D3.3 Explain thermal, kinetic, potential, heat, power, and efficiency quantities

Ontario Grade 11 Physics

Energy and Society

Ontario Grade 11 Physics — D3.3

Energy is a quantity used to describe changes and transfers in physical systems. This lesson focuses on six related terms: thermal energy, kinetic energy, potential energy, heat, power, and efficiency. First review that a scalar has size but no direction. Energy, heat, power, and efficiency are scalars. They do not point north, up, or in any other direction. For calculations, define the system—the object or group of objects being considered—and state what energy transfer is being described. Since these quantities are scalars, a positive spatial direction is not needed for the equations in this lesson. We will use positive values for energy amounts and energy transferred into a system.

What you will learn

Explain thermal, kinetic, potential, and heat quantities and tell how they differ.
Use energy relationships to calculate kinetic energy and gravitational potential energy.
Explain power as the rate of energy transfer and calculate it.
Explain efficiency as the useful energy output compared with the energy input.

1. Energy in a system: thermal, kinetic, and potential

A system is the object or group of objects chosen for a description. For example, a book alone can be a system, or the book and Earth can be treated together. State the system because it affects which forms of energy are being discussed.

Kinetic energy is energy associated with an object's motion. An object moving faster has more kinetic energy than the same object moving more slowly. Mass also matters: at the same speed, a more massive object has more kinetic energy. The symbol

E_k

is commonly used for kinetic energy. It is measured in joules, abbreviated J.

Potential energy is stored energy associated with an object's position or arrangement. In this lesson, gravitational potential energy is the energy associated with an object's height above a chosen reference level. The reference level is the height assigned zero gravitational potential energy for the calculation. Changing that level changes the reported potential energy, but not the height difference between two positions. The symbol

E_p

is used for gravitational potential energy.

Thermal energy is energy associated with the motion and arrangement of particles within a substance. A warm object generally has more thermal energy than an otherwise similar cooler object, but thermal energy also depends on the amount and kind of material. Temperature describes how hot or cold something is; it is not the same quantity as total thermal energy. A small hot object can have less thermal energy than a much larger warm object.

The system and the surroundings are useful terms. The surroundings are everything outside the selected system that can interact with it. Energy can be transferred between a system and its surroundings. In this lesson, energy amounts and energy transfers are reported in joules.

E_k=\frac{1}{2}mv^2

Kinetic energy is associated with motion.
Gravitational potential energy is associated with height relative to a chosen reference level.
Thermal energy is associated with particle motion and arrangement.
Energy is a scalar, measured in joules (J).

2. Heat is energy transferred

Heat is energy transferred from one place or object to another because of a temperature difference. The symbol

Q

is often used for heat transferred, and its SI unit is the joule. The SI unit is the standard unit used in science.

Heat is not the name for energy stored inside an object. Thermal energy describes energy associated with particles in a system; heat describes energy crossing from one system to another because of a temperature difference. After a transfer, the receiving system may have a different thermal energy.

For example, if a warm mug is placed in a cooler room, energy transfers from the mug to the surrounding air because of the temperature difference. If the mug is the system, the transfer is outward. If the air is the system, the transfer is inward. Saying which system is being considered makes the direction of transfer clear.

In this lesson, we will describe heat amounts as positive magnitudes and use words such as into or out of the system to state the direction. This avoids confusing the direction of energy transfer with the value of a scalar quantity.

Q=\text{energy transferred by heating}

Heat is energy transferred because of a temperature difference.
Thermal energy describes a system; heat describes energy crossing its boundary.
State whether energy transfers into or out of the selected system.

3. Gravitational potential energy and system boundaries

Near Earth's surface, gravitational potential energy can be calculated from an object's mass and its height difference above a chosen reference level. The symbol

g

represents the strength of Earth's gravitational field near the surface. Use

g=9.8\ \mathrm{m/s^2}

for the examples here.

In the relationship, mass is measured in kilograms, height difference in metres, and the gravitational field strength in metres per second squared. The result is in joules. A height difference is used rather than an absolute height, so the reference level must be stated.

A change in gravitational potential energy is a scalar change. It has no direction like a vector. Instead, describe whether the energy increased or decreased and identify the system. For example, raising a backpack increases its gravitational potential energy relative to the floor. Lowering it decreases that energy relative to the same level.

This model applies to changes in height near Earth's surface. It provides a way to describe potential energy, not a direction for an energy vector. The height change can be stated as a positive magnitude when the object is raised.

E_p=mgh

Choose and state the height reference level.
Use height difference in metres and mass in kilograms.
A rise in height means an increase in gravitational potential energy.

4. Power and efficiency describe how energy is transferred or used

Power tells how quickly energy is transferred or used. A device that transfers the same amount of energy in less time has greater power. The symbol

P

represents power. Its SI unit is the watt, abbreviated W, and one watt equals one joule per second.

Efficiency compares useful energy output with total energy input. It tells what fraction of the input becomes the intended useful output. Efficiency is often written as a percentage. A device cannot deliver more useful energy than the energy supplied to it, so its efficiency cannot be greater than 100 percent under this definition.

For example, for a lamp, light may be the intended useful output. Some input energy also transfers to the surroundings as thermal energy. If the useful output is less than the input, the efficiency is below 100 percent. The word useful depends on the task: thermal energy may be useful for a heater but not for a lamp.

Power and efficiency answer different questions. Power compares energy transfer with time. Efficiency compares useful output with input. Both are scalars. Power has units of watts; efficiency has no unit because it is a ratio of two energy amounts with the same unit.

P=\frac{E}{t}

Power is energy transferred per unit time, measured in watts (W).
Efficiency is useful energy output divided by energy input.
Efficiency may be reported as a percentage and has no unit.

Worked example

Kinetic energy of a moving cart

A cart of mass

2.4\ \mathrm{kg}

moves at

3.0\ \mathrm{m/s}

. Find its kinetic energy. The system is the cart. The energy amount is a scalar, so it has no direction.

Identify values
The cart's mass is $2.4\ \mathrm{kg}$ and its speed is $3.0\ \mathrm{m/s}$ . The unknown is the cart's kinetic energy.
Choose the relationship
Kinetic energy depends on mass and the square of speed. This relationship gives an energy amount in joules.
$E_k=\frac{1}{2}mv^2$
Substitute and calculate
Substitute the values with their units. The squared speed contributes units of square metres per square second.
$E_k=\frac{1}{2}(2.4\ \mathrm{kg})(3.0\ \mathrm{m/s})^2=10.8\ \mathrm{J}$
Round and check
The input values have two significant figures, so report $11\ \mathrm{J}$ . The units reduce to joules, and a positive energy amount is reasonable for a moving cart.

Answer: The cart's kinetic energy is

11\ \mathrm{J}

.

Check: The result is positive and has energy units. A cart of a few kilograms moving at a few metres per second having an energy of about ten joules is reasonable.

Worked example

Gravitational potential energy of a raised backpack

A

5.0\ \mathrm{kg}

backpack is lifted

1.2\ \mathrm{m}

above the floor. Treat the backpack and Earth as the system, and use the floor as the zero-height reference. Find the increase in gravitational potential energy.

Identify values
The mass is $5.0\ \mathrm{kg}$ , the height increase is $1.2\ \mathrm{m}$ , and near Earth's surface use $g=9.8\ \mathrm{m/s^2}$ . The backpack rises, so its gravitational potential energy increases.
Choose the relationship
Gravitational potential energy near Earth's surface depends on mass, gravitational field strength, and height above the reference level.
$E_p=mgh$
Substitute and calculate
Use the height increase measured from the floor. The units combine to kilograms times metres squared per second squared, which is a joule.
$E_p=(5.0\ \mathrm{kg})(9.8\ \mathrm{m/s^2})(1.2\ \mathrm{m})=58.8\ \mathrm{J}$
Round and check
The measurements have two significant figures, so report $59\ \mathrm{J}$ . The energy change is positive because the backpack was raised. The unit is joules, and the size is reasonable for lifting a few kilograms by about a metre.

Answer: The backpack's gravitational potential energy increases by

59\ \mathrm{J}

.

Check: The positive sign matches the upward height change. The result has units of joules and is the right general scale for a small backpack raised a short distance.

Worked example

Power and efficiency of a small device

A device receives

240\ \mathrm{J}

of energy over

12\ \mathrm{s}

. It provides

180\ \mathrm{J}

as useful output. Find its power during the transfer and its efficiency. Treat the device as the system. Energy amounts and power are scalars.

Calculate power
Power is energy transferred divided by the time taken. Use the input energy and the transfer time to describe the device's input power.
$P=\frac{E}{t}=\frac{240\ \mathrm{J}}{12\ \mathrm{s}}=20\ \mathrm{W}$
Calculate efficiency
Efficiency is useful output energy divided by input energy, expressed as a percentage. Both energy values use joules, so the units cancel.
$\eta=\frac{E_{\mathrm{useful}}}{E_{\mathrm{input}}}\times100\%=\frac{180\ \mathrm{J}}{240\ \mathrm{J}}\times100\%=75\%$
Check the results
The power is $20\ \mathrm{J/s}$ , or $20\ \mathrm{W}$ . The efficiency is below 100 percent because the useful output is less than the input. Both results are reasonable, and neither requires a direction because each is a scalar.

Answer: The input power is

20\ \mathrm{W}

and the efficiency is 75%.

Check: Power has units of joules per second, equivalent to watts. The efficiency has no unit and is below 100 percent, consistent with

180\ \mathrm{J}

useful output from

240\ \mathrm{J}

input.

Common mistakes and how to avoid them

Calling the energy stored in a warm object heat.

Correction: Thermal energy describes energy associated with particles in the object. Heat is energy transferred because of a temperature difference.

Treating temperature and thermal energy as the same quantity.

Correction: Temperature describes how hot or cold something is. Thermal energy also depends on how much material is present and on the material itself.

Giving gravitational potential energy without stating a reference height.

Correction: Name the zero-height level and use the height difference from that level.

Reporting power in joules or efficiency in watts.

Correction: Power is measured in watts. Efficiency is a ratio and is reported as a number or percentage without a unit.

Assuming all input energy is useful output energy.

Correction: Efficiency compares only the intended useful output with the total input. The useful output can be less than the input.

Lesson summary

Kinetic energy is associated with motion; gravitational potential energy is associated with height relative to a reference level.
Thermal energy is associated with particle motion and arrangement. Heat is energy transferred because of a temperature difference.
Energy and heat are measured in joules. Power is energy transferred per time and is measured in watts.
Efficiency is useful energy output divided by energy input, often written as a percentage.
State the system and reference level, preserve units, round to appropriate significant figures, and check that the result is physically reasonable.

Check your understanding

Question 1

Which statement best describes heat?

Energy stored inside every warm object.
Energy transferred because of a temperature difference.
The measure of how hot an object is.
Useful output divided by input.

Show answer and explanation

Energy transferred because of a temperature difference.

Heat describes energy transfer caused by a temperature difference. Thermal energy describes energy associated with particles within a system.

Question 2

A device transfers

90\ \mathrm{J}

of energy in

3.0\ \mathrm{s}

. What is its power?

$30\ \mathrm{W}$
$270\ \mathrm{W}$
$30\ \mathrm{J}$
$0.033\ \mathrm{W}$

Show answer and explanation

30\ \mathrm{W}

Power is energy divided by time:

90\ \mathrm{J}/3.0\ \mathrm{s}=30\ \mathrm{J/s}=30\ \mathrm{W}

. The result has two significant figures and is a scalar.

Question 3

A system takes in

200\ \mathrm{J}

and provides

150\ \mathrm{J}

of useful output. What is its efficiency?

75%
25%
133%
$50\ \mathrm{W}$

Show answer and explanation

75%

Divide useful output by input and multiply by 100 percent:

150/200\times100\%=75\%

. It is below 100 percent because useful output is less than input.

Key terms

Scalar: A quantity with size but no direction.
System: The object or group of objects chosen for a description.
Kinetic energy: Energy associated with an object's motion.
Potential energy: Stored energy associated with position or arrangement; here, gravitational potential energy is associated with height.
Thermal energy: Energy associated with the motion and arrangement of particles in a substance.
Heat: Energy transferred because of a temperature difference.
Power: The amount of energy transferred or used per unit time.
Efficiency: The fraction of input energy that becomes the intended useful output.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation D3.3. 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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D3.3 · Explain thermal, kinetic, potential, heat, power, and efficiency quantities

Ontario Grade 11 Physics

Ontario Grade 11 Physics — D3.3

What you will learn

1. Energy in a system: thermal, kinetic, and potential

2. Heat is energy transferred

3. Gravitational potential energy and system boundaries

4. Power and efficiency describe how energy is transferred or used

Kinetic energy of a moving cart

Gravitational potential energy of a raised backpack

Power and efficiency of a small device

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through SPH3U

About this lesson and its review