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D3.1 · Describe energy transfers using conservation of energy

Learn to describe energy transfers using conservation of energy through clear examples and targeted practice.

Ontario Grade 11 Physics

Energy and Society

Ontario Grade 11 Physics — D3.1

Energy can move from one object or place to another and can change form. A battery, for example, transfers energy to a lamp, which then transfers energy to its surroundings. To describe these events, first decide what objects are included in the system. The system is the object or group of objects being considered. Choose an arrow direction for energy entering or leaving that system. Energy is a scalar: it has an amount but no direction like a force or velocity. Arrows in an energy diagram show the direction of transfer, not a vector direction of energy.

What you will learn

Describe energy transfers between parts of a system.
Use conservation of energy to account for energy before and after a transfer.
Distinguish energy that remains useful for a purpose from energy transferred to the surroundings.

1. Prerequisite bridge: energy and systems

A joule, abbreviated J, is the SI unit of energy. Energy is a scalar quantity, so a value such as 12 J has no north, left, or upward direction. In contrast, a vector has both a magnitude and a direction. A force is an example of a vector. Do not assign a vector direction to energy itself.

A system is the part of the situation chosen for study. Everything outside it is called the surroundings. The system boundary is an imaginary line separating the system from the surroundings. Energy can cross this boundary. A transfer is the movement of energy from one object or part of a system to another.

Before describing a transfer, name the system and set an arrow convention. In this lesson, an arrow pointing into the system means energy enters; an arrow pointing out means energy leaves. This convention describes transfer direction only. It is not a positive direction for motion.

Energy is measured in joules (J) and is a scalar.
Name the system before accounting for energy.
Use arrows to show energy entering or leaving.

2. The conservation rule

Conservation of energy means that energy is not created or destroyed in a transfer. It may move between objects, or it may change form. To account for energy, include all the relevant parts of the system and its surroundings. If energy leaves a smaller chosen system, it has not vanished; it has entered something outside that system.

For a system that receives or releases energy, compare the energy it has at the start and at the end. The change in the system’s energy is accounted for by energy transferred in and energy transferred out. For a larger system that includes both the original object and its surroundings, the energy total stays the same, provided no energy crosses the larger boundary.

Energy can appear in different forms. For example, moving objects have kinetic energy, raised objects can have gravitational potential energy, and warm objects have thermal energy. Electrical and chemical energy are also common forms. A transfer can change energy from one form to another. These names describe forms, not separate kinds of energy that escape the conservation rule.

An energy-flow diagram is a simple way to show the account. Label the system, draw arrows for transfers, and name the energy form when it is known. A small system may have an outgoing arrow that is not useful for its intended task. That energy still counts in the account; it may have warmed the surroundings or produced sound.

E_{\text{initial}}=E_{\text{final}}

Energy transferred out of one system enters another part of a larger system.
Energy can be transferred and can change form, but the total is conserved.
Include surroundings when energy leaving the chosen system must be accounted for.

3. Reading energy accounts

For a simple numerical account, use the same energy unit on both sides. The energy total before a transfer equals the energy total afterward when the account includes all relevant destinations. If one part gains energy, another part or an energy store must supply it. The numerical values should balance.

For example, consider a lamp and the nearby surroundings as one system. Energy supplied electrically can be transferred into light and thermal energy. If the account gives 40 J supplied, and 12 J is transferred as light, the rest of the supplied energy must be accounted for in other forms or transfers. It is not correct to say the remainder disappeared.

The energy-transfer arrows have directions, but energy amounts are scalars. Do not add a direction such as east to a number of joules. Instead, state which object or part receives the energy. When describing motion in a physical situation, a positive direction may be useful for the motion, but it does not change the scalar nature of energy.

Use consistent units and account for every energy transfer.
A numerical difference may represent energy transferred to another form or part of the system.
Energy-flow arrows show which way energy is transferred.

4. A reliable conservation method

Start by naming the system and its boundary. Decide whether the surroundings are included. Then identify the initial energy and the energy transfers or forms at the end. Write an energy account before calculating. Rearrange it with ordinary algebra if an unknown amount is requested.

Check that each value has units of joules and that the account balances. Ask whether the receiving object or energy form makes sense for the situation. If the system is defined too narrowly, energy may seem to be missing. Expand the system boundary or identify where the energy went.

Conservation is an accounting rule, not a claim that every transfer is useful. A device may transfer energy into its intended output and also into thermal energy or sound in its surroundings. Both transfers belong in a complete account.

E_{in}=E_{

\text{useful}

}+E_{

\text{other}

}

Define the system, list the transfers, and then calculate.
Check units, total energy, and whether each destination is physically sensible.
An unwanted transfer is still part of the energy account.

A simple energy-flow account

Part of account	Energy amount	Direction of transfer
Input	50.0 J	Into system
Light	18.0 J	Out of lamp; received within the full system
Other forms	32.0 J	Transferred within the full system

Worked example

A lamp’s energy account

A lamp receives 50.0 J of electrical energy during a short interval. In that interval, 18.0 J is transferred as light. Treat the lamp and nearby surroundings as the system. How much energy is transferred in other forms?

Set the system
The system is the lamp plus its nearby surroundings. Energy enters the system electrically. The final account includes light and other forms, such as thermal energy.
Write conservation account
The incoming energy equals the total energy accounted for after the transfer. Subtract the light energy to find the amount in other forms. E_{in}=E_{ $\text{light}$ }+E_{ $\text{other}$ }
Substitute and solve
Keep the units in the calculation. Both given values are stated to three significant figures, so report the result to three significant figures.
$E_{\text{other}}=50.0\,\mathrm{J}-18.0\,\mathrm{J}=32.0\,\mathrm{J}$

Answer: The lamp and surroundings receive 32.0 J in other forms, in addition to the 18.0 J transferred as light.

Check: The account balances: 18.0 J + 32.0 J = 50.0 J. The unit is joules, and a positive amount of other transferred energy is reasonable.

Worked example

Energy transferred from a battery

A battery’s chemical energy decreases by 240 J while it powers a small device. The device and its surroundings receive 165 J as electrical energy and 75 J as thermal energy. Check whether the account conserves energy.

Define the account
Choose the battery, device, and surroundings as the full system. Energy moves from the battery’s chemical store and is transferred into the device and surroundings. The amounts are scalar joule values; the energy-flow direction is from the battery to the receiving parts.
Add the received energy
The energy supplied by the battery must match the total energy received in the complete account.
$E_{\text{received}}=165\,\mathrm{J}+75\,\mathrm{J}=240\,\mathrm{J}$
Compare totals
The calculated received total matches the battery’s decrease. Therefore, the values are consistent with conservation of energy.
$240\,\mathrm{J}=240\,\mathrm{J}$

Answer: The account conserves energy: 240 J leaves the battery’s chemical store and 240 J is received by the device and surroundings.

Check: All quantities use joules. The energy flows outward from the battery and into the device and surroundings. The equality shows no energy is missing from this account.

Worked example

Finding energy transferred to surroundings

A device receives 3.60 kJ of energy. Its intended output is 2.25 kJ. Assume the full account has only the intended output and energy transferred to the surroundings. Find the energy transferred to the surroundings.

Choose the boundary
Treat the device and surroundings as the complete system. Energy enters the system, then is accounted for as intended output and transfer to the surroundings.
Set up the balance
The total energy received equals the sum of the two destinations. Convert by subtraction using the same unit for each quantity. E_{in}=E_{ $\text{intended}$ }+E_{ $\text{surroundings}$ }
Calculate
Subtract the intended output from the input. Both values have three significant figures, so retain three significant figures in the answer.
$E_{\text{surroundings}}=3.60\,\mathrm{kJ}-2.25\,\mathrm{kJ}=1.35\,\mathrm{kJ}$

Answer: The energy transferred to the surroundings is 1.35 kJ.

Check: The balance is 2.25 kJ + 1.35 kJ = 3.60 kJ. The result is positive and smaller than the total input, as expected. In SI units, 1.35 kJ is 1350 J.

Common mistakes and how to avoid them

Saying energy has disappeared when it is not in the intended output.

Correction: Look for another destination, such as thermal energy or sound, and include it in the account.

Treating energy as a vector and assigning it a direction such as upward.

Correction: Energy is a scalar. Use arrows to show where energy transfers, and state the receiving object or part.

Choosing a system that excludes the surroundings, then claiming the energy was destroyed.

Correction: State the boundary clearly. If energy leaves the chosen system, identify the surroundings that receive it.

Assuming that conservation means all transferred energy is useful.

Correction: Conservation accounts for all energy, including transfers that do not serve the device’s intended purpose.

Lesson summary

Energy is a scalar measured in joules.
A system boundary determines which objects are included in an energy account.
Energy can transfer between objects and change form, but it is conserved.
Account for every energy destination and check that the total before and after agrees.

Check your understanding

Question 1

A device receives 90 J. It transfers 55 J as its intended output. If these are the only two destinations, how much is transferred in other forms?

35 J
55 J
90 J
145 J

Show answer and explanation

35 J

The total input equals the intended output plus other transfers, so the remainder is 90 J − 55 J = 35 J.

Question 2

A heater transfers energy from its element to the room. Which statement best follows conservation of energy?

Energy vanishes after leaving the element.
Energy enters the room and is included if the room is part of the system.
Energy must have a vector direction like force.
Only useful energy counts in the total.

Show answer and explanation

Energy enters the room and is included if the room is part of the system.

Energy that leaves the element enters the room. Whether it is included in the account depends on the chosen system boundary.

Question 3

A system begins with 120 J. The account lists 70 J and 50 J in its final energy destinations. Is the account consistent?

Yes, because the final total is 120 J.
No, because energy cannot change form.
No, because joules cannot be added.
Yes, but only if energy has a direction.

Show answer and explanation

Yes, because the final total is 120 J.

The final account totals 70 J + 50 J = 120 J, matching the initial energy.

Key terms

Energy: A scalar quantity that can be transferred or changed in form; it is measured in joules.
System: The object or group of objects selected for study.
Surroundings: Everything outside the chosen system.
System boundary: The imagined separation between a system and its surroundings.
Transfer: Movement of energy from one object or part of a system to another.
Conservation of energy: The rule that energy is not created or destroyed; it can move or change form.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation D3.1. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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