Energy: Stores, Transfers, and Conservation

Learn where energy is stored, how it moves from store to store, and why the total amount never changes even though some of it always ends up wasted. Draw Sankey diagrams, calculate efficiency, use power ratings and kilowatt-hours to work out what appliances cost to run, and compare the energy in foods from their labels.

Grade 6, Grade 8Lesson 1 of 2 in Physics for Ages 11 to 14 Course

What you will learn

  1. 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 joules
      Use 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 holds
      Explain 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.
  2. Name the ways energy moves between stores and describe the energy changes in everyday events, devices and living things.
    • Identify the ways energy is transferred
      Describe 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 devices
      Follow 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.
  3. 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 energy
      State 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 it
      Tell 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 diagrams
      Show energy transfers to scale with Sankey diagrams, read values from them, and use simple energy transfer diagrams when amounts are not known.
  4. 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 efficiency
      Use 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 efficiency
      Use efficiency to compare lamps, motors, engines and heaters, tell efficiency apart from power, and explain why more efficient devices save energy and money.
  5. 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 transferred
      Explain what a power rating in watts means and calculate energy transferred from power and time.
    • Measure energy in kilowatt-hours
      Use 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 appliances
      Calculate running costs and electricity bills from kilowatt-hours and price per kilowatt-hour, compare appliances, and plan a simple home energy audit.
  6. 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 body
      Convert 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 it
      Carry 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.

Energy Stores and Transfers study guide

6 chapters

1

Describe 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
StoreWhere to find it
KineticA moving object, such as a rolling bicycle
Gravitational potentialAn object and Earth, with the object raised above a chosen level
Elastic potentialA spring, bow, or band that is stretched, bent, twisted, or squashed
ThermalEvery object, including cold objects
ChemicalFood, fuel, muscles, and batteries
MagneticMagnets that attract or repel each other
ElectrostaticCharged objects that attract or repel each other
NuclearThe 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:

1 kJ=1,000 J1 MJ=1,000,000 J

For example, 2.5 kJ means 2.5 groups of 1,000 J:

2.5×1,000=2,500 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 massSpeedKinetic energy
1 kg2 m/s2 J
1 kg4 m/s8 J
1 kg6 m/s18 J
2 kg2 m/s4 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.
2

Explain 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:

IdeaWhat it tells you
TemperatureHow hot something is
Thermal storeEnergy held in an object
HeatingEnergy 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
  1. Choose your system.
  2. Describe what changes: speed, height, stretch, temperature, or chemical state.
  3. Name the stores that decrease and increase.
  4. Name the transfer pathways.
  5. 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.
3

Account 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:

input energy=useful output+wasted output
Find a missing amount

A kettle receives 240,000 J. The water gains 216,000 J. The remaining energy warms the kettle and air:

240,000−216,000=24,000 J

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:

500−350=150 J

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:

1.52.0=0.75=75%

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 transferA way to reduce it
Moving machine parts warm through frictionAdd suitable oil or grease: lubrication
A vehicle pushes through air or waterUse a smooth, streamlined shape to reduce drag
A hot tank warms the roomAdd thermal insulation to slow outward heating
Loose parts shake and make noiseTighten the parts to reduce vibration
A filament lamp produces much unwanted warmingChoose 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.

  1. Draw the input shaft 20 squares wide.
  2. Continue a useful shaft 14 squares wide straight ahead.
  3. Branch off a heating shaft 5 squares wide.
  4. Add a sound branch 1 square wide.
  5. Label the input and every output with their amounts and pathways.

Check the values:

140+50+10=200 J

Check the widths:

14+5+1=20 squares

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:

400−100−20=280 J

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:

140200=1420=0.70

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.
4

Calculate 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
efficiency=useful energy outputtotal energy input

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:

216,000÷240,000=0.90=90%

A filament lamp receives 60 J each second and wastes 57 J by heating. First find useful light output:

60−57=3 J

Then divide useful by input:

3÷60=0.05=5%

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:

efficiency=useful power outputtotal power input

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:

useful energy=efficiency×input energy

An engine receives 400 kJ at 25% efficiency. Change 25% to 0.25 first:

0.25×400=100 kJ

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:

input energy=useful energyefficiency

A device must deliver 180 J usefully at 60% efficiency:

180÷0.60=300 J

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:

LED: 3÷9≈0.33=33% filament: 3÷60=0.05=5%

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
QuantityQuestion it answers
PowerHow fast is energy transferred?
EfficiencyWhat 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.
5

Work 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:

P=EtE=P×tt=EP

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:

1,000×90=90,000 J=90 kJ

For a 1,500 W hair dryer used for 5 minutes, change minutes to seconds first:

5×60=300 s 1,500×300=450,000 J

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:

9×36,000=324,000 J

A 1,500 W hair dryer used for 3 minutes operates for 180 s:

1,500×180=270,000 J

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:

1 kWh=1,000×3,600=3,600,000 J=3.6 MJ

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
E (kWh)=P (kW)×t (h)

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:

1.5×3=4.5 kWh

A 9 W lamp used for 5 hours has power 0.009 kW:

0.009×5=0.045 kWh

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:

20÷60=13 h 1.5×13=0.5 kWh

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:

energy used=new reading−old reading

For readings of 45,210 kWh and 45,830 kWh:

45,830−45,210=620 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:

10÷1,000=0.010 kW 0.010×2=0.02 kWh

Convert the resulting energy to joules:

0.02×3,600,000=72,000 J

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
cost=energy in kWh×price per kWh

A 1.5 kW hair dryer runs for 10 minutes a day over 30 days. First combine the times:

30×10=300 minutes=5 hours

Then find the energy:

1.5×5=7.5 kWh

Finally find the cost:

7.5×18=135 cents

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:

620×0.18=111.60 dollars

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:

0.051×1,460=74.46 kWh saved 74.46×0.18=13.4028 dollars

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:

0.001×20×365=7.3 kWh per year

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.
6

Explain 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.

1 kcal=4.184 kJ≈4.2 kJ

To convert Calories to kJ, multiply by 4.184. A 190 Calorie snack bar contains:

190×4.184=794.96 kJ≈795 kJ

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:

1,600×30100=480 kJ

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:

rise=50−20=30 °C

The final temperature alone is not the rise. About 4.2 J warms one gram of water by one degree Celsius:

water energy (J)≈water mass (g)×4.2×rise (°C)

For this water:

20×4.2=84 84×30=2,520 J=2.52 kJ
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:

2.52÷18.4≈0.14

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

6 Walkthroughs

1

Find stores and compare their amounts

12 steps
Name energy stores, then use mass, speed, height, and arrangement to compare them.
  1. 1
    IntroductionEnergy 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.

  2. 2
    ExplanationPick 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.

  3. 3
    ExampleMotion, 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.

  4. 4
    ExplanationThermal 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.

  5. 5
    ExplanationStores 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.

  6. 6
    ChallengeA 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.

  7. 7
    ExampleChange 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:

    2×12=24 J

    The comparison needs the fixed-speed condition. If adding the load also slowed the cart, both changes would affect the result.

  8. 8
    ExampleNow 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:

    4×12=48 J

    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.

  9. 9
    ExplanationCompare 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.

  10. 10
    ChallengeTemperature 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.

  11. 11
    ChallengeOne 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.

  12. 12
    RecapName 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.

2

Trace energy through an event

11 steps
Follow forces, currents, heating, and radiation, and connect store changes with observations.

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  1. 1
    IntroductionFrom a starting store to a change
  2. 2
    ExplanationForces transfer energy
  3. 3
    ExplanationA current carries the transfer
  4. 4
    ExplanationTemperature differences and waves
  5. 5
    ChallengeA chilled can warms
  6. 6
    ExampleStart a store diagram
  7. 7
    ExampleFollow the light onward
  8. 8
    ExampleTurn observations into evidence
  9. 9
    ChallengeExplain a falling object
  10. 10
    ChallengeExplain a braking bicycle
  11. 11
    RecapDescribe what moved and how
3

Balance amounts and draw a Sankey diagram

14 steps
Track conserved energy, reduce a wasted transfer, and represent all outputs with scaled widths.

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  1. 1
    IntroductionA motor has several destinations
  2. 2
    ExplanationEnergy must go somewhere
  3. 3
    ExampleSubtract to find the remainder
  4. 4
    ChallengeA slowing swing
  5. 5
    ExplanationUseful depends on the job
  6. 6
    ExplanationSpreading makes reuse difficult
  7. 7
    ChallengeChoose the improvement that fits
  8. 8
    ExampleChoose a width scale
  9. 9
    ExampleCheck every split
  10. 10
    ChallengeRead a different scale
  11. 11
    Key InsightWidths give the useful fraction
  12. 12
    ConnectionShow power or show stores
  13. 13
    ChallengePredict the changed diagram
  14. 14
    RecapKeep all destinations in view
4

Calculate and compare useful shares

12 steps
Find efficiency, rearrange for an input, and compare devices giving the same useful output.

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  1. 1
    IntroductionA fraction of the whole input
  2. 2
    ExplanationPut useful output on top
  3. 3
    ExampleFind useful output before dividing
  4. 4
    ExampleTurn the amount into a percentage
  5. 5
    ChallengeMatch the units
  6. 6
    ExampleWork backward to an input
  7. 7
    TipUse the same ratio for power
  8. 8
    ExampleCompare equal light
  9. 9
    ChallengePower does not settle efficiency
  10. 10
    ConnectionName the waste you would cut
  11. 11
    ChallengeAn input saving for the same job
  12. 12
    RecapKeep the numerator useful
5

From appliance ratings to a bill

15 steps
Calculate joules, kilowatt-hours, and costs while keeping input ratings and operating time clear.

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  1. 1
    IntroductionA rate becomes a total
  2. 2
    ExplanationWatts mean joules each second
  3. 3
    ExampleCount the operating seconds
  4. 4
    ExampleFind the joules
  5. 5
    ChallengeCompare rate and time
  6. 6
    ExplanationSwitch to household energy units
  7. 7
    ExampleUse kilowatts and hours
  8. 8
    ChallengeMinutes are sixtieths
  9. 9
    ExampleRead the meter difference
  10. 10
    ExamplePrice a single use
  11. 11
    ExampleAdd up repeated uses
  12. 12
    ChallengePrice the meter period
  13. 13
    ConnectionChoose useful audit information
  14. 14
    ChallengeFind a monthly saving
  15. 15
    RecapMatch each pair of units
6

Compare labels and a burning test

14 steps
Scale food portions, convert energy units, and account for energy captured by water.

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  1. 1
    IntroductionThe same store, two measurements
  2. 2
    ExplanationCells transfer food energy
  3. 3
    ExplanationNutrients supply different amounts
  4. 4
    ExampleConvert a label unit
  5. 5
    ExampleScale the portion
  6. 6
    ChallengeCompare unequal portions
  7. 7
    Key InsightEnergy can be compared across sources
  8. 8
    ExplanationMake the burning comparison fair
  9. 9
    ExampleFind the water’s rise
  10. 10
    ExampleCalculate the captured energy
  11. 11
    ExampleReport energy per gram burned
  12. 12
    ChallengeWhat the water did not measure
  13. 13
    ChallengeCompare a label with the sample
  14. 14
    RecapCompare the right amounts

Energy Stores and Transfers practice questions

50 Practice Questions in 5 sets

Set 1: Stores, devices, and energy accounts10 Practice Questions

Question 1 of 10

A charged plastic strip attracts a small paper piece. Which potential store is linked to this interaction?
  1. Gravitational
  2. Electrostatic
  3. Nuclear
  4. Elastic
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Answer: B
The charged strip attracts the paper through an electrical interaction. This links their arrangement to an electrostatic store. Gravitational energy also involves attraction, but it does not explain the effect of the strip’s charge.

Question 2 of 10

A Sankey input arrow is 24 mm wide. The scale is 5 J per millimeter. What input energy does it show?
  1. 29 J
  2. 4.8 J
  3. 240 J
  4. 120 J
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Answer: D
Each millimeter of width represents 5 J, so a width of 24 mm represents 120 J. The width measures how much energy flows in the diagram. Dividing 24 by 5 would reverse the scale conversion and would not give the represented amount.

Question 3 of 10

A student chooses a toy robot’s motor alone as the system. Where does its battery belong in the energy account?
  1. The surroundings
  2. Both sides at once
  3. Neither side at all
  4. The chosen system
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Answer: A
The system contains only the chosen motor, so the separate battery belongs to the surroundings. Energy can enter the motor from the battery across that boundary. The boundary follows the chosen parts, even when a circuit connects them.

Question 4 of 10

A 25 g portion of seeds contains 150 Calories. How much energy would 100 g contain?
  1. 37.5 Calories
  2. 150 Calories
  3. 600 Calories
  4. 375 Calories
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Answer: C
One hundred grams is four times the 25 g portion, so it contains 600 Calories. Scaling to equal mass makes comparisons between foods fair. Keeping 150 Calories would treat four portions as if they still contained the energy of just one.

Question 5 of 10

A 240 W soldering station runs for 2.5 minutes. How much energy enters it?
  1. 3,600 J
  2. 600 J
  3. 6,000 J
  4. 36,000 J
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Answer: D
The operating time is 2.5 times 60, or 150 seconds. Multiplying 240 W by 150 s gives 36,000 J. The 600 J result uses 2.5 as seconds; watts must be paired with seconds when finding joules.

Question 6 of 10

A sample warms 35 g of water by 16 °C. Use 4.2 J per gram per degree. About how much energy does the water gain?
  1. 560 J
  2. 2,352 J
  3. 5,880 J
  4. 147 J
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Answer: B
The water gain is 35 times 4.2 times 16, or 2,352 J. Both the amount of water and its temperature rise affect the result. The 560 J value multiplies mass by rise but leaves out the 4.2 J needed per gram per degree.

Question 7 of 10

A workshop tool receives 42,000 J over 140 seconds. What is its average input power?
  1. 300 W
  2. 30 W
  3. 3,000 W
  4. 5,880,000 W
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Answer: A
Average power is energy divided by time, so 42,000 J divided by 140 s is 300 W. This tells how much energy enters per second over that period. Multiplying energy by time would not give a rate and produces the very large wrong result.

Question 8 of 10

A hoist must deliver 420 J usefully. It is 70% efficient and keeps no energy overall. How much input is wasted?
  1. 600 J
  2. 126 J
  3. 180 J
  4. 294 J
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Answer: C
The required input is 420 divided by 0.70, or 600 J. Subtract the 420 J useful output to get 180 J wasted. Taking 30% of 420 gives 126 J, but the wasted percentage applies to input, not to useful output.

Question 9 of 10

An aquarium pump takes 8 W continuously. A replacement does the same job at 5 W. Over 30 days, at 18 cents per kWh, how much energy cost is saved?
  1. 1.296 cents
  2. 38.88 cents
  3. 64.8 cents
  4. 103.68 cents
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Answer: B
The input reduction is 0.003 kW over 720 hours, saving 2.16 kWh. Multiplying by 18 cents gives 38.88 cents saved. The 103.68 cents result is the old pump’s full cost and does not subtract the replacement’s use.

Question 10 of 10

A 300 W monitor runs for 4 hours. A 1,800 W heat gun runs for 30 minutes. How do their energy inputs compare?
  1. The heat gun uses 1.5 kWh more.
  2. The heat gun uses 0.3 kWh more.
  3. The monitor uses 1.0 kWh more.
  4. The monitor uses 0.3 kWh more.
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Answer: D
The monitor uses 0.3 times 4, or 1.2 kWh. The heat gun uses 1.8 times 0.5, or 0.9 kWh, so the monitor uses 0.3 kWh more. Ranking by power alone misses the much longer running time of the monitor.
Set 2: Energy in everyday situations10 Practice Questions

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Question 1 of 10

An electric doorbell tells someone a visitor has arrived. What is its useful energy output?
  1. Warming of its casing
  2. Unwanted casing vibration
  3. Sound from the bell
  4. Warming of its wire
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Question 2 of 10

A model train takes an electrical input of 18 W. What energy enters it each second?
  1. 1,080 J
  2. 18 J
  3. 180 J
  4. 0.018 J
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Question 3 of 10

Two identical springs are each stretched 4 cm. A stiffer spring is also stretched 4 cm. How does its elastic store compare with either of the others?
  1. It is larger than either identical spring’s store.
  2. It is smaller than either identical spring’s store.
  3. It must match the sum of both identical stores.
  4. It matches each because all stretches are equal.
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Question 4 of 10

A compressed spring pushes a model sled across a level floor. What main store change supplies its motion?
  1. The spring’s elastic store increases as the sled’s kinetic store increases.
  2. The spring’s elastic store decreases as the sled’s gravitational store increases.
  3. The spring’s kinetic store decreases as the sled’s elastic store increases.
  4. The spring’s elastic store decreases as the sled’s kinetic store increases.
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Question 5 of 10

A fan uses 1.8 kWh over a week. Electricity costs 18 cents per kWh. What is its energy running cost?
  1. 32.4 cents
  2. 10 cents
  3. 324 cents
  4. 3.24 cents
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Question 6 of 10

A 720 W bread maker runs steadily for 45 minutes. What energy does it use?
  1. 5.4 kWh
  2. 0.96 kWh
  3. 0.54 kWh
  4. 0.324 kWh
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Question 7 of 10

A pump receives 2.4 kJ and gives 1,800 J usefully. What is its efficiency?
  1. 0.75%
  2. 133%
  3. 25%
  4. 75%
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Question 8 of 10

A scooter and rider have 48 J of kinetic energy. Their speed doubles while their total mass stays the same. What is their new kinetic energy?
  1. 96 J
  2. 192 J
  3. 384 J
  4. 24 J
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Question 9 of 10

A food test captures 3,360 J in the water. The sample starts at 1.6 g and leaves 0.4 g unburned. What captured energy per gram burned should be reported?
  1. 8.4 kJ/g
  2. 0.36 kJ/g
  3. 2.8 kJ/g
  4. 2.1 kJ/g
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Question 10 of 10

A 0.8 g food sample burns completely and transfers 1.68 kJ to water. Its label gives 1,500 kJ per 100 g. What percentage of the sample’s label energy reaches the water?
  1. 14%
  2. 11.2%
  3. 1.4%
  4. 21%
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Set 3: Rates, useful shares, and food10 Practice Questions

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Question 1 of 10

A bent diving board is held still before a diver jumps. Which store increases when the board bends?
  1. Gravitational potential
  2. Chemical
  3. Kinetic
  4. Elastic potential
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Question 2 of 10

A process transfers 3.7 kJ. How many joules is that?
  1. 3,700 J
  2. 370 J
  3. 37,000 J
  4. 0.0037 J
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Question 3 of 10

A drill receives 760 J and delivers 570 J usefully. Its own stores are unchanged overall. How much energy is wasted?
  1. 95 J
  2. 570 J
  3. 190 J
  4. 1,330 J
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Question 4 of 10

A drink supplies 84 kcal. Using 1 kcal = 4.184 kJ, about how much energy is that?
  1. 84 kJ
  2. 351 kJ
  3. 20 kJ
  4. 3,515 kJ
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Question 5 of 10

A rolling marble hits a second marble that was still. The first slows and the second moves. How do these observations support an energy transfer?
  1. Kinetic energy moves from the second marble into the first.
  2. Kinetic energy leaves the first marble and reaches the second.
  3. Kinetic energy stays in the first marble as the second creates its own.
  4. Both marbles lose kinetic energy because contact slows moving objects.
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Question 6 of 10

A small engine receives 650 kJ at 28% efficiency. How much is useful output?
  1. 182 kJ
  2. 18.2 kJ
  3. 468 kJ
  4. 2,321 kJ
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Question 7 of 10

A Sankey diagram uses 15 J per square of width. Its useful branch is 9 squares and its wasted branches are 3 and 6 squares. What is the input, and what fraction is useful?
  1. 180 J and 75%
  2. 270 J and 75%
  3. 270 J and 50%
  4. 135 J and 50%
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Question 8 of 10

A home uses 160 kWh in a billing period at 18 cents per kWh. The bill adds one fixed charge of 11 dollars. What total charge results?
  1. 28.80 dollars
  2. 50.80 dollars
  3. 189.80 dollars
  4. 39.80 dollars
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Question 9 of 10

A 1.2 kW iron is used for 15 minutes daily for 20 days. At 18 cents per kWh, what is the energy cost?
  1. 432 cents
  2. 64.8 cents
  3. 108 cents
  4. 216 cents
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Question 10 of 10

A ride car starts from rest on a hill and rolls without a motor. Friction warms the track. Why can it not reach a second hilltop at the same height?
  1. Some starting energy has reached thermal stores.
  2. The first downhill path creates too little energy.
  3. Some starting energy was destroyed by the track.
  4. Its mass decreases as its speed becomes greater.
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Set 4: Follow energy through several changes10 Practice Questions

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Question 1 of 10

A solar-powered calculator works in sunlight. How does energy travel from the Sun to the calculator?
  1. By radiation
  2. By conduction
  3. By electric current
  4. By sound waves
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Question 2 of 10

A meter reading rises from 27,840 kWh to 28,115 kWh. How much energy was supplied between readings?
  1. 28,115 kWh
  2. 285 kWh
  3. 275 kWh
  4. 55,955 kWh
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Question 3 of 10

Two motors lift identical loads through the same height. One needs less electrical input for that lift. What does this show?
  1. It must have a higher input power rating.
  2. It transfers more useful energy to the load.
  3. It must take less time to complete the lift.
  4. It is more efficient for this lifting job.
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Question 4 of 10

A fan receives 540 J. Its Sankey diagram shows 360 J useful output and 45 J sound. What heating output is missing?
  1. 495 J
  2. 135 J
  3. 225 J
  4. 180 J
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Question 5 of 10

Two same-size refrigerators have labels of 360 and 280 kWh per year. At the same unit price, why does the second have a lower estimated energy cost?
  1. It transfers energy 80 kW more slowly throughout the year.
  2. It must run its motor for exactly 80 fewer hours.
  3. It needs 80 kWh less for the yearly cooling job.
  4. It keeps 80 kWh of electricity stored after cooling.
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Question 6 of 10

A winch operates at 240 W input for 25 s and lifts with 65% efficiency. Its own stores are unchanged overall. How much energy is wasted over that time?
  1. 2,100 J
  2. 3,900 J
  3. 6,000 J
  4. 84 J
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Question 7 of 10

A thermostat-controlled heater draws 1.6 kW when on. Over 5 hours it is on for a total of 90 minutes. What energy does it receive?
  1. 1.44 kWh
  2. 8.0 kWh
  3. 3.2 kWh
  4. 2.4 kWh
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Question 8 of 10

A 180 Calorie snack is compared with a 500 W appliance. Using 4.184 kJ per Calorie, about how long would the same energy amount run the appliance?
  1. 50 minutes
  2. 25 minutes
  3. 90 minutes
  4. 6 minutes
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Question 9 of 10

Cart B has twice the mass of cart A and moves at half its speed. Cart A has 36 J of kinetic energy. How much does B have?
  1. 36 J
  2. 72 J
  3. 9 J
  4. 18 J
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Question 10 of 10

A motorized cart receives 1,000 J while speeding up: 600 J increases its kinetic store, 300 J heats rubbing axle parts, and 100 J is transferred through air resistance. A change can cut either wasted transfer in half. What change saves more energy, and how much?
  1. Lubricate the axle parts; save 150 J.
  2. Streamline the body; save 50 J.
  3. Streamline the body; save 150 J.
  4. Lubricate the axle parts; save 300 J.
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Set 5: Connect energy, measurements, and costs10 Practice Questions

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Question 1 of 10

Which energy store in a bowl of rice supplies energy to the body?
  1. Thermal
  2. Kinetic
  3. Elastic potential
  4. Chemical
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Question 2 of 10

A room-temperature spoon is placed in colder yogurt. In which direction is energy transferred by heating?
  1. From the yogurt only after it becomes warmer
  2. From the yogurt to the spoon
  3. From the spoon to the yogurt
  4. From both equally, with no net transfer
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Question 3 of 10

Two identical jars contain the same mass of water. One is at 32 °C and one at 19 °C. How do their thermal stores compare?
  1. The 32 °C water has more thermal energy.
  2. Both have equal thermal energy because their materials match.
  3. The 19 °C water has more thermal energy.
  4. Both have equal thermal energy because their masses match.
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Question 4 of 10

A bicycle chain warms because of friction. Why can adding suitable oil reduce the energy needed for the same ride?
  1. It increases the useful friction inside the chain.
  2. It reduces unwanted heating at moving contacts.
  3. It removes the need for tire grip on the road.
  4. It changes wasted energy back into chemical energy.
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Question 5 of 10

Food A has 1,500 kJ per 100 g; food B has 1,200 kJ per 100 g. A 20 g portion of A and a 30 g portion of B are served. Which portion supplies more energy, and by how much?
  1. A supplies 300 kJ more.
  2. B supplies 60 kJ more.
  3. B supplies 300 kJ more.
  4. A supplies 60 kJ more.
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Question 6 of 10

Two lamps each provide 4 W of light. Lamp R takes in 16 W and lamp S takes in 40 W. How much less wasted power does R produce?
  1. 12 W
  2. 36 W
  3. 28 W
  4. 24 W
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Question 7 of 10

A device receives 480 J and is 62.5% efficient, with unchanged stores overall. At 20 J per square of width, how wide should its wasted Sankey branch be?
  1. 9 squares
  2. 24 squares
  3. 12 squares
  4. 15 squares
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Question 8 of 10

A battery receives 900 J while charging. Its chemical store increases by 720 J and its thermal store by 60 J. How much energy leaves the battery during that period?
  1. 180 J
  2. 240 J
  3. 120 J
  4. 840 J
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Question 9 of 10

A battery-powered motor pulls a cart up a ramp. The cart starts and ends at rest. What account describes the useful store change and the pathways from battery to cart?
  1. Chemical to kinetic, electrically through the motor and mechanically to the cart.
  2. Chemical to gravitational, electrically through the motor and mechanically to the cart.
  3. Chemical to gravitational, mechanically through the wire and electrically to the cart.
  4. Thermal to gravitational, electrically through the motor and mechanically to the cart.
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Question 10 of 10

A 75 W desk lamp and a 12 W replacement give the same useful light. Each would run 5 hours daily for 200 days. At 18 cents per kWh, how much does replacing it save?
  1. 216 cents
  2. 1,350 cents
  3. 1,134 cents
  4. 567 cents
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Stuck on your own question? Homework Help

Key Terms

70 Key Terms, each with its definition

A

Aerobic respiration
Aerobic respiration is respiration that uses oxygen to release energy from food in cells, supporting the body's ongoing activities.
Aerobic respiration supplies energy as muscles work during a walk.
Annual energy-use label
An annual energy-use label estimates the energy an appliance uses in a year, allowing comparisons between models doing similar jobs.
Compare refrigerators of the same size using the kWh values on each annual energy-use label.
Atomic nucleus
An atomic nucleus is the center of an atom; the types and numbers of nuclei affect the energy in a nuclear store.
Splitting a very heavy atomic nucleus can release energy, as happens with uranium fuel.

C

Chemical store
A chemical store holds energy associated with substances such as foods, fuels, and batteries, which can release energy through reactions.
A candle's chemical store decreases as its wax burns and transfers energy to the room.
Conservation of energy
Conservation of energy is the rule that energy cannot be created or destroyed; decreases must be matched by transfers or gains elsewhere.
Conservation of energy includes the warmer brakes when a car's kinetic energy decreases.

D

Decimal efficiency
A decimal efficiency writes the useful share as a number from zero to one, such as 0.75 for a useful share of three quarters.
Use the decimal efficiency 0.25 when multiplying an input by a 25% useful share.
Dissipation
Dissipation is energy spreading out into the surroundings, usually warming them slightly and becoming harder to gather for reuse.
Dissipation spreads a bicycle's kinetic energy into brakes, tires, road, and air as it stops.

E

Efficiency
Efficiency is the useful fraction of a total input, found by dividing useful output by input using matching energy or power units.
A motor delivering 900 W usefully from 1,200 W input has an efficiency of 75%.
Elastic potential store
An elastic potential store holds energy in an object that is stretched, squashed, bent, or twisted and can spring back.
A compressed toy spring has an elastic potential store before it launches the toy.
Electric current
An electric current is a flow of electric charge that can transfer energy around a circuit without using up the charge.
An electric current continues through a lamp as energy reaches the filament and surroundings.
Electrical transfer
An electrical transfer moves energy through an electric current from a source to parts of a circuit, such as a lamp or motor.
A battery supplies an electrical transfer that turns the motor of a model car.
Electricity meter
An electricity meter measures the cumulative electrical energy supplied; subtracting readings gives the energy used between them.
An electricity meter rising by 620 kWh shows 620 kWh supplied during that period.
Electrostatic store
An electrostatic store holds energy linked to the arrangement of charged objects that attract or repel each other.
Pulling an attracting charged balloon away from hair increases the electrostatic store.
Energy
Energy is a quantity measured in joules that can be held in stores and transferred when objects or their surroundings change.
A moving skateboard has energy that can be transferred when it hits a soft barrier.
Energy account
An energy account tracks all energy entering, leaving, and changing stores within a chosen system over a stated period.
A charging battery's energy account includes energy it keeps as well as energy transferred away.
Energy per gram
Energy per gram compares energy amounts for equal food masses, helping show which food holds more energy for its mass.
Fat has more energy per gram than carbohydrate: about 37 kJ compared with about 17 kJ.
Energy transfer diagram
An energy transfer diagram uses boxes for stores and labeled arrows for pathways to show where energy goes during a change.
An energy transfer diagram can link a battery's chemical store to a filament's thermal store.
Energy transformation
An energy transformation describes a change between forms of energy, using another vocabulary for changes in stores and transfers.
A falling ball's energy transformation can be described as gravitational potential energy becoming kinetic energy.
Evidence
Evidence is an observation or measurement used to support a claim, such as a speed change that supports an energy transfer.
A box beginning to slide after a collision is evidence that energy reached its kinetic store.

F

Fair test
A fair test changes the factor being studied while keeping other factors that affect the result alike, so comparisons are meaningful.
A fair test of foods keeps water mass and flame distance alike while changing the food type.
Food Calorie
A food Calorie is the energy unit used on US Nutrition Facts labels; one food Calorie equals one kcal, or 4.184 kJ.
A snack with 190 food Calories holds about 795 kJ in its chemical store.
Force
A force is a push or pull, measured in newtons, that can transfer energy mechanically when it moves something.
A hand applies a force to a bowstring while pulling it back and increasing the bow's elastic store.

G

Gravitational potential store
A gravitational potential store holds energy linked to the positions of attracting masses, such as a raised object and Earth.
Lifting a book from the floor increases the gravitational potential store of the book and Earth.

H

Heating
Heating is energy transfer caused by a temperature difference, from a hotter object to a cooler one.
Heating transfers energy from a warm hand to the colder ice cube held in it.
Home energy audit
A home energy audit lists appliance inputs and operating times to estimate energy use and identify changes that could save energy.
A home energy audit can compare a high-power appliance used briefly with a small input left on all day.

I

Incomplete combustion
Incomplete combustion is burning that does not fully react the fuel, leaving some chemical energy unreleased in the burning test.
Incomplete combustion can help explain why a classroom food test captures less energy than its label value.
Input energy
Input energy is the amount transferred into a chosen system during the period being studied, before it is divided among destinations.
A motor with 500 J of input energy can transfer 350 J usefully and 150 J in wasted ways.

J

Joule
A joule (J) is the standard unit of energy; lifting an apple about 1 meter takes roughly one joule.
The joule lets you compare energy amounts in motion, warming, food, and electrical transfers.

K

Kilocalorie
A kilocalorie (kcal) is an energy unit equal to 1,000 small calories and to one food Calorie, or 4.184 kilojoules.
A label listing 100 kilocalories describes the same energy as 100 food Calories.
Kilowatt
A kilowatt (kW) is a power unit equal to 1,000 watts, describing how fast energy is transferred rather than how much has accumulated.
A 1,500 W heater has an electrical input of 1.5 kilowatts when running at that power.
Kilowatt-hour
A kilowatt-hour (kWh) is the energy transferred by a power of one kilowatt over one hour, equal to 3.6 million joules.
A 1 kW appliance used for two hours transfers two kilowatt-hours of energy.
Kinetic store
A kinetic store holds the energy of a moving object; its amount depends on the object's mass and speed.
A rolling bowling ball has a kinetic store that decreases when the pins slow it down.

L

LED lamp
An LED lamp gives light using light-emitting diodes and can provide the same useful light as a filament lamp with less electrical input.
An LED lamp needing 9 W for a stated light output takes less input than a 60 W filament lamp giving the same light.
Lubrication
Lubrication adds a suitable substance, such as oil or grease, between moving surfaces to reduce friction and unwanted heating.
Lubrication of a bicycle chain reduces unwanted transfers at its moving contacts.

M

Magnetic store
A magnetic store holds energy linked to the arrangement of magnets that interact by attracting or repelling each other.
Pulling two attracting magnets apart increases their magnetic store as you work against the attraction.
Mass
Mass measures the amount of matter in an object; at a fixed speed, a larger mass gives the object more kinetic energy.
Doubling a cart's mass doubles its kinetic energy if its speed stays the same.
Mass burned
The mass burned is the starting sample mass minus unburned material left afterward, used for energy per gram burned.
A 1.5 g sample leaving 0.5 g unburned has a mass burned of 1.0 g.
Mean
A mean is the average found by adding repeated measurements and dividing by their number, reducing the effect of chance variation.
Finding a mean temperature rise from repeated trials makes a comparison of foods less dependent on one trial.
Mechanical transfer
A mechanical transfer moves energy when a force moves something, as in lifting, stretching, pushing, or squashing.
The bowstring's push gives a mechanical transfer from the bow's elastic store to the arrow's motion.

N

Nuclear store
A nuclear store holds energy associated with atomic nuclei, the centers of atoms; nuclear changes can release some of it.
Joining light nuclei in the Sun releases energy from the nuclear store.

O

Output branch
An output branch is an arrow leaving a split in a Sankey diagram, showing a particular useful or wasted transfer and its amount.
A sound output branch must be included when checking that all output widths total the input width.

P

Percentage efficiency
A percentage efficiency gives the useful output for every hundred parts of input, found by multiplying decimal efficiency by 100.
A percentage efficiency of 60% means 60 of every 100 J reaches the useful job.
Potential energy
Potential energy is energy linked to the position or arrangement of things that interact through pushes or pulls.
A raised ball has potential energy in its arrangement with Earth even while it is still.
Power
Power is the rate of energy transfer, found by dividing energy by time; it measures how much energy is transferred each second.
A toaster's power of 1,000 W means it receives 1,000 J each second while operating at that input.
Power rating
A power rating describes a device's input or output rate under stated operating conditions; electrical use needs the input rating.
A microwave's cooking power rating is an output, so use its electrical input to calculate outlet energy.

R

Radiation
Radiation transfers energy through electromagnetic waves, including light and infrared, which can travel across empty space.
Radiation carries energy from the Sun to Earth through the space between them.
Reasoning
Reasoning explains why evidence supports a claim by connecting observations with the scientific ideas that account for them.
When a ball slows as it hits a box and the box moves, reasoning links these observations to a transfer between their kinetic stores.
Reference level
A reference level is the chosen height from which gravitational potential energy is compared, such as the floor or ground.
Using the floor as a reference level makes it easy to compare the height of a book on a shelf with a book on a desk.
Respiration
Respiration is a set of chemical reactions in cells that releases energy from food for movement, warmth, and other body activities.
Respiration releases energy even when you are asleep and your organs keep working.
Running cost
A running cost is the money spent operating an appliance over a period, calculated from its energy use and the price per energy unit.
A refrigerator using 300 kWh yearly has an energy running cost of 54 dollars at 18 cents per kWh.

S

Sankey diagram
A Sankey diagram uses arrow widths proportional to energy or power amounts to show how an input divides into useful and wasted outputs.
In a Sankey diagram, 200 J of input can divide into branches of 140 J, 50 J, and 10 J.
Scale
A scale links a diagram's measured width with the energy or power it represents, and stays the same for every branch.
At a scale of 10 J per square, a 50 J heating branch must be five squares wide.
Serving
A serving is the stated portion used for a food-label value; the amount eaten may contain more or less than one serving.
A 30 g serving of cereal at 1,600 kJ per 100 g supplies 480 kJ.
Sound
Sound carries energy as vibrations through matter, such as air or water; it cannot travel across empty space.
A ringing bell sends sound through air as vibrating particles push on nearby particles.
Speed
Speed describes how fast an object moves; doubling it at fixed mass gives four times the kinetic energy.
A bicycle ridden at twice its earlier speed has four times the kinetic energy at the same mass.
Standby
Standby is a low-power state in which a device still takes electrical energy while waiting for use, often for many hours.
A television left on standby at 1 W for 20 hours daily uses 7.3 kWh over a year.
Stiffness
Stiffness describes how strongly an object resists a change in shape; a stiffer spring stores more energy at equal stretch.
Two springs with different stiffness can hold different elastic energy despite matching stretches.
Streamlining
Streamlining shapes an object to reduce air or water resistance, cutting the energy transferred to unwanted warming during motion.
Streamlining a vehicle reduces drag as it moves through the air.
Surroundings
The surroundings are everything outside a chosen system, including objects that can gain energy as the system loses it.
As soup cools, energy is transferred from the soup to its surroundings, including the bowl and air.
System
A system is the object or group of objects chosen for study, which sets the boundary used to track energy going in and out.
Choosing only the water as your system leaves the kettle and room outside its boundary.

T

Temperature rise
A temperature rise is the final temperature minus the initial temperature, used to estimate energy gained during warming.
A change from 20 °C to 50 °C gives a temperature rise of 30 °C, not 50 °C.
Thermal insulation
Thermal insulation is material or a design feature that slows energy transfer by heating between a system and its surroundings.
Thermal insulation around a hot water tank reduces unwanted energy transfer into the room.
Thermal store
A thermal store holds energy in an object that depends on its temperature, mass, and material; cold objects have thermal stores too.
A warm bath has a large thermal store because it contains a large mass of warm water.
Thermostat
A thermostat controls temperature by switching an appliance's heating or cooling operation on and off as needed.
A thermostat can switch a heater off for part of the day, reducing use below full power times 24 hours.
Transfer pathway
A transfer pathway is a way energy moves between stores: mechanically, electrically, by heating, or by radiation.
Lifting a bag and warming a drink involve different transfer pathways.

U

Unit price
A unit price is the money charged for each unit of energy, such as cents per kWh, used to turn an energy amount into a cost.
At a unit price of 18 cents per kWh, using 10 kWh gives an energy charge of 180 cents.
Useful output
A useful output is energy transferred in a way that serves the intended job, such as light from a lamp or sound from an alarm.
Warming bread is a toaster's useful output, while warming the surrounding air is unwanted.

W

Wasted output
A wasted output is energy transferred in a way that does not serve the intended job, often ending in thermal stores nearby.
A lamp's wasted output includes unwanted heating even though the energy still exists.
Watt
A watt (W) is the power unit equal to one joule transferred each second; it measures a rate rather than a total energy amount.
A motor receiving 300 joules each second has an input power of 300 watts.
Work
Work is energy transferred by a force moving something; it describes a mechanical transfer rather than a store.
A person does work on a spring while compressing it, increasing the spring's elastic store.

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