Changes of state and specific latent heat

What you'll learn

Why temperature stays constant while a substance changes state.
What latent heat and specific latent heat mean.
How to use $E = m L$ for melting, freezing, boiling and condensing.
How to interpret heating/cooling graphs and describe a latent heat experiment.

The starting point: internal energy

Before latent heat makes sense, you need the idea of internal energy.

Definition

Internal energy

The internal energy of a substance is the total energy stored by its particles, including their kinetic energy because they move and their potential energy because of their positions and forces between them.

Temperature is linked to the average kinetic energy of the particles. If you heat a solid, liquid or gas and it does not change state, the particles usually move faster, so the temperature rises.

However, when a substance is changing state, something different happens: the energy is used to change the arrangement or separation of the particles instead.

Key Idea

Temperature is not the whole story

Heating can increase the temperature, but it can also change the internal energy by changing the particles’ positions during a change of state.

Changes of state

A change of state is a physical change between solid, liquid and gas. It is physical because no new substance is made.

Common changes of state include:

Melting: solid to liquid
Freezing: liquid to solid
Boiling or evaporating: liquid to gas/vapour
Condensing: gas/vapour to liquid
Subliming: solid directly to gas

During a change of state, the substance is still the same material. For example, ice, liquid water and steam are all water.

Latent heat: energy during a change of state

Definition

Latent heat

Latent heat is the energy transferred when a substance changes state. During the change of state, the energy changes the internal energy, but the temperature does not change.

The word “latent” means hidden. The energy is “hidden” from the thermometer because the temperature reading stays the same even though energy is still being transferred.

For example, if ice is melting at 0 °C, energy is being supplied, but the temperature remains 0 °C until all the ice has melted.

Example

Explaining a melting plateau

A beaker contains ice and water at 0 °C. It is heated, but the thermometer stays at 0 °C until all the ice has melted. Explain why.

While ice is melting, the energy supplied is used to change the arrangement of the particles from a solid structure to a liquid arrangement.
This increases the potential energy part of the internal energy, because particles become less fixed in position.
The average kinetic energy of the particles does not increase during the change of state, so the temperature stays constant.
Once all the ice has melted, further energy increases the particles’ average kinetic energy, so the temperature of the water can rise.

Specific latent heat

Definition

Specific latent heat

The specific latent heat of a substance is the energy required to change the state of 1 kilogram of the substance with no change in temperature.

The symbol for specific latent heat is $L$ . Its unit is joules per kilogram, written as J/kg.

There are two important types at GCSE:

Specific latent heat of fusion: energy needed to change 1 kg from solid to liquid, with no temperature change.
Specific latent heat of vaporisation: energy needed to change 1 kg from liquid to vapour, with no temperature change.

The reverse changes release the same amount of energy:

Freezing releases latent heat of fusion.
Condensing releases latent heat of vaporisation.

Tip

Fusion and vaporisation

Fusion means the solid-liquid change. Vaporisation means the liquid-gas change.

Heating and cooling graphs

A heating graph shows how temperature changes as energy is supplied. If the heater power is constant, the horizontal axis might be time instead of energy, because energy supplied is proportional to heating time.

The most important parts are the flat sections. These are the changes of state, where energy is still being transferred but the temperature is constant.

Heating curve showing warming sections and latent heat plateaus

On a heating graph:

Sloping sections mean the substance is staying in the same state and its temperature is increasing.
Flat sections mean the substance is changing state and its temperature is constant.
The first flat section is usually melting.
The second flat section is usually boiling.

On a cooling graph, the pattern is reversed. Flat sections can show condensing or freezing, because energy is being transferred away from the substance while its temperature stays constant.

Example

Interpreting a heating graph

A pure substance is heated with a constant-power heater. Its graph has a flat section at 40 °C lasting 3 minutes and another flat section at 120 °C lasting 9 minutes.

The flat section at 40 °C is the melting point, because the first plateau on a heating graph is where solid changes to liquid.
The flat section at 120 °C is the boiling point, because the later plateau is where liquid changes to gas.
Since the heater power is constant, a longer time means more energy has been supplied.
The boiling plateau lasts longer than the melting plateau, so vaporising this sample requires more energy than melting it.

Common Mistake

Thinking flat means no energy transfer

A flat section on a heating graph does not mean the heater has stopped transferring energy. It means the energy is changing the state instead of raising the temperature.

The specific latent heat equation

The equation for energy transferred during a change of state is:

E = m L

where:

$E$ is the energy transferred in joules, J
$m$ is the mass in kilograms, kg
$L$ is the specific latent heat in joules per kilogram, J/kg

You can also rearrange it:

\frac{E}{m}

\frac{E}{L}

Example

Calculating energy to melt ice

Calculate the energy needed to melt 0.50 kg of ice at 0 °C. The specific latent heat of fusion of ice is $3.34 \times 10^5 \text{ J/kg}$ .

Choose the latent heat of fusion because the change is solid to liquid.
Substitute into $E = m L$ :
$J\begin{aligned} E &= 0.50 \times 3.34 \times 10^5 \\ E &= 1.67 \times 10^5 \text{ J} \end{aligned}$
The energy needed is $1.67 \times 10^5 \text{ J}$ , which is 167 kJ.

Common Mistake

Using grams instead of kilograms

The mass in $E = m L$ must be in kilograms. If the question gives grams, convert first: 250 g is 0.250 kg.

Specific heat capacity versus specific latent heat

These two ideas are very easy to mix up, so compare the situation carefully.

Specific heat capacity is used when the temperature changes but the state stays the same. Its equation is:

mc\Delta \theta

Specific latent heat is used when the state changes but the temperature stays the same. Its equation is:

E = m L

So:

Use specific heat capacity on sloping parts of a heating/cooling graph.
Use specific latent heat on flat parts of a heating/cooling graph.

Example

Choosing the correct energy equation

A 0.20 kg substance is already at its melting point. It melts completely, then the liquid warms by 15 °C. Its specific latent heat of fusion is $1.8 \times 10^5 \text{ J/kg}$ and its specific heat capacity as a liquid is 1200 J/kg °C. Calculate the total energy transferred.

Split the process into two stages: melting uses $E = m L$ , then warming the liquid uses $mc\Delta \theta$ .
Calculate the energy for melting:
$J\begin{aligned} E &= 0.20 \times 1.8 \times 10^5 \\ E &= 3.6 \times 10^4 \text{ J} \end{aligned}$
Calculate the energy for warming the liquid:
$J\begin{aligned} E &= 0.20 \times 1200 \times 15 \\ E &= 3600 \text{ J} \end{aligned}$
Add the two energy transfers:
$J\begin{aligned} E_{\text{total}} &= 3.6 \times 10^4 + 3600 \\ E_{\text{total}} &= 3.96 \times 10^4 \text{ J} \end{aligned}$

Common Mistake

Only use $E = m L$ for the state change

If the substance also warms up or cools down before or after the state change, you need a separate specific heat capacity calculation for that part.

Measuring the specific latent heat of fusion of water

You may be asked to describe an experiment to measure the specific latent heat of fusion of ice/water.

The basic idea is:

Use an electrical heater to transfer a known amount of energy to melting ice.
Measure the mass of water produced by the melting.
Use $\frac{E}{m}$ .

One school method uses an immersion heater in crushed ice, with electrical measurements used to calculate the energy supplied.

Experiment setup for measuring the specific latent heat of fusion of ice

A typical method:

Place crushed melting ice in an insulated funnel or container.
Allow any water already present to drain away, so the ice is at about 0 °C.
Set up an immersion heater in the ice.
Measure the potential difference $V$ across the heater and the current $I$ through it.
Switch on the heater for a measured time $t$ .
Collect the melted water and measure its mass $m$ in kilograms.
Calculate the electrical energy transferred using:
$E = V I t$
Calculate the specific latent heat using:
$\frac{E}{m}$

In practice, some ice melts because of energy from the surroundings, not just from the heater. A better experiment measures this background melting and subtracts it from the total mass collected.

Example

Finding specific latent heat from practical data

A heater is run at 6.0 V and 2.0 A for 300 s. During this time, 0.015 kg of water is collected. A background test shows that 0.003 kg would have melted without the heater. Calculate the specific latent heat of fusion.

Correct the mass melted by the heater:
$kg\begin{aligned} m &= 0.015 - 0.003 \\ m &= 0.012 \text{ kg} \end{aligned}$
Calculate the electrical energy supplied:
$J\begin{aligned} E &= VIt \\ E &= 6.0 \times 2.0 \times 300 \\ E &= 3600 \text{ J} \end{aligned}$
Calculate the specific latent heat:
$J/kg\begin{aligned} L &= \frac{E}{m} \\ L &= \frac{3600}{0.012} \\ L &= 3.0 \times 10^5 \text{ J/kg} \end{aligned}$

Tip

Practical accuracy

Use insulation and a background melting correction. Otherwise, the mass of water collected may include ice melted by the room, not just by the heater.

Exam technique

In the exam

Decide whether the temperature is changing or the state is changing: sloping graph means $mc\Delta \theta$ , flat graph means $E = m L$ .
Convert mass into kilograms before using the latent heat equation.
State clearly whether you are using latent heat of fusion or latent heat of vaporisation.
For practical questions, mention measuring $V$ , $I$ , $t$ and $m$ , then using $E = V I t$ and $\frac{E}{m}$ .

Self review

Check yourself

Why does temperature stay constant while ice melts?
What is the difference between specific latent heat of fusion and specific latent heat of vaporisation?
On a heating graph, which parts use $E = m L$ and which parts use $mc\Delta \theta$ ?

Changes of state and specific latent heat

What you'll learn

Why temperature stays constant while a substance changes state.
What latent heat and specific latent heat mean.
How to use $E = m L$ for melting, freezing, boiling and condensing.
How to interpret heating/cooling graphs and describe a latent heat experiment.

The starting point: internal energy

Before latent heat makes sense, you need the idea of internal energy.

Definition

Internal energy

However, when a substance is changing state, something different happens: the energy is used to change the arrangement or separation of the particles instead.

Key Idea

Temperature is not the whole story

Heating can increase the temperature, but it can also change the internal energy by changing the particles’ positions during a change of state.

Changes of state

A change of state is a physical change between solid, liquid and gas. It is physical because no new substance is made.

Common changes of state include:

Melting: solid to liquid
Freezing: liquid to solid
Boiling or evaporating: liquid to gas/vapour
Condensing: gas/vapour to liquid
Subliming: solid directly to gas

During a change of state, the substance is still the same material. For example, ice, liquid water and steam are all water.

Latent heat: energy during a change of state

Definition

Latent heat

Latent heat is the energy transferred when a substance changes state. During the change of state, the energy changes the internal energy, but the temperature does not change.

The word “latent” means hidden. The energy is “hidden” from the thermometer because the temperature reading stays the same even though energy is still being transferred.

For example, if ice is melting at 0 °C, energy is being supplied, but the temperature remains 0 °C until all the ice has melted.

Example

Explaining a melting plateau

A beaker contains ice and water at 0 °C. It is heated, but the thermometer stays at 0 °C until all the ice has melted. Explain why.

While ice is melting, the energy supplied is used to change the arrangement of the particles from a solid structure to a liquid arrangement.
This increases the potential energy part of the internal energy, because particles become less fixed in position.
The average kinetic energy of the particles does not increase during the change of state, so the temperature stays constant.
Once all the ice has melted, further energy increases the particles’ average kinetic energy, so the temperature of the water can rise.

Specific latent heat

Definition

Specific latent heat

The specific latent heat of a substance is the energy required to change the state of 1 kilogram of the substance with no change in temperature.

The symbol for specific latent heat is $L$ . Its unit is joules per kilogram, written as J/kg.

There are two important types at GCSE:

Specific latent heat of fusion: energy needed to change 1 kg from solid to liquid, with no temperature change.
Specific latent heat of vaporisation: energy needed to change 1 kg from liquid to vapour, with no temperature change.

The reverse changes release the same amount of energy:

Freezing releases latent heat of fusion.
Condensing releases latent heat of vaporisation.

Tip

Fusion and vaporisation

Fusion means the solid-liquid change. Vaporisation means the liquid-gas change.

Heating and cooling graphs

The most important parts are the flat sections. These are the changes of state, where energy is still being transferred but the temperature is constant.

Heating curve showing warming sections and latent heat plateaus

On a heating graph:

Sloping sections mean the substance is staying in the same state and its temperature is increasing.
Flat sections mean the substance is changing state and its temperature is constant.
The first flat section is usually melting.
The second flat section is usually boiling.

On a cooling graph, the pattern is reversed. Flat sections can show condensing or freezing, because energy is being transferred away from the substance while its temperature stays constant.

Example

Interpreting a heating graph

A pure substance is heated with a constant-power heater. Its graph has a flat section at 40 °C lasting 3 minutes and another flat section at 120 °C lasting 9 minutes.

The flat section at 40 °C is the melting point, because the first plateau on a heating graph is where solid changes to liquid.
The flat section at 120 °C is the boiling point, because the later plateau is where liquid changes to gas.
Since the heater power is constant, a longer time means more energy has been supplied.
The boiling plateau lasts longer than the melting plateau, so vaporising this sample requires more energy than melting it.

Common Mistake

Thinking flat means no energy transfer

A flat section on a heating graph does not mean the heater has stopped transferring energy. It means the energy is changing the state instead of raising the temperature.

The specific latent heat equation

The equation for energy transferred during a change of state is:

E = m L

where:

$E$ is the energy transferred in joules, J
$m$ is the mass in kilograms, kg
$L$ is the specific latent heat in joules per kilogram, J/kg

You can also rearrange it:

\frac{E}{m}

\frac{E}{L}

Example

Calculating energy to melt ice

Calculate the energy needed to melt 0.50 kg of ice at 0 °C. The specific latent heat of fusion of ice is $3.34 \times 10^5 \text{ J/kg}$ .

Choose the latent heat of fusion because the change is solid to liquid.
Substitute into $E = m L$ :
$J\begin{aligned} E &= 0.50 \times 3.34 \times 10^5 \\ E &= 1.67 \times 10^5 \text{ J} \end{aligned}$
The energy needed is $1.67 \times 10^5 \text{ J}$ , which is 167 kJ.

Common Mistake

Using grams instead of kilograms

The mass in $E = m L$ must be in kilograms. If the question gives grams, convert first: 250 g is 0.250 kg.

Specific heat capacity versus specific latent heat

These two ideas are very easy to mix up, so compare the situation carefully.

Specific heat capacity is used when the temperature changes but the state stays the same. Its equation is:

mc\Delta \theta

Specific latent heat is used when the state changes but the temperature stays the same. Its equation is:

E = m L

So:

Use specific heat capacity on sloping parts of a heating/cooling graph.
Use specific latent heat on flat parts of a heating/cooling graph.

Example

Choosing the correct energy equation

Split the process into two stages: melting uses $E = m L$ , then warming the liquid uses $mc\Delta \theta$ .
Calculate the energy for melting:
$J\begin{aligned} E &= 0.20 \times 1.8 \times 10^5 \\ E &= 3.6 \times 10^4 \text{ J} \end{aligned}$
Calculate the energy for warming the liquid:
$J\begin{aligned} E &= 0.20 \times 1200 \times 15 \\ E &= 3600 \text{ J} \end{aligned}$
Add the two energy transfers:
$J\begin{aligned} E_{\text{total}} &= 3.6 \times 10^4 + 3600 \\ E_{\text{total}} &= 3.96 \times 10^4 \text{ J} \end{aligned}$

Common Mistake

Only use $E = m L$ for the state change

If the substance also warms up or cools down before or after the state change, you need a separate specific heat capacity calculation for that part.

Measuring the specific latent heat of fusion of water

You may be asked to describe an experiment to measure the specific latent heat of fusion of ice/water.

The basic idea is:

Use an electrical heater to transfer a known amount of energy to melting ice.
Measure the mass of water produced by the melting.
Use $\frac{E}{m}$ .

One school method uses an immersion heater in crushed ice, with electrical measurements used to calculate the energy supplied.

Experiment setup for measuring the specific latent heat of fusion of ice

A typical method:

Place crushed melting ice in an insulated funnel or container.
Allow any water already present to drain away, so the ice is at about 0 °C.
Set up an immersion heater in the ice.
Measure the potential difference $V$ across the heater and the current $I$ through it.
Switch on the heater for a measured time $t$ .
Collect the melted water and measure its mass $m$ in kilograms.
Calculate the electrical energy transferred using:
$E = V I t$
Calculate the specific latent heat using:
$\frac{E}{m}$

In practice, some ice melts because of energy from the surroundings, not just from the heater. A better experiment measures this background melting and subtracts it from the total mass collected.

Example

Finding specific latent heat from practical data

Correct the mass melted by the heater:
$kg\begin{aligned} m &= 0.015 - 0.003 \\ m &= 0.012 \text{ kg} \end{aligned}$
Calculate the electrical energy supplied:
$J\begin{aligned} E &= VIt \\ E &= 6.0 \times 2.0 \times 300 \\ E &= 3600 \text{ J} \end{aligned}$
Calculate the specific latent heat:
$J/kg\begin{aligned} L &= \frac{E}{m} \\ L &= \frac{3600}{0.012} \\ L &= 3.0 \times 10^5 \text{ J/kg} \end{aligned}$

Tip

Practical accuracy

Use insulation and a background melting correction. Otherwise, the mass of water collected may include ice melted by the room, not just by the heater.

Exam technique

In the exam

Decide whether the temperature is changing or the state is changing: sloping graph means $mc\Delta \theta$ , flat graph means $E = m L$ .
Convert mass into kilograms before using the latent heat equation.
State clearly whether you are using latent heat of fusion or latent heat of vaporisation.
For practical questions, mention measuring $V$ , $I$ , $t$ and $m$ , then using $E = V I t$ and $\frac{E}{m}$ .

Self review

Check yourself

Why does temperature stay constant while ice melts?
What is the difference between specific latent heat of fusion and specific latent heat of vaporisation?
On a heating graph, which parts use $E = m L$ and which parts use $mc\Delta \theta$ ?

Changes of state and specific latent heat

What you'll learn

The starting point: internal energy

Changes of state

Latent heat: energy during a change of state

Specific latent heat

Heating and cooling graphs

The specific latent heat equation

Specific heat capacity versus specific latent heat

Measuring the specific latent heat of fusion of water

You've reached the end

Changes of state and specific latent heat

What you'll learn

The starting point: internal energy

Changes of state

Latent heat: energy during a change of state

Specific latent heat

Heating and cooling graphs

The specific latent heat equation

Specific heat capacity versus specific latent heat

Measuring the specific latent heat of fusion of water

You've reached the end

Changes of state and specific latent heat

What you'll learn

The starting point: internal energy

Changes of state

Latent heat: energy during a change of state

Specific latent heat

Heating and cooling graphs

The specific latent heat equation

Specific heat capacity versus specific latent heat

Measuring the specific latent heat of fusion of water

You've reached the end

Changes of state and specific latent heat Revision Guide

Changes of state and specific latent heat

What you'll learn

The starting point: internal energy

Changes of state

Latent heat: energy during a change of state

Specific latent heat

Heating and cooling graphs

The specific latent heat equation

Specific heat capacity versus specific latent heat

Measuring the specific latent heat of fusion of water

You've reached the end

Changes of state and specific latent heat Revision Guide