Thermal Energy Revision Notes for VCE SSCE Physics

Thermal Energy

Introduction

What is temperature?

Temperature is what a thermometer measures. It is related to, but not the same as, the total amount of thermal energy in an object.

When you grab an object with a higher temperature than your hand, thermal energy moves into your hand and the object feels hot. If the temperature is lower than your hand, thermal energy flows out of your hand and the object feels cold.

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Thermal energy is the sum of all the random potential and kinetic energies of the atoms and molecules that make up an object or system.

Translational kinetic energy is the energy associated with an object of mass $m$ travelling with speed $v$ .

When thermal energy increases, temperature increases. When thermal energy decreases, temperature decreases. However, the exact relationship is complicated.

The tiny sparks from a birthday cake sparkler have a temperature over 1000°C, but they will not burn your skin. They do not have enough thermal energy because the number of molecules involved is very small.

Heat is the flow of thermal energy between two bodies of different temperature. Thermal energy always flows from hotter objects to colder ones because molecules in hotter objects have more random translational kinetic energy and potential energy.

Hot and cold burns

When too much thermal energy passes into our skin, we get a burn as cells are damaged. When too much thermal energy passes out of our skin, the cells are also damaged. This is called a 'cold burn', 'ice burn', or frostbite.

Cold burns can occur from:

Being outside in low temperatures for extended periods
Exposure to expanding gas from compressed or liquid sources (aerosol cans)
Liquid nitrogen or helium spills
Contact with metal cooled by such substances

chatImportant

Cold burns are just as serious as hot burns and often require medical treatment, but hot and cold burns are managed very differently.

Temperature scales

The two most common temperature scales are Celsius and Kelvin, although Fahrenheit is also used in some countries.

infoNote

Celsius (°C) is a unit of temperature where the boiling point of water is 100°C and the freezing point is 0°C.

Kelvin (K) is a unit of temperature where the boiling point of water is 373.15 K and the freezing point is 273.15 K. Zero kelvin (0 K) corresponds to absolute zero.

Scale	Unit	Freezing point of water	Boiling point of water
Celsius	degree, symbol °C	0°C	100°C
Kelvin	kelvin, symbol K	273.15 K	373.15 K
Fahrenheit	degree, symbol °F	32°F	212°F

Converting between Celsius and Kelvin

The size of one degree Celsius equals the size of one kelvin. To convert from degrees Celsius to kelvins, simply add 273.15 to the Celsius number:

chatImportant

$T_{\text{K}} = T_{\text{°C}} + 273.15$

Note: The Kelvin scale does not have degrees. Its unit is the kelvin (lowercase k) and its symbol is uppercase K. Temperatures in kelvins do not have degree signs, just a number followed by a space and K.

Absolute zero

Zero kelvin is absolute zero, corresponding to the state where molecules have effectively zero kinetic energy. It is not possible to cool an object any further. There are no negative temperatures on the Kelvin scale.

Heat transfer methods

Conduction

Conduction is the process of thermal energy transfer through interactions between nearby atoms, molecules and electrons.

Conduction is the most significant method of thermal energy transfer in solids because molecules are closely packed together. Vibrations caused by heating readily cause nearby particles to vibrate through interactions, transferring thermal energy through the solid.

When two objects at different temperatures are in contact, thermal energy flows as heat from the hotter object to the colder one. This occurs because the kinetic and potential energies of particles in the hotter object are greater, on average, than those in the colder object.

Thermal conductivity

The rate at which conduction occurs depends on the material involved. Some materials conduct better than others.

infoNote

Good conductors:

Metals (due to free electrons that can move freely throughout the metal)
Copper has the highest thermal conductivity

Poor conductors (good insulators):

Non-metals (no free electrons)
Gases (particles are far apart, interactions are rare)

Material	Thermal conductivity (arbitrary units)
Copper	17000
Aluminium	10000
Household bricks	55
Window glass	40
Water	25
Concrete	20
Compacted snow	Between 25 and 5.0
Polyvinylchloride (PVC)	8.0
Ethanol	7.2
Charcoal	3.5
Fibreglass	2.0
Nitrogen gas	1
Oxygen gas	1

In this table, air is set at 1.0. Copper has 8500 times the thermal conductivity of fibreglass.

High conductivity is desirable for saucepan bases (copper), while low conductivity is desirable for handles (fibreglass or other insulators).

infoNote

Factors affecting conduction:

Material thickness: Thicker layers provide better insulation
Surface area: Greater contact area means better conduction and less effective insulation
Temperature gradient: Greater temperature differences result in greater energy flow

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Worked Example: Firewalk

People can walk barefoot over hot coals at 500°C without getting burned feet. This is possible because:

Low thermal conductivity of charcoal means slow heat flow into feet
Low specific heat of charcoal means low amount of heat available
Brief contact time (few seconds) during a brisk walk across 5 m firepit

Convection

Convection is the process of thermal energy transfer through the movement of a fluid or gas.

Convection is the main form of thermal energy transfer in liquids and gases. It occurs when there is significant flow of the liquid or gas itself, moving thermal energy by bodily movement of the material.

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Types of convection:

Natural convection: Driven by warmer fluid rising and cooler fluid falling due to density differences
Forced convection: Driven by fans or pumps

In a domestic setting, air is warmed by a heater and becomes less dense, so it rises to the ceiling. There it cools by conduction and radiation, becoming more dense and sinking to the floor. This drives a circulating convection current.

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Worked Example: Sea Breeze and Land Breeze

During the day: Hot sunshine warms the land faster than the sea. Air heated by the land becomes less dense and rises. Cool air above the ocean is pulled over to replace it, creating a sea breeze.

At night: When the sun goes down, the land cools faster than the sea. The ocean is now warmer than the land and warms the air, making it less dense and causing it to rise. Air cooled by the land is pulled over by warmer air rising above the ocean, creating a land breeze.

Radiation

Thermal energy from the Sun reaches Earth after travelling through the near-perfect vacuum of space as electromagnetic radiation. The Sun's electromagnetic spectrum is 93% infrared and visible radiation and 7% ultraviolet.

All objects with temperatures above 0 K emit electromagnetic radiation. This is thermal radiation, a result of thermal energy. Earth re-radiates this received electromagnetic radiation at longer wavelengths, deep into the infrared region.

infoNote

Key points about thermal radiation:

The hotter an object, the shorter the wavelength of radiation
At 700 K, emitted thermal radiation becomes visible ('red hot')
Perfect radiators are called 'blackbody' radiators
Blackbody radiators are also perfect absorbers

Surface effects on radiation:

Shiny and white surfaces (including snow and ice) reflect much radiation
Black and matt surfaces absorb most radiation energy

Evaporative cooling

Evaporative cooling is the process of cooling that occurs in liquids when high-energy molecules evaporate and carry away energy from the system.

Hot drinks without lids lose considerable thermal energy through evaporative cooling. This process also occurs when we sweat, especially when there is wind blowing.

Mechanism of evaporative cooling

Within a liquid, molecules are free to move around and interact with each other, resulting in a wide range of kinetic energies for different molecules.

When molecules with higher than average kinetic energy are near the liquid surface, some have enough energy to escape the bonds of the liquid and move into the air. Now in a gas state, the molecules move away from the system (evaporation).

The evaporating molecules carry away the extra energy they obtained from collisions within the system. This means that evaporating molecules reduce both the thermal energy and the average kinetic energy of the remaining liquid molecules, lowering the temperature and creating a cooling effect.

Applications of evaporative cooling

lightbulbExample

Application: Coolgardie Safe

A box that keeps contents cool through evaporative cooling. Water from a tank on top drips onto hessian sackcloth covering the safe. The water diffuses through the cloth by capillary action and evaporates, taking away heat and cooling the safe.

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Application: Aboriginal Water Carriers

The kangaroo or wallaby skin water container is an important innovation developed by Aboriginal and Torres Strait Islander peoples to carry water through hot and arid environments.

The water carrier is made by removing the skin whole and making a bag from it. The skin is rubbed with tree resin to preserve it and make it waterproof. Water slowly diffuses through the skin and evaporates from the outside surface without making it wet, keeping the water relatively cool.

This principle is thought to have inspired the design of the Coolgardie safe.

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Application: Evaporative Air Conditioning

Popular in dry and warmer parts of Australia. The principle is similar to the Coolgardie safe, with a fan run by electricity. Hot air is drawn through a porous material kept wet by circulating water. As water evaporates from the material, it cools the air passing through.

Specific heat capacity

Specific heat capacity is the energy required to raise the temperature of 1 kg of a material by 1 K. Units are J kg⁻¹ K⁻¹. Its value depends on the material being heated. It is given the symbol $c$ .

Formula for temperature change

The symbol $Q$ is used for the amount of thermal energy that must be added to a system in the form of heat to raise the temperature of a material.

chatImportant

$Q = mc\Delta T$

Where:

$Q$ = Amount of thermal energy required to increase the temperature of a material by $\Delta T$ (J)
$m$ = Mass of the material being heated (kg)
$c$ = Specific heat capacity of the material being heated (J kg⁻¹ K⁻¹)
$\Delta T$ = Change in temperature before and after heating (K)

Specific heat capacity values

Material	Specific heat capacity (J kg⁻¹ K⁻¹)
Water	4190
Wood	1300–2400
Wheat	1000–2500
Aluminium	890
Concrete	880
Household bricks	850
Window glass	800
Copper	385
Nitrogen gas	1
Oxygen gas	1

Properties of water

Water has a relatively high specific heat capacity. This means:

More energy is required to heat water
Water releases more energy when it cools down
Water takes a long time to heat up and cool down

infoNote

Consequences:

Environments near lakes and oceans are protected from temperature extremes
On very hot days, large bodies of water absorb thermal energy, minimising temperature rise
On cold days, water releases thermal energy, minimising temperature drop

Applications:

Hot water bottles: Keep warm for a long time due to high specific heat capacity of water
Wheat-filled bags: Can be heated in microwaves, taking advantage of wheat's high specific heat capacity without risk of water leakage
Car radiators: Water is ideal for engine cooling due to its high specific heat capacity
Water wall thermal storage: Houses with water-filled walls have high thermal energy capacity, smoothing out temperature extremes

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Worked Example: Heating Water

Question: How much energy needs to be added to 2 kg of water to raise its temperature from 20°C to 100°C? Take the specific heat capacity of water, $c$ , to be 4190 J kg⁻¹ K⁻¹.

Solution:

Using $Q = mc\Delta T$ , where:

$m = 2$ kg
$c = 4190$ J kg⁻¹ K⁻¹
$\Delta T = 80$ K

gives:

Q = 2 \times 4190 \times 80

= 670400 \text{ J}

= 670 \text{ kJ}

Therefore, 670 kJ of energy is required to heat the water.

Change of state

Change of state occurs when a substance changes from one state (solid, liquid or gas) to another by absorbing or releasing energy.

infoNote

Types of changes:

Melting: Change of state from solid to liquid
Fusion: Change of state from liquid to solid
Vaporisation: Change of state from liquid to gas
Condensation: Change of state from gas to liquid

When a substance changes state, energy is added or taken away, changing the interaction of molecules with each other by either breaking bonds or allowing them to form.

chatImportant

Important: Changes of state do not change the temperature of the substance. The energy is solely involved in the change of state.

Specific latent heat

Specific latent heat is the energy needed to be absorbed or released per kilogram of a substance to cause a change of state, in units J kg⁻¹. It depends on both the substance and the change of state. It is given the symbol $L$ .

chatImportant

$Q = mL$

Where:

$Q$ = Amount of thermal energy required (or released) in a change of state (J)
$m$ = Mass of the substance changing state (kg)
$L$ = Specific latent heat of the substance (J kg⁻¹)

Specific latent heat values

Material	Specific latent heat of fusion (kJ kg⁻¹)	Specific latent heat of vaporisation (kJ kg⁻¹)
Carbon dioxide	184	574
Ethanol	108	846
Lead	23	871
Sulfur	39	1510
Water	334	2256

infoNote

Note: The specific latent heat of vaporisation is much larger than the specific latent heat of fusion for the same substance.

Water phase diagram

The diagram shows what happens when ice at -20°C is heated steadily, continuing after it all becomes steam:

A to B: Ice heating

Water remains in solid state (ice)
Temperature and thermal energy related by $Q = m c_{\text{ice}} \Delta T$
Note: $c_{\text{ice}} = 2093$ J kg⁻¹ K⁻¹ (different from $c_{\text{water}}$ )

B to C: Melting

Mixture of ice and water remains at 0°C
All thermal energy added is used breaking bonds between ice molecules
Energy needed: $Q = m L_{\text{melting}}$
$L_{\text{melting}}$ for water = 334 kJ kg⁻¹

C to D: Water heating

Thermal energy related to temperature by $Q = m c_{\text{water}} \Delta T$

D to E: Vaporising (boiling)

Water temperature remains constant at 100°C
Thermal energy used to break bonds between water molecules
Energy needed: $Q = m L_{\text{vaporisation}}$
$L_{\text{vaporisation}}$ for water = 2256 kJ kg⁻¹

Beyond E: Steam heating

Temperature of steam increases

chatImportant

Important conclusion: Food cooked in boiling water will not cook faster if the water is boiling rapidly rather than just boiling. The temperature is the same in both cases: 100°C.

Energy release in reverse processes

When the process is reversed, thermal energy is released:

Condensation: $Q = m L_{\text{condensation}}$

Note: $L_{\text{vaporisation}} = L_{\text{condensation}}$

chatImportant

Allowing steam to condense on your hand can result in a nasty burn because energy is released.

Fusion (freezing): $Q = m L_{\text{fusion}}$

Note: $L_{\text{melting}} = L_{\text{fusion}}$

When water freezes into ice, thermal energy is released and absorbed by the freezer compartment.

lightbulbExample

Worked Example: Phase Change of Water

Question: How much energy needs to be added to 2.0 kg of ice at 0.0°C to convert all the ice into water? Compare this to the amount of energy needed to convert 2.0 kg of water at 100°C into steam.

Solution:

Use $L_{\text{fusion}}$ for water as 334 kJ kg⁻¹ and $L_{\text{vaporisation}}$ for water as 2256 kJ kg⁻¹.

To convert ice into water, use $Q = mL$ :

$m = 2$ kg
$L = 334$ kJ kg⁻¹

Q = 2 \times 334 \times 10^3

= 668 \times 10^3

= 668 \text{ kJ}

To convert water into steam, use $Q = mL$ :

$m = 2$ kg
$L = 2256$ kJ kg⁻¹

Q = 2 \times 2256 \times 10^3

= 4512 \times 10^3

= 4512 \text{ kJ}

Comparison: It takes 3844 kJ more energy to convert 2.0 kg of water at 100°C into steam than to convert 2.0 kg of ice at 0.0°C into water. It takes almost seven times the energy to change from water to steam than from ice to water.

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Worked Example: Cooling a Drink

Question: A container of 1.00 kg of water at 20°C is cooled by adding 100 g of ice at 0°C. Assume the container is insulated. Find the final temperature when all ice has melted and the entire container is at the same temperature.

Solution:

The ice gains energy:

$Q_1$ when melting
$Q_2$ when warming to final temperature $T$

The drink loses energy:

$Q_3$ when cooling to final temperature $T$

By conservation of energy: $Q_1 + Q_2 = Q_3$

Step 1: Find $Q_1$ using $Q = mL$ :

$m_{\text{ice}} = 0.100$ kg
$L = 334$ kJ kg⁻¹

Q_1 = 0.100 \times 334000

= 33400 \text{ J}

Step 2: Find $Q_2$ using $Q = mc\Delta T$ :

$m_{\text{water}} = 0.100$ kg
$c_{\text{water}} = 4190$ J kg⁻¹ K⁻¹
$\Delta T = T - 273$ K

Q_2 = 0.100 \times 4190 \times (T - 273)

= 419.0 \times (T - 273) \text{ J}

Step 3: Find $Q_3$ using $Q = mc\Delta T$ :

$m_{\text{water}} = 1.000$ kg
$c_{\text{water}} = 4190$ J kg⁻¹ K⁻¹
$\Delta T = 293 - T$ K

Q_3 = 1.000 \times 4190 \times (293 - T)

= 4190 \times (293 - T) \text{ J}

Step 4: Apply conservation of energy:

$33400 + 419.0(T - 273) = 4190 \times (293 - T)$

Solving for $T$ :

T = \dfrac{33400 - 419 \times 273 - 4190 \times 293}{-419 - 4190}

= 283.9 \text{ K}

Hence, the final temperature of the water is 10.9°C.

Remember!

bookmarkSummary

Key Points to Remember:

Temperature is what a thermometer measures and indicates the direction of heat flow between objects
Thermal energy is the sum of all random potential and kinetic energies of atoms and molecules in a system
Heat is the flow of thermal energy from hotter to colder objects
Convert between Celsius and Kelvin by adding or subtracting 273.15
Three methods of heat transfer are conduction (dominant in solids), convection (dominant in liquids and gases), and radiation (works in vacuum)
Evaporative cooling occurs when high-energy molecules escape from a liquid surface, taking energy with them
Use $Q = mc\Delta T$ to calculate energy required to change temperature
Use $Q = mL$ to calculate energy required (or released) during a change of state
Water has high specific heat capacity (4190 J kg⁻¹ K⁻¹), making it useful for thermal energy storage
Temperature remains constant during a change of state even though energy is being added or removed

Thermal Energy (VCE SSCE Physics): Revision Notes

Thermal Energy

Introduction

What is temperature?

Hot and cold burns

Temperature scales

Converting between Celsius and Kelvin

Absolute zero

Heat transfer methods

Conduction

Thermal conductivity

Convection

Radiation

Evaporative cooling

Mechanism of evaporative cooling

Applications of evaporative cooling

Specific heat capacity

Formula for temperature change

Specific heat capacity values

Properties of water

Change of state

Specific latent heat

Specific latent heat values

Water phase diagram

Energy release in reverse processes

Remember!

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