angles to its direction. Keep the branch widths the same as they turn.
Find a missing branch
Another diagram has 400 J input, 100 J useful output, and 20 J sound. The heating branch must show the rest:
At 20 J per square, the widths would be 20 squares input, 5 useful, 1 sound, and 14 heating. The heating branch is the largest output, even if it is drawn shorter than the useful branch.
Use watts or find a fraction
A Sankey diagram can show power in watts. A 60 W filament lamp giving 3 W of light has 57 W of wasted output. All labels on that diagram must use power, not a mixture of W and J.
The useful fraction can be found from amounts or widths. For the first motor:
So 70% of the input is useful. The diagram's scale cancels because all widths use the same scale.
When amounts are unknown, use a simple stores-and-pathways diagram. Drawing equal-width Sankey branches without numbers would suggest equal amounts, even though you have no evidence for that claim.
Key Takeaways
- Sankey arrow width represents an amount; length does not.
- Use one scale and one kind of unit throughout.
- Output widths add to input width.
- Find a missing output by subtracting all known outputs.
- Useful width divided by input width gives the useful fraction.
4Calculate and compare efficiency
Two lamps can give the same light while taking in very different amounts of energy. Efficiency compares the useful part with the whole input. It helps explain why one device needs less energy for the same job. You will calculate that share using energy or power, find a missing input or output, and compare devices fairly. You will also connect each suggested improvement to the unwanted transfer it reduces.
4.1 Find the useful fraction
Efficiency tells you what share of a device's input is useful. A device that sends three quarters of its input to the intended job has efficiency 0.75, or 75%.
Calculate efficiency
Use matching units before dividing. Multiply the decimal by 100 for a percentage. Efficiency is a ratio, so it has no unit.
A kettle receives 240,000 J and transfers 216,000 J to the water:
A filament lamp receives 60 J each second and wastes 57 J by heating. First find useful light output:
Then divide useful by input:
Dividing 57 by 60 would give the wasted fraction. It would not give efficiency.
Use power instead
You can compare useful output power with input power:
A motor takes in 1,200 W and provides 900 W usefully. Its efficiency is 900 divided by 1,200: 0.75, or 75%. Power works because it compares energy transferred in the same amount of time.
Find a useful output
Multiply the input by the decimal efficiency:
An engine receives 400 kJ at 25% efficiency. Change 25% to 0.25 first:
It transfers 100 kJ usefully and wastes 300 kJ. Multiplying by 25 would treat 25% as twenty-five whole inputs.
Find the input needed
Divide the useful output by decimal efficiency:
A device must deliver 180 J usefully at 60% efficiency:
The needed input is larger than the useful output. Of the 300 J, 120 J is wasted.
Check the units and result
For 0.5 kJ useful output from 2,000 J input, first convert 0.5 kJ to 500 J. The ratio is 500 divided by 2,000, giving 0.25 or 25%. Using 0.5 directly would mix units.
Efficiency cannot exceed 100% when all inputs are counted and the device is not drawing down its own stores. A result above 100% often comes from reversing the division. Also distinguish 0.7 from 0.7%: 0.7 is 70%. A room heater can be close to 100% efficient for room warming because nearly all its electrical input ends up warming that room.
Key Takeaways
- Efficiency = useful output ÷ total input, using matching units.
- Energy ratios and power ratios both give efficiency.
- Efficiency has no unit; multiply its decimal by 100 for percent.
- Useful output = decimal efficiency × input.
- Input = useful output ÷ decimal efficiency.
- Check unit conversions and the direction of division.
4.2 Compare devices doing the same job
A fair efficiency comparison starts with a clear job. For lamps, that might be giving the same amount of light. For motors, it might be lifting the same load through the same height.
Compare equal light outputs
Suppose a 9 W LED lamp and a 60 W filament lamp each give 3 W as light. Their efficiencies are:
The LED wastes 6 W, while the filament lamp wastes 57 W.
Both lamps do the same lighting job. The LED needs much less input for it. Over the same operating time, it uses less electrical energy and costs less to run at the same unit price.
Separate power from efficiency
| Quantity | Question it answers |
|---|---|
| Power | How fast is energy transferred? |
| Efficiency | What fraction of the input is useful? |
A 1,500 W room heater has high power and can be close to 100% efficient for warming the room. The 9 W LED above has low power and 33% efficiency for light output. A low power rating alone cannot tell you the useful fraction.
A large motor can be powerful and efficient. A small motor can have low power and waste a large share. You need useful output and total input to judge efficiency.
Improve the largest wasted transfer
Electric motors usually transfer a larger share of their input usefully than gasoline engines. Engines transfer much of their fuel energy to hot engine parts, exhaust, and air. This helps explain why a similar electric car needs less energy to cover the same distance.
An improvement should address a real unwanted transfer. Lubrication cuts heating from friction in moving parts. Streamlining reduces drag. Insulation slows heating from a hot oven or water tank into the room. A better lamp design can give the required light with less wasted heating.
Compare energy labels
Annual-use labels estimate electrical energy in kWh per year. Compare appliances doing similar jobs: for example, refrigerators of the same size. A larger refrigerator may use more energy simply because it has more space to cool.
A model with lower annual use costs less to run at the same electricity price. Its purchase price may be higher, so compare both purchase and running costs when choosing one. If the electricity supply burns fuel, needing less electrical energy also reduces the associated fuel use and pollution.
Key Takeaways
- Compare devices with the same useful job or output.
- A more efficient device needs less input for equal useful output.
- Power is a rate; efficiency is a fraction.
- Reduce a named waste, such as friction, drag, or outward heating.
- Compare annual energy labels for appliances with similar size and purpose.
5Work out energy use and cost from power ratings
A watt tells you how fast energy is transferred. A bill charges for how much energy was transferred over time. Connecting those ideas takes careful use of seconds, hours, watts, and kilowatts. You will use appliance ratings to find joules and kilowatt-hours, read changes on an electricity meter, and turn energy use into a running cost. A simple home audit brings the calculations together.
5.1 Power tells you energy per second
A lamp marked 60 W transfers 60 J each second. Power measures the rate of energy transfer. It tells you how quickly an energy amount is being transferred.
Watts and kilowatts
One watt (W) means one joule per second. One kilowatt (kW) is 1,000 W. Typical electrical inputs include a 9 W LED lamp, a television around 100 W, a 1,000 W toaster, and a 1,500 W hair dryer or space heater. Appliances that heat things often have high power ratings.
Energy, power, and time are linked:
Here, power is in W, energy in J, and time in seconds. At steady power, twice the running time transfers twice the energy.
Work out an energy amount
A toaster takes in 1,000 W for 90 s. Multiply the energy per second by the number of seconds:
For a 1,500 W hair dryer used for 5 minutes, change minutes to seconds first:
Using 5 seconds in that multiplication would make the answer 60 times too small.
To find power, divide energy by time. A motor transferring 6,000 J in 20 s has power 6,000 divided by 20, or 300 W. To find a time, divide the energy needed by the power available. Each formula follows the same energy-per-second relationship.
Include how long it runs
High power does not always mean the greatest total energy use. A 9 W lamp running for 10 hours operates for 36,000 s:
A 1,500 W hair dryer used for 3 minutes operates for 180 s:
The lamp transfers more energy because it runs much longer.
Read the right rating
Use the appliance's electrical input to calculate energy taken from an outlet. A microwave sold as “1,000 W” may be describing cooking output. Its electrical input is higher, often around 1,500 W. Look for the input value on its label plate.
A refrigerator or oven can switch on and off as its thermostat controls temperature. Its maximum running power multiplied by 24 hours overstates daily use when it cycles off. Use the time actually running, a suitable average power, or an annual energy-use label. A charger's rating may give maximum output; its input also changes as the battery fills.
Key Takeaways
- Power measures energy transferred each second; 1 W = 1 J/s.
- 1 kW = 1,000 W.
- For joules, multiply watts by seconds.
- Energy depends on running time as well as power.
- Use electrical input and allow for appliances switching on and off.
5.2 Count energy in kilowatt-hours
Household energy amounts would be very large numbers in joules. A kilowatt-hour (kWh) is a larger energy unit, useful for appliances and electricity meters.
What one kWh means
A 1 kW appliance running for one hour transfers 1 kWh. Since 1 kW is 1,000 W and an hour is 3,600 seconds:
A kilowatt-hour is an amount of energy. A kilowatt is a power, or rate. An appliance does not have a “kWh power rating.” Its energy use also depends on how long it runs.
Multiply kilowatts by hours
First divide watts by 1,000 and minutes by 60. A 1,500 W space heater used for 3 hours has power 1.5 kW:
A 9 W lamp used for 5 hours has power 0.009 kW:
The small decimal is sensible for a low-power lamp used for only a few hours.
Handle minutes as part of an hour
A 1.5 kW hair dryer runs for 20 minutes. This is one third of an hour, not 0.20 hours:
Using the fraction keeps the calculation exact. You can round the final answer when needed. “Kilowatts per hour” is not the energy unit; multiplying power by time gives kilowatt-hours.
Read a meter
An electricity meter records a running total of energy supplied. Subtract the earlier reading from the later one:
For readings of 45,210 kWh and 45,830 kWh:
The home used 620 kWh between readings. The later reading alone includes energy from before that period.
Convert an appliance amount to joules
A charger takes an average electrical input of 10 W for 2 hours. Use the average input because charging power changes:
Convert the resulting energy to joules:
To go from joules to kWh, divide by 3,600,000. The conversion describes the same amount in different units, just as meters and centimeters can describe the same length.
Key Takeaways
- A kWh is an energy amount, not a power.
- 1 kWh = 3,600,000 J = 3.6 MJ.
- Energy in kWh = power in kW × time in hours.
- Divide minutes by 60, not by 100.
- Meter use is the new reading minus the old reading.
5.3 Turn energy use into cost
Electricity costs depend on energy used and the price charged for each kilowatt-hour. Use 18 cents per kWh for these examples.
Find the running cost
A 1.5 kW hair dryer runs for 10 minutes a day over 30 days. First combine the times:
Then find the energy:
Finally find the cost:
That is $1.35. If you multiply by 0.18 dollars instead, the answer is already in dollars. Do not turn 135 cents into 135 dollars.
Read an energy charge
For a home using 620 kWh, the energy charge is:
If the bill also lists a fixed monthly charge of $12, add it once. The total is $123.60. A fixed charge does not depend on how many kWh were used. Fuel bills follow the same amount-times-unit-price idea, using the unit listed on the bill.
Compare yearly use
At 4 hours daily for 365 days, a 60 W lamp runs for 1,460 hours. A 9 W LED providing similar light saves 51 W, or 0.051 kW:
Rounded at the end, that saves about $13.40 per year.
An annual energy label can shorten this calculation. A refrigerator labeled 400 kWh per year costs $72 at the example price. A similar model using 300 kWh costs $54. The yearly saving is $18.
Include standby
A television drawing 1 W on standby for 20 hours daily uses:
At 18 cents per kWh, that costs about $1.31. Each standby input is small, but many devices over long times can add up.
Make a home energy audit
List appliances, their electrical inputs, and daily running times. Convert inputs to kW and times to hours. Multiply each pair to find kWh per day, then multiply by the unit price. Add the energy amounts for a daily total.
Use annual labels or measured averages for cycling appliances. Compare the calculated daily amounts before choosing changes: heating and cooling appliances, or devices used for many hours, often offer the largest savings. A short use of a powerful appliance can cost less than a smaller input left on all day.
Key Takeaways
- Cost = kWh used × price per kWh.
- Keep cents and dollars consistent.
- Add any stated fixed charge separately.
- Annual labels and standby times help compare long-term use.
- An audit compares both power and running time.
6Explain the energy in food
Food holds energy in a chemical store. Your body transfers that energy as it moves, stays warm, grows, and keeps its organs working. Food labels let you compare amounts using Calories or kilojoules. A burning-food experiment offers another way to investigate the store: some released energy warms water. Tracking the energy that reaches other places helps explain why the classroom result is low.
6.1 Food labels and the body
Food holds energy in a chemical store. Cells release energy through respiration. In aerobic respiration, oxygen takes part in the reactions. Plants first transfer energy from sunlight into the chemical store of the substances they make.
Calories and kilojoules
A food Calorie, with a capital C, is one kilocalorie (kcal). It is a unit of energy, not an ingredient or a material. One kcal equals 1,000 small calories.
To convert Calories to kJ, multiply by 4.184. A 190 Calorie snack bar contains:
To go the other way, divide. A food amount containing 1,000 kJ holds about 239 kcal.
Compare the same amount of food
Use per 100 g values to compare how energy-rich foods are. Use per serving values for the energy in the portion eaten. Different serving sizes can change which number looks larger.
A cereal contains 1,600 kJ per 100 g. A 30 g serving is 30 hundredths of that amount:
Doubling the serving doubles its energy. A label's per-serving number does not describe the whole package unless the package is one serving.
Fat gives about 37 kJ per gram, or 9 kcal. Carbohydrate and protein each give about 17 kJ per gram, or 4 kcal. So 10 g of fat supplies about 370 kJ; 10 g of sugar supplies about 170 kJ. Water, vitamins, and minerals supply no energy.
Where the energy goes
Energy from food supports movement, body warmth, the heart, lungs, brain, growth, and repair. Muscles transfer energy mechanically when you lift or push. Energy taken in beyond what the body transfers is added to its chemical stores, mostly as fat. Drawing more energy from stores than is taken in reduces them.
US food labels use 2,000 Calories per day as a general reference. Actual needs vary with age, body size, sex, and activity. The label reference is not one target for every person.
Connect food with power and kWh
An energy amount of 2,000 Calories is about 8,368 kJ. Spread over 86,400 seconds in a day, this is an average rate of about 97 W. Activity changes the rate: running transfers energy faster than sitting.
A 250 Calorie snack holds about 1,046 kJ. That equals about 0.29 kWh, enough energy for a 1,500 W hair dryer to run for roughly 12 minutes. Comparing the units lets you compare the amounts in food and electrical supplies. In the body, most transferred energy eventually reaches thermal stores of the body and surroundings.
Key Takeaways
- One food Calorie = 1 kcal = 4.184 kJ.
- Compare foods per equal mass, then scale to the serving.
- Fat supplies more energy per gram than carbohydrate or protein.
- Respiration releases energy for body activity.
- 2,000 Calories is a labeling reference; individual needs vary.
- Food energy can be compared with electrical energy using J or kWh.
6.2 Measure energy captured from burning food
Burning food releases energy from its chemical store. Some of that energy can warm water. Measuring the water's temperature rise gives an estimate of the energy the water received.
Set up the comparison
In a supervised school experiment, place a measured mass of water in a clamped boiling tube. Weigh the food sample. Mount it on a needle, light it, and hold it below the tube. Measure the water temperature before and after, and record any food left unburned.
Wear eye protection and work over a heatproof mat. Keep hair and loose clothing away from flames. Do not burn nuts or nut products where anyone may have a nut allergy.
For fair comparisons, use equal starting food masses, equal water masses, and the same flame-to-tube distance. Keep the setup and starting conditions alike. Burn each sample completely where possible. Repeat tests and calculate a mean to reduce the effect of chance variation.
Calculate the temperature rise
Subtract the starting temperature from the final temperature. If 20 g of water warms from 20 °C to 50 °C:
The final temperature alone is not the rise. About 4.2 J warms one gram of water by one degree Celsius:
For this water:
Compare per gram
If 1.0 g of food burned, divide the captured energy by 1.0 g. The measured result is 2.52 kJ per gram. If residue remains, use the mass actually burned when reporting energy released per gram burned.
A label showing 1,840 kJ per 100 g means 18.4 kJ per gram. The classroom result captures about 14% of that value:
A larger temperature rise per gram indicates more captured energy only when water masses and capture conditions match. Twice as much water needs twice as much energy for the same rise.
Explain a low result
The flame also warms the glass, clamp, and surrounding air. Radiation escapes. Some food may burn incompletely or remain as residue. Energy still held chemically in unburned food was not released.
The released energy is shared between the water and everything else it warms. Conservation still holds; the water measurement captures only part of that account. Shielding drafts and keeping a suitable, consistent flame distance can increase the share reaching the water. Laboratory equipment captures energy far more carefully. The same classroom method can compare fuels by using the mass of fuel burned.
Key Takeaways
- Water temperature rise = final temperature − starting temperature.
- Water energy in J ≈ water mass in g × 4.2 × rise in °C.
- Divide by food mass burned to report energy per gram burned.
- Control water mass and capture conditions for fair comparisons.
- Energy outside the water and incomplete burning help explain low results.
Energy Stores and Transfers examples
1Find stores and compare their amounts
12 steps
- 1IntroductionEnergy before anything moves
A wound-up toy can move after you let it go. Before release it is still, yet its spring already holds energy. A raised book is still too, but can gain speed when dropped.
We need more than “moving” and “not moving” to describe energy. Store names tell us where to look; comparisons tell us how much a store changes.
- 2ExplanationPick a system and a unit
Choose the object or group you will study. That is your system. Everything else is its surroundings. For a hot mug, you might choose just the drink or the mug and drink together.
Measure energy in joules (J). One kJ is 1,000 J; one MJ is 1,000,000 J. A store is a way of holding energy, not a container full of a material called energy.
- 3ExampleMotion, height, and shape
A rolling suitcase has a kinetic store. A suitcase held on a high luggage rack has gravitational potential energy in its arrangement with Earth.
A bent tent pole has an elastic potential store. It can transfer energy as it springs back. The store name changes with the situation; an object can belong to more than one store at once.
- 4ExplanationThermal and chemical stores
Every object has a thermal store, including a cold drink. Warming the same object increases that store. Food, fuel, and batteries have chemical stores that can release energy through reactions.
A hot battery-powered toy can have thermal, chemical, and kinetic energy at once. It does not need to finish using one store before another can matter.
- 5ExplanationStores in interactions and nuclei
Magnets have a magnetic store linked to their arrangement. Charged objects have an electrostatic store. Moving objects against their attraction or repulsion can add energy.
The nuclear store is associated with nuclei, the centers of atoms. Splitting very heavy nuclei or joining very light nuclei can release energy. These are different processes from emptying a battery’s chemical store.
- 6ChallengeA stone on a wall
A stone rests on top of a wall. Does its zero speed mean it has no energy? Name a store that supports your answer.
---reveal---
No. The stone and Earth have a gravitational potential store because the stone is raised. Its thermal and nuclear stores also remain. Zero speed means zero kinetic energy, not zero energy in every store.
- 7ExampleChange only mass
A moving cart has 12 J of kinetic energy. Add a load so the moving mass doubles, but keep the same speed.
At fixed speed, doubling mass doubles kinetic energy:
The comparison needs the fixed-speed condition. If adding the load also slowed the cart, both changes would affect the result.
- 8ExampleNow change only speed
Return to the cart with 12 J at its original mass and speed. This time keep its mass fixed and double its speed.
Doubling speed multiplies kinetic energy by four:
On a speed graph, the energy curve gets steeper. It is not a straight line: each equal speed increase adds more energy than the last.
- 9ExplanationCompare position and stretch
Lifting the same mass higher increases its gravitational store. Near Earth, doubling the height lifted doubles the added energy. Gravity strength matters too: the same lift stores less on the Moon.
More stretch increases an elastic store while the object can spring back. At equal stretch, a stiffer spring stores more. Pulling attracting magnets apart also increases their store because you work against their pull.
- 10ChallengeTemperature is only one clue
Two buckets contain the same mass of water at the same temperature. Then more water at that temperature is added to one bucket. How do the thermal stores compare?
---reveal---
The bucket with more water has the larger thermal store. Mass increased while material and temperature stayed the same. Equal temperatures do not guarantee equal thermal energies.
- 11ChallengeOne change helps and one opposes
A cart’s mass is halved and its speed doubles. Its original kinetic energy was 20 J. What is its new energy, and does it still have other stores?
---reveal---
Halving mass gives a factor of one half; doubling speed gives a factor of four. Together they double the energy to 40 J. The cart also has stores such as thermal energy; the calculation concerns its kinetic store only.
- 12RecapName the store, then compare
Choose the system and measure energy in J, kJ, or MJ. Name stores using motion, position, shape, temperature, substances, or interactions.
For comparisons, keep track of what stays fixed. Mass and speed affect kinetic energy differently. A temperature reading alone cannot compare stores when mass or material differs.
2Trace energy through an event
11 steps
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- 1IntroductionFrom a starting store to a change
- 2ExplanationForces transfer energy
- 3ExplanationA current carries the transfer
- 4ExplanationTemperature differences and waves
- 5ChallengeA chilled can warms
- 6ExampleStart a store diagram
- 7ExampleFollow the light onward
- 8ExampleTurn observations into evidence
- 9ChallengeExplain a falling object
- 10ChallengeExplain a braking bicycle
- 11RecapDescribe what moved and how
3Balance amounts and draw a Sankey diagram
14 steps
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- 1IntroductionA motor has several destinations
- 2ExplanationEnergy must go somewhere
- 3ExampleSubtract to find the remainder
- 4ChallengeA slowing swing
- 5ExplanationUseful depends on the job
- 6ExplanationSpreading makes reuse difficult
- 7ChallengeChoose the improvement that fits
- 8ExampleChoose a width scale
- 9ExampleCheck every split
- 10ChallengeRead a different scale
- 11Key InsightWidths give the useful fraction
- 12ConnectionShow power or show stores
- 13ChallengePredict the changed diagram
- 14RecapKeep all destinations in view
4Calculate and compare useful shares
12 steps
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- 1IntroductionA fraction of the whole input
- 2ExplanationPut useful output on top
- 3ExampleFind useful output before dividing
- 4ExampleTurn the amount into a percentage
- 5ChallengeMatch the units
- 6ExampleWork backward to an input
- 7TipUse the same ratio for power
- 8ExampleCompare equal light
- 9ChallengePower does not settle efficiency
- 10ConnectionName the waste you would cut
- 11ChallengeAn input saving for the same job
- 12RecapKeep the numerator useful
5From appliance ratings to a bill
15 steps
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- 1IntroductionA rate becomes a total
- 2ExplanationWatts mean joules each second
- 3ExampleCount the operating seconds
- 4ExampleFind the joules
- 5ChallengeCompare rate and time
- 6ExplanationSwitch to household energy units
- 7ExampleUse kilowatts and hours
- 8ChallengeMinutes are sixtieths
- 9ExampleRead the meter difference
- 10ExamplePrice a single use
- 11ExampleAdd up repeated uses
- 12ChallengePrice the meter period
- 13ConnectionChoose useful audit information
- 14ChallengeFind a monthly saving
- 15RecapMatch each pair of units
6Compare labels and a burning test
14 steps
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- 1IntroductionThe same store, two measurements
- 2ExplanationCells transfer food energy
- 3ExplanationNutrients supply different amounts
- 4ExampleConvert a label unit
- 5ExampleScale the portion
- 6ChallengeCompare unequal portions
- 7Key InsightEnergy can be compared across sources
- 8ExplanationMake the burning comparison fair
- 9ExampleFind the water’s rise
- 10ExampleCalculate the captured energy
- 11ExampleReport energy per gram burned
- 12ChallengeWhat the water did not measure
- 13ChallengeCompare a label with the sample
- 14RecapCompare the right amounts
Energy Stores and Transfers practice questions
Set 1: Stores, devices, and energy accounts10 Practice Questions
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Set 3: Rates, useful shares, and food10 Practice Questions
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Set 4: Follow energy through several changes10 Practice Questions
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Set 5: Connect energy, measurements, and costs10 Practice Questions
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Stuck on your own question? Homework Help
Key Terms
A
Aerobic respiration
Annual energy-use label
Atomic nucleus
C
Chemical store
Conservation of energy
D
Decimal efficiency
Dissipation
E
Efficiency
Elastic potential store
Electric current
Electrical transfer
Electricity meter
Electrostatic store
Energy
Energy account
Energy per gram
Energy transfer diagram
Energy transformation
Evidence
F
Fair test
Food Calorie
Force
G
Gravitational potential store
H
Heating
Home energy audit
I
Incomplete combustion
Input energy
J
Joule
K
Kilocalorie
Kilowatt
Kilowatt-hour
Kinetic store
L
LED lamp
Lubrication
M
Magnetic store
Mass
Mass burned
Mean
Mechanical transfer
N
Nuclear store
O
Output branch
P
Percentage efficiency
Potential energy
Power
Power rating
R
Radiation
Reasoning
Reference level
Respiration
Running cost
S
Sankey diagram
Scale
Serving
Sound
Speed
Standby
Stiffness
Streamlining
Surroundings
System
T
Temperature rise
Thermal insulation
Thermal store
Thermostat
Transfer pathway
U
Unit price
Useful output
W
Wasted output
Watt
Work
- 1Energy Stores and Transfers
- 2Heat Transfer
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