Heating, specific heat and latent heat

What you'll learn

How heating changes the energy stored in particles.
Why temperature sometimes rises, but sometimes stays constant during a change of state.
How to use the equations for specific heat capacity and specific latent heat.
How insulation and the water core practical link to these ideas.

Starting point: particles and energy

In the particle model, all substances are made of tiny particles. In a solid, particles vibrate about fixed positions. In a liquid, they can move past each other. In a gas, they are far apart and move freely.

Heating means transferring energy into a system. In this topic, a system usually means the substance you are focusing on, such as water in a beaker or ice in a test tube.

Definition

Temperature and thermal energy

Temperature tells you about the average kinetic energy of the particles. Thermal energy is the energy stored by the particles overall, including their kinetic energy and energy due to their positions and attractions between particles.

Temperature is not the same thing as energy. A large bath of warm water can store more thermal energy than a tiny cup of very hot water because there is much more mass.

What heating does to a system

When you heat a substance, one of two main things can happen:

its temperature increases, because the particles gain kinetic energy and move or vibrate faster
it changes state, because energy is used to change the arrangement or separation of the particles

A change of state is a physical change between solid, liquid and gas, such as melting, freezing, boiling or condensing. No new substance is made.

A heating curve is a useful way to see the difference. If energy is supplied at a steady rate, time is proportional to energy supplied, so the horizontal axis can be “time” or “energy supplied”.

Heating curve for water showing sloped warming sections and flat melting and boiling sections

Key Idea

Slopes and plateaus

On a sloping part of a heating curve, temperature rises. On a flat part, the substance is changing state, so temperature stays constant while energy changes the potential energy between particles.

Example

Interpreting a heating curve

A sample of ice is heated steadily from below 0 °C until it becomes steam.

On the first sloping section, the ice is still solid, so energy increases the kinetic energy of the particles and the temperature rises.
At 0 °C, the graph is flat because the ice is melting. The energy supplied changes the arrangement of particles rather than increasing their average kinetic energy.
From 0 °C to 100 °C, the liquid water warms up, so the particles move faster and the temperature rises.
At 100 °C, the graph is flat again because the water is boiling. Energy is used to separate particles into a gas.

Specific heat capacity

Definition

Specific heat capacity

The specific heat capacity, symbol $c$ , of a substance is the energy needed to raise the temperature of 1 kg of the substance by 1 °C, without changing its state.

A substance with a high specific heat capacity needs a lot of energy for each degree Celsius rise. Water has a high specific heat capacity, which is why it takes a while to heat a kettle or warm up a swimming pool.

For Edexcel 1PH0, this is a “use” equation, so it is provided on the equation sheet. You still need to know when to choose it, what each symbol means, and how to rearrange it.

ΔQ=m×c×Δθ\Delta Q = m \times c \times \Delta \theta

where:

$ΔQ\Delta Q$ is the change in thermal energy, in joules (J)
$m$ is mass, in kilograms (kg)
$c$ is specific heat capacity, in joules per kilogram degree Celsius (J/kg °C)
$Δθ\Delta \theta$ is change in temperature, in degrees Celsius (°C)

Example

Heating water

A kettle heats 0.75 kg of water from 20 °C to 80 °C. The specific heat capacity of water is 4200 J/kg °C. Calculate the energy transferred to the water.

Choose the specific heat capacity equation because the water’s temperature changes and it does not change state.
Calculate the temperature change: $Δθ=80∘C−20∘C=60∘C\Delta \theta = 80^\circ\text{C} - 20^\circ\text{C} = 60^\circ\text{C}$ .
Substitute into the equation: $J\Delta Q = 0.75 \times 4200 \times 60 = 189000\ \text{J}$ .
Write the result clearly: the energy transferred is 189000 J, or $1.89 \times 10^5\ \text{J}$ .

Common Mistake

Using the final temperature

In $ΔQ=m×c×Δθ\Delta Q = m \times c \times \Delta \theta$ , use the temperature change, not the final temperature. Also convert mass into kilograms before substituting.

Specific latent heat

Definition

Specific latent heat

The specific latent heat, symbol $L$ , of a substance is the energy needed to change the state of 1 kg of the substance without changing its temperature.

The word latent means “hidden”. The energy is being transferred, but it does not show up as a temperature rise.

There are two common types:

specific latent heat of fusion: energy for melting or freezing
specific latent heat of vaporisation: energy for boiling or condensing

For Edexcel 1PH0, this is also provided on the equation sheet:

\times L

where:

$Q$ is the thermal energy needed for the change of state, in joules (J)
$m$ is mass, in kilograms (kg)
$L$ is specific latent heat, in joules per kilogram (J/kg)

The units for latent heat do not include °C because the temperature is not changing.

Example

Melting ice

Calculate the energy needed to melt 0.20 kg of ice at 0 °C. The specific latent heat of fusion of ice is 334000 J/kg.

Choose the latent heat equation because the ice is changing state from solid to liquid at constant temperature.
Substitute into the equation: $\times 334000 = 66800\ \text{J}$ .
Interpret the answer: 66800 J is needed to melt the ice, but the temperature remains at 0 °C until all the ice has melted.

Tip

Choosing the right equation

If the temperature changes, use $ΔQ=m×c×Δθ\Delta Q = m \times c \times \Delta \theta$ . If the state changes, use $\times L$ . If both happen, split the process into stages and add the energies.

Reducing unwanted energy transfer

Thermal insulation means reducing unwanted energy transfer. It can keep hot things hot or cold things cold.

Energy can be transferred by:

conduction: energy transfer through particles in a material, especially in solids
convection: energy transfer by the movement of a liquid or gas
infrared radiation: energy transfer by electromagnetic waves

A material with low thermal conductivity transfers energy by conduction slowly. Foam, wool, fibreglass and trapped air are useful insulators because they reduce conduction and often reduce convection too.

Common insulation methods include:

thick insulation layers, which make conduction slower
trapped air pockets, which reduce convection currents
lids and draught excluders, which stop warm air escaping
shiny or reflective surfaces, which reduce infrared radiation

Example

Insulating a hot water tank

A hot water tank is fitted with a thick foam jacket and a shiny outer surface.

The thick foam has low thermal conductivity, so it reduces energy transfer by conduction from the hot tank to the colder air.
Air trapped in the foam cannot circulate easily, so convection is reduced.
The shiny surface reflects infrared radiation, so less energy is transferred away by radiation.

Core practical: investigating water

In this core practical, you investigate water by finding its specific heat capacity and by obtaining a temperature-time graph for melting ice.

This setup is used to measure the specific heat capacity of water using an immersion heater, thermometer, insulation and electrical measurements.

Specific heat capacity of water practical setup with insulated beaker, immersion heater, thermometer, meters and balance

Finding the specific heat capacity of water

A typical method is:

Measure the mass of water using a balance.
Put the water in an insulated beaker or calorimeter with a lid.
Measure the starting temperature.
Use an immersion heater to transfer energy to the water for a measured time.
Measure the voltage, current and time, then calculate energy supplied using $\times I \times t$ .
Stir the water and record the final temperature.
Calculate $c$ using $\frac{\Delta Q}{m \times \Delta \theta}$ .

Example

Finding specific heat capacity from practical data

A student heats 0.250 kg of water. The heater has a voltage of 12.0 V and a current of 2.0 A for 180 s. The temperature rises from 18.0 °C to 22.0 °C.

Calculate the electrical energy supplied: $\times I \times t = 12.0 \times 2.0 \times 180 = 4320\ \text{J}$ .
Calculate the temperature change: $Δθ=22.0∘C−18.0∘C=4.0∘C\Delta \theta = 22.0^\circ\text{C} - 18.0^\circ\text{C} = 4.0^\circ\text{C}$ .
Rearrange and substitute: $\frac{4320}{0.250 \times 4.0} = 4320\ \text{J kg}^{-1}\,^\circ\text{C}^{-1}$ .
Compare with the accepted value of about 4200 J/kg °C for water; the result is close, but heat losses and thermometer uncertainty can affect it.

Melting ice temperature-time graph

For the melting ice part, you record temperature at regular time intervals as ice is heated or allowed to warm. Plot temperature on the vertical axis and time on the horizontal axis.

You should see the temperature stay near 0 °C while the ice melts. Once all the ice has become water, the temperature can start rising again.

Common Mistake

Forgetting heat losses

In the specific heat capacity practical, not all electrical energy reaches the water. Some energy heats the beaker, heater and surroundings, so insulation and a lid improve the result.

Exam technique

In the exam

Decide whether the question is about a temperature change, a state change, or both.
Convert mass to kilograms and use temperature change, not just the final temperature.
For graph questions, write: sloping section means temperature rises; flat section means change of state at constant temperature.
In practical questions, mention insulation, stirring, measuring mass, measuring temperature change, and reducing energy loss.

Self review

Check yourself

Why does the temperature stay constant while ice is melting?
Which equation would you use to calculate the energy needed to warm 0.40 kg of water by 25 °C?
Name one way to reduce energy transfer by conduction, convection and infrared radiation.

Heating, specific heat and latent heat

What you'll learn

How heating changes the energy stored in particles.
Why temperature sometimes rises, but sometimes stays constant during a change of state.
How to use the equations for specific heat capacity and specific latent heat.
How insulation and the water core practical link to these ideas.

Starting point: particles and energy

Heating means transferring energy into a system. In this topic, a system usually means the substance you are focusing on, such as water in a beaker or ice in a test tube.

Definition

Temperature and thermal energy

Temperature is not the same thing as energy. A large bath of warm water can store more thermal energy than a tiny cup of very hot water because there is much more mass.

What heating does to a system

When you heat a substance, one of two main things can happen:

its temperature increases, because the particles gain kinetic energy and move or vibrate faster
it changes state, because energy is used to change the arrangement or separation of the particles

A change of state is a physical change between solid, liquid and gas, such as melting, freezing, boiling or condensing. No new substance is made.

Heating curve for water showing sloped warming sections and flat melting and boiling sections

Key Idea

Slopes and plateaus

On a sloping part of a heating curve, temperature rises. On a flat part, the substance is changing state, so temperature stays constant while energy changes the potential energy between particles.

Example

Interpreting a heating curve

A sample of ice is heated steadily from below 0 °C until it becomes steam.

On the first sloping section, the ice is still solid, so energy increases the kinetic energy of the particles and the temperature rises.
At 0 °C, the graph is flat because the ice is melting. The energy supplied changes the arrangement of particles rather than increasing their average kinetic energy.
From 0 °C to 100 °C, the liquid water warms up, so the particles move faster and the temperature rises.
At 100 °C, the graph is flat again because the water is boiling. Energy is used to separate particles into a gas.

Specific heat capacity

Definition

Specific heat capacity

The specific heat capacity, symbol $c$ , of a substance is the energy needed to raise the temperature of 1 kg of the substance by 1 °C, without changing its state.

For Edexcel 1PH0, this is a “use” equation, so it is provided on the equation sheet. You still need to know when to choose it, what each symbol means, and how to rearrange it.

ΔQ=m×c×Δθ\Delta Q = m \times c \times \Delta \theta

where:

$ΔQ\Delta Q$ is the change in thermal energy, in joules (J)
$m$ is mass, in kilograms (kg)
$c$ is specific heat capacity, in joules per kilogram degree Celsius (J/kg °C)
$Δθ\Delta \theta$ is change in temperature, in degrees Celsius (°C)

Example

Heating water

A kettle heats 0.75 kg of water from 20 °C to 80 °C. The specific heat capacity of water is 4200 J/kg °C. Calculate the energy transferred to the water.

Choose the specific heat capacity equation because the water’s temperature changes and it does not change state.
Calculate the temperature change: $Δθ=80∘C−20∘C=60∘C\Delta \theta = 80^\circ\text{C} - 20^\circ\text{C} = 60^\circ\text{C}$ .
Substitute into the equation: $J\Delta Q = 0.75 \times 4200 \times 60 = 189000\ \text{J}$ .
Write the result clearly: the energy transferred is 189000 J, or $1.89 \times 10^5\ \text{J}$ .

Common Mistake

Using the final temperature

In $ΔQ=m×c×Δθ\Delta Q = m \times c \times \Delta \theta$ , use the temperature change, not the final temperature. Also convert mass into kilograms before substituting.

Specific latent heat

Definition

Specific latent heat

The specific latent heat, symbol $L$ , of a substance is the energy needed to change the state of 1 kg of the substance without changing its temperature.

The word latent means “hidden”. The energy is being transferred, but it does not show up as a temperature rise.

There are two common types:

specific latent heat of fusion: energy for melting or freezing
specific latent heat of vaporisation: energy for boiling or condensing

For Edexcel 1PH0, this is also provided on the equation sheet:

\times L

where:

$Q$ is the thermal energy needed for the change of state, in joules (J)
$m$ is mass, in kilograms (kg)
$L$ is specific latent heat, in joules per kilogram (J/kg)

The units for latent heat do not include °C because the temperature is not changing.

Example

Melting ice

Calculate the energy needed to melt 0.20 kg of ice at 0 °C. The specific latent heat of fusion of ice is 334000 J/kg.

Choose the latent heat equation because the ice is changing state from solid to liquid at constant temperature.
Substitute into the equation: $\times 334000 = 66800\ \text{J}$ .
Interpret the answer: 66800 J is needed to melt the ice, but the temperature remains at 0 °C until all the ice has melted.

Tip

Choosing the right equation

If the temperature changes, use $ΔQ=m×c×Δθ\Delta Q = m \times c \times \Delta \theta$ . If the state changes, use $\times L$ . If both happen, split the process into stages and add the energies.

Reducing unwanted energy transfer

Thermal insulation means reducing unwanted energy transfer. It can keep hot things hot or cold things cold.

Energy can be transferred by:

conduction: energy transfer through particles in a material, especially in solids
convection: energy transfer by the movement of a liquid or gas
infrared radiation: energy transfer by electromagnetic waves

Common insulation methods include:

thick insulation layers, which make conduction slower
trapped air pockets, which reduce convection currents
lids and draught excluders, which stop warm air escaping
shiny or reflective surfaces, which reduce infrared radiation

Example

Insulating a hot water tank

A hot water tank is fitted with a thick foam jacket and a shiny outer surface.

The thick foam has low thermal conductivity, so it reduces energy transfer by conduction from the hot tank to the colder air.
Air trapped in the foam cannot circulate easily, so convection is reduced.
The shiny surface reflects infrared radiation, so less energy is transferred away by radiation.

Core practical: investigating water

In this core practical, you investigate water by finding its specific heat capacity and by obtaining a temperature-time graph for melting ice.

This setup is used to measure the specific heat capacity of water using an immersion heater, thermometer, insulation and electrical measurements.

Specific heat capacity of water practical setup with insulated beaker, immersion heater, thermometer, meters and balance

Finding the specific heat capacity of water

A typical method is:

Measure the mass of water using a balance.
Put the water in an insulated beaker or calorimeter with a lid.
Measure the starting temperature.
Use an immersion heater to transfer energy to the water for a measured time.
Measure the voltage, current and time, then calculate energy supplied using $\times I \times t$ .
Stir the water and record the final temperature.
Calculate $c$ using $\frac{\Delta Q}{m \times \Delta \theta}$ .

Example

Finding specific heat capacity from practical data

A student heats 0.250 kg of water. The heater has a voltage of 12.0 V and a current of 2.0 A for 180 s. The temperature rises from 18.0 °C to 22.0 °C.

Calculate the electrical energy supplied: $\times I \times t = 12.0 \times 2.0 \times 180 = 4320\ \text{J}$ .
Calculate the temperature change: $Δθ=22.0∘C−18.0∘C=4.0∘C\Delta \theta = 22.0^\circ\text{C} - 18.0^\circ\text{C} = 4.0^\circ\text{C}$ .
Rearrange and substitute: $\frac{4320}{0.250 \times 4.0} = 4320\ \text{J kg}^{-1}\,^\circ\text{C}^{-1}$ .
Compare with the accepted value of about 4200 J/kg °C for water; the result is close, but heat losses and thermometer uncertainty can affect it.

Melting ice temperature-time graph

For the melting ice part, you record temperature at regular time intervals as ice is heated or allowed to warm. Plot temperature on the vertical axis and time on the horizontal axis.

You should see the temperature stay near 0 °C while the ice melts. Once all the ice has become water, the temperature can start rising again.

Common Mistake

Forgetting heat losses

In the specific heat capacity practical, not all electrical energy reaches the water. Some energy heats the beaker, heater and surroundings, so insulation and a lid improve the result.

Exam technique

In the exam

Decide whether the question is about a temperature change, a state change, or both.
Convert mass to kilograms and use temperature change, not just the final temperature.
For graph questions, write: sloping section means temperature rises; flat section means change of state at constant temperature.
In practical questions, mention insulation, stirring, measuring mass, measuring temperature change, and reducing energy loss.

Self review

Check yourself

Why does the temperature stay constant while ice is melting?
Which equation would you use to calculate the energy needed to warm 0.40 kg of water by 25 °C?
Name one way to reduce energy transfer by conduction, convection and infrared radiation.

Heating, specific heat and latent heat

What you'll learn

Starting point: particles and energy

What heating does to a system

Specific heat capacity

Specific latent heat

Reducing unwanted energy transfer

Core practical: investigating water

Finding the specific heat capacity of water

Melting ice temperature-time graph

Recap questions

Heating, specific heat and latent heat

What you'll learn

Starting point: particles and energy

What heating does to a system

Specific heat capacity

Specific latent heat

Reducing unwanted energy transfer

Core practical: investigating water

Finding the specific heat capacity of water

Melting ice temperature-time graph

Recap questions

Heating, specific heat and latent heat

What you'll learn

Starting point: particles and energy

What heating does to a system

Specific heat capacity

Specific latent heat

Reducing unwanted energy transfer

Core practical: investigating water

Finding the specific heat capacity of water

Melting ice temperature-time graph

Recap questions

Heating, specific heat and latent heat Revision Guide

Heating, specific heat and latent heat

What you'll learn

Starting point: particles and energy

What heating does to a system

Specific heat capacity

Specific latent heat

Reducing unwanted energy transfer

Core practical: investigating water

Finding the specific heat capacity of water

Melting ice temperature-time graph

Recap questions

Heating, specific heat and latent heat Revision Guide