Energy stored in a system

Definition

System

An object or group of objects whose energy stores are being considered.

Definition

Internal energy

The total energy stored by the particles of a system in their kinetic and potential energy stores.

Definition

Heating

The transfer of energy from a hotter object to a cooler object because of the temperature difference between them.

A system is the object or group of objects you are studying, such as a pan of water on a hob.
The particles in a system store energy in two ways.
1. The particles are always moving or vibrating, so they have energy in their kinetic energy stores.
2. The particles attract one another and are held at certain distances apart, so they also have energy in their potential energy stores.
The total kinetic and potential energy of all the particles is the internal energy of the system.
Heating transfers energy into a system from something hotter, such as a hob, a flame or an electric heater.
That energy goes into the particles, so heating always increases the internal energy of the system.
The extra energy then has one of two effects: it either raises the temperature of the system or produces a change of state.
Cooling works the other way round, because energy leaves the system, its internal energy decreases, and the substance either falls in temperature or changes state.

Raising the temperature

Definition

Temperature

A measure of how hot or cold an object is, which depends on the average kinetic energy of its particles.

When a substance is heated and is not changing state, the energy transferred goes mainly into the kinetic energy stores of its particles.
The particles then move faster, so the average kinetic energy of the particles goes up.
Temperature depends on the average kinetic energy of the particles, so a higher average kinetic energy means a higher temperature.
In a solid, heating makes the particles vibrate faster and further about their fixed positions.
In a liquid, heating makes the particles slide past one another more quickly.
In a gas, heating makes the particles travel faster in random directions and collide more often.

Producing a change of state

Definition

Melting point

The temperature at which a pure solid changes into a liquid.

Definition

Boiling point

The temperature at which a pure liquid changes into a gas throughout the whole of the liquid.

When a solid reaches its melting point, further heating stops raising its temperature and makes the solid melt instead.
During melting, the energy transferred goes into the potential energy stores of the particles rather than their kinetic energy stores.
This energy is used to overcome the forces of attraction that hold the particles in fixed positions, so the particles break out of their regular pattern and can move past one another.
The average kinetic energy of the particles does not change, so the temperature stays constant until all of the solid has melted.
Pure ice melts at $∘C0\ ^\circ\text{C}$ , and a glass of iced water stays at about $∘C0\ ^\circ\text{C}$ until every piece of ice has gone, even though it is taking in energy from the warm room.
When a liquid reaches its boiling point, further heating makes it boil, and the energy is used to pull the particles completely apart so that they escape as a gas.
Water boils at $∘C100\ ^\circ\text{C}$ at normal atmospheric pressure, and a pan of boiling pasta water stays at $∘C100\ ^\circ\text{C}$ however high the hob is turned up, with the extra energy making it boil away faster.
Once the change of state is complete, the energy goes back into the kinetic energy stores of the particles and the temperature starts to rise again.
The same idea works in reverse, because a liquid that is freezing or a gas that is condensing gives out energy while its temperature stays constant.
The internal energy of a system therefore goes up during melting and boiling, even though its temperature does not.

Heating curves

Definition

Heating curve

A graph of temperature against time for a substance heated at a steady rate, showing where its temperature rises and where it changes state.

A heating curve shows how the temperature of a substance changes with time when it is heated at a steady rate.
Temperature goes on the vertical axis in $∘C^\circ\text{C}$ , and time goes on the horizontal axis in $s\text{s}$ or $min\text{min}$ .
For ice taken from a freezer at $−18 ∘C-18\ ^\circ\text{C}$ $- 18^{\circ} C$ and heated steadily, the graph has four main sections.
1. The line first slopes upwards as the solid ice warms from $∘C-18\ ^\circ\text{C}$ to $∘C0\ ^\circ\text{C}$ .
2. The line then runs flat at $∘C0\ ^\circ\text{C}$ while the ice melts, with solid and liquid present together.
3. The line slopes upwards again as the liquid water warms from $∘C0\ ^\circ\text{C}$ to $∘C100\ ^\circ\text{C}$ .
4. The line runs flat a second time at $∘C100\ ^\circ\text{C}$ while the water boils and turns into steam.
The flat sections show where the substance is changing state, and the sloping sections show where its temperature is rising in a single state.
The flat section for boiling lasts much longer than the one for melting, because separating the particles completely to form a gas takes far more energy than loosening them to form a liquid.
A cooling curve is the mirror image, with a flat section at the boiling point while the gas condenses and another at the melting point while the liquid freezes.

Example

Reading a heating curve

A beaker of crushed ice starts at $∘C-10\ ^\circ\text{C}$ and is heated at a steady rate.
From $0$ to $2$ minutes the temperature rises to $∘C0\ ^\circ\text{C}$ , so the ice is warming as a solid and its particles are gaining kinetic energy.
From $2$ to $9$ minutes the temperature stays at $∘C0\ ^\circ\text{C}$ , so the ice is melting and the energy is overcoming the forces between the particles.
From $9$ minutes onwards the temperature rises steadily, so all the ice has melted and the liquid water is warming.
The internal energy of the contents of the beaker increases during all three sections, including the flat one.

Practical

Recording the temperature of ice as it is heated

Aim: to record the temperature of crushed ice at regular intervals as it is heated until the water boils, and to plot a heating curve from the readings.
Apparatus: a $cm3250\ \text{cm}^3$ beaker, crushed ice straight from a freezer, a thermometer with a range of $∘C-10\ ^\circ\text{C}$ to $∘C110\ ^\circ\text{C}$ , a clamp stand with boss and clamp, a stirring rod, a Bunsen burner with tripod, gauze and heatproof mat, a stopwatch and eye protection.
Method:
- Fill the beaker about half full with crushed ice, because small pieces pack closely around the thermometer bulb and warm evenly.
- Clamp the thermometer so that its bulb sits in the middle of the ice and does not touch the bottom or sides of the beaker, where the glass is hotter than the contents.
- Read the starting temperature with your eye level with the top of the liquid column, and expect it to be a little below $∘C0\ ^\circ\text{C}$ .
- Light the Bunsen burner on a small blue flame under the gauze and start the stopwatch at the same moment.
- Stir the contents gently with the stirring rod and record the temperature every $s30\ \text{s}$ , writing beside each reading whether you see solid only, solid and liquid, liquid only, or bubbling liquid.
- Keep the flame the same size all the way through, so that energy is supplied at a steady rate.
- Carry on until the water has been boiling steadily for about $3$ minutes, then turn off the gas.
- Plot temperature on the vertical axis against time on the horizontal axis, and join the points with a smooth line.
Variables: time is the independent variable, temperature is the dependent variable, and the mass of ice and the size of the flame are kept the same.
Results: the temperature rises to $∘C0\ ^\circ\text{C}$ , stays level while the ice melts, rises steadily through the liquid, and then levels off close to $∘C100\ ^\circ\text{C}$ while the water boils.
Watch out: a bulb touching the glass reads too high, an unstirred beaker leaves warm water at the bottom and ice at the top so the flat section looks sloped, and reading the scale from above or below gives a parallax error.
Safety: wear eye protection, stand up while heating, keep clear of the steam because it scalds, never stir with the thermometer because it can break, and leave the beaker to cool before moving it.

Common Mistake

Do not say that the temperature rises while a substance melts or boils, because the energy is going into the potential energy stores of the particles.
Do not say that no energy is being transferred during a flat section of a heating curve, because heating carries on and the internal energy keeps increasing.
Do not confuse temperature with internal energy, because a bath of warm water has far more internal energy than a mug of boiling water even though its temperature is lower.
Do not use the phrase heat energy, because heating is a way of transferring energy rather than a store of energy.

Exam technique

Explaining the flat sections

A question about a flat section of a heating curve usually carries two or three marks.
State that energy is still being transferred to the substance, so its internal energy is increasing.
State that this energy is used to overcome the forces of attraction between the particles, so that they can change their arrangement.
State that the kinetic energy of the particles is not increasing, so the temperature stays the same.
For a sloping section, link the rising temperature to the particles gaining kinetic energy and moving faster.

Self review

Name the two energy stores that together make up the internal energy of a system.
Describe the two effects that heating can have on a substance.
Explain why the temperature of melting ice stays at $∘C0\ ^\circ\text{C}$ even though energy is being transferred to it.
Sketch the shape of a heating curve for ice warmed from $∘C-10\ ^\circ\text{C}$ until the water boils.
State the range of thermometer you would choose to record the temperature of ice as it is heated to boiling.

Energy stored in a system

Definition

System

An object or group of objects whose energy stores are being considered.

Definition

Internal energy

The total energy stored by the particles of a system in their kinetic and potential energy stores.

Definition

Heating

The transfer of energy from a hotter object to a cooler object because of the temperature difference between them.

A system is the object or group of objects you are studying, such as a pan of water on a hob.
The particles in a system store energy in two ways.
1. The particles are always moving or vibrating, so they have energy in their kinetic energy stores.
2. The particles attract one another and are held at certain distances apart, so they also have energy in their potential energy stores.
The total kinetic and potential energy of all the particles is the internal energy of the system.
Heating transfers energy into a system from something hotter, such as a hob, a flame or an electric heater.
That energy goes into the particles, so heating always increases the internal energy of the system.
The extra energy then has one of two effects: it either raises the temperature of the system or produces a change of state.
Cooling works the other way round, because energy leaves the system, its internal energy decreases, and the substance either falls in temperature or changes state.

Raising the temperature

Definition

Temperature

A measure of how hot or cold an object is, which depends on the average kinetic energy of its particles.

When a substance is heated and is not changing state, the energy transferred goes mainly into the kinetic energy stores of its particles.
The particles then move faster, so the average kinetic energy of the particles goes up.
Temperature depends on the average kinetic energy of the particles, so a higher average kinetic energy means a higher temperature.
In a solid, heating makes the particles vibrate faster and further about their fixed positions.
In a liquid, heating makes the particles slide past one another more quickly.
In a gas, heating makes the particles travel faster in random directions and collide more often.

Producing a change of state

Definition

Melting point

The temperature at which a pure solid changes into a liquid.

Definition

Boiling point

The temperature at which a pure liquid changes into a gas throughout the whole of the liquid.

When a solid reaches its melting point, further heating stops raising its temperature and makes the solid melt instead.
During melting, the energy transferred goes into the potential energy stores of the particles rather than their kinetic energy stores.
This energy is used to overcome the forces of attraction that hold the particles in fixed positions, so the particles break out of their regular pattern and can move past one another.
The average kinetic energy of the particles does not change, so the temperature stays constant until all of the solid has melted.
Pure ice melts at $∘C0\ ^\circ\text{C}$ , and a glass of iced water stays at about $∘C0\ ^\circ\text{C}$ until every piece of ice has gone, even though it is taking in energy from the warm room.
When a liquid reaches its boiling point, further heating makes it boil, and the energy is used to pull the particles completely apart so that they escape as a gas.
Water boils at $∘C100\ ^\circ\text{C}$ at normal atmospheric pressure, and a pan of boiling pasta water stays at $∘C100\ ^\circ\text{C}$ however high the hob is turned up, with the extra energy making it boil away faster.
Once the change of state is complete, the energy goes back into the kinetic energy stores of the particles and the temperature starts to rise again.
The same idea works in reverse, because a liquid that is freezing or a gas that is condensing gives out energy while its temperature stays constant.
The internal energy of a system therefore goes up during melting and boiling, even though its temperature does not.

Heating curves

Definition

Heating curve

A graph of temperature against time for a substance heated at a steady rate, showing where its temperature rises and where it changes state.

A heating curve shows how the temperature of a substance changes with time when it is heated at a steady rate.
Temperature goes on the vertical axis in $∘C^\circ\text{C}$ , and time goes on the horizontal axis in $s\text{s}$ or $min\text{min}$ .
For ice taken from a freezer at $−18 ∘C-18\ ^\circ\text{C}$ $- 18^{\circ} C$ and heated steadily, the graph has four main sections.
1. The line first slopes upwards as the solid ice warms from $∘C-18\ ^\circ\text{C}$ to $∘C0\ ^\circ\text{C}$ .
2. The line then runs flat at $∘C0\ ^\circ\text{C}$ while the ice melts, with solid and liquid present together.
3. The line slopes upwards again as the liquid water warms from $∘C0\ ^\circ\text{C}$ to $∘C100\ ^\circ\text{C}$ .
4. The line runs flat a second time at $∘C100\ ^\circ\text{C}$ while the water boils and turns into steam.
The flat sections show where the substance is changing state, and the sloping sections show where its temperature is rising in a single state.
The flat section for boiling lasts much longer than the one for melting, because separating the particles completely to form a gas takes far more energy than loosening them to form a liquid.
A cooling curve is the mirror image, with a flat section at the boiling point while the gas condenses and another at the melting point while the liquid freezes.

Example

Reading a heating curve

A beaker of crushed ice starts at $∘C-10\ ^\circ\text{C}$ and is heated at a steady rate.
From $0$ to $2$ minutes the temperature rises to $∘C0\ ^\circ\text{C}$ , so the ice is warming as a solid and its particles are gaining kinetic energy.
From $2$ to $9$ minutes the temperature stays at $∘C0\ ^\circ\text{C}$ , so the ice is melting and the energy is overcoming the forces between the particles.
From $9$ minutes onwards the temperature rises steadily, so all the ice has melted and the liquid water is warming.
The internal energy of the contents of the beaker increases during all three sections, including the flat one.

Practical

Recording the temperature of ice as it is heated

Aim: to record the temperature of crushed ice at regular intervals as it is heated until the water boils, and to plot a heating curve from the readings.
Apparatus: a $cm3250\ \text{cm}^3$ beaker, crushed ice straight from a freezer, a thermometer with a range of $∘C-10\ ^\circ\text{C}$ to $∘C110\ ^\circ\text{C}$ , a clamp stand with boss and clamp, a stirring rod, a Bunsen burner with tripod, gauze and heatproof mat, a stopwatch and eye protection.
Method:
- Fill the beaker about half full with crushed ice, because small pieces pack closely around the thermometer bulb and warm evenly.
- Clamp the thermometer so that its bulb sits in the middle of the ice and does not touch the bottom or sides of the beaker, where the glass is hotter than the contents.
- Read the starting temperature with your eye level with the top of the liquid column, and expect it to be a little below $∘C0\ ^\circ\text{C}$ .
- Light the Bunsen burner on a small blue flame under the gauze and start the stopwatch at the same moment.
- Stir the contents gently with the stirring rod and record the temperature every $s30\ \text{s}$ , writing beside each reading whether you see solid only, solid and liquid, liquid only, or bubbling liquid.
- Keep the flame the same size all the way through, so that energy is supplied at a steady rate.
- Carry on until the water has been boiling steadily for about $3$ minutes, then turn off the gas.
- Plot temperature on the vertical axis against time on the horizontal axis, and join the points with a smooth line.
Variables: time is the independent variable, temperature is the dependent variable, and the mass of ice and the size of the flame are kept the same.
Results: the temperature rises to $∘C0\ ^\circ\text{C}$ , stays level while the ice melts, rises steadily through the liquid, and then levels off close to $∘C100\ ^\circ\text{C}$ while the water boils.
Watch out: a bulb touching the glass reads too high, an unstirred beaker leaves warm water at the bottom and ice at the top so the flat section looks sloped, and reading the scale from above or below gives a parallax error.
Safety: wear eye protection, stand up while heating, keep clear of the steam because it scalds, never stir with the thermometer because it can break, and leave the beaker to cool before moving it.

Common Mistake

Do not say that the temperature rises while a substance melts or boils, because the energy is going into the potential energy stores of the particles.
Do not say that no energy is being transferred during a flat section of a heating curve, because heating carries on and the internal energy keeps increasing.
Do not confuse temperature with internal energy, because a bath of warm water has far more internal energy than a mug of boiling water even though its temperature is lower.
Do not use the phrase heat energy, because heating is a way of transferring energy rather than a store of energy.

Exam technique

Explaining the flat sections

A question about a flat section of a heating curve usually carries two or three marks.
State that energy is still being transferred to the substance, so its internal energy is increasing.
State that this energy is used to overcome the forces of attraction between the particles, so that they can change their arrangement.
State that the kinetic energy of the particles is not increasing, so the temperature stays the same.
For a sloping section, link the rising temperature to the particles gaining kinetic energy and moving faster.

Self review

Name the two energy stores that together make up the internal energy of a system.
Describe the two effects that heating can have on a substance.
Explain why the temperature of melting ice stays at $∘C0\ ^\circ\text{C}$ even though energy is being transferred to it.
Sketch the shape of a heating curve for ice warmed from $∘C-10\ ^\circ\text{C}$ until the water boils.
State the range of thermometer you would choose to record the temperature of ice as it is heated to boiling.

1.2.3 Heating, temperature and changes of state

Energy stored in a system

Raising the temperature

Producing a change of state

Heating curves

Reading a heating curve

Recording the temperature of ice as it is heated

Explaining the flat sections

Review 1.2.3 Heating, temperature and changes of state by teaching Genie

1.2.3 Heating, temperature and changes of state

Energy stored in a system

Raising the temperature

Producing a change of state

Heating curves

Reading a heating curve

Recording the temperature of ice as it is heated

Explaining the flat sections

Review 1.2.3 Heating, temperature and changes of state by teaching Genie

1.2.3 Heating, temperature and changes of state

Energy stored in a system

Raising the temperature

Producing a change of state

Heating curves

Reading a heating curve

Recording the temperature of ice as it is heated

Explaining the flat sections

Review 1.2.3 Heating, temperature and changes of state by teaching Genie

1.2.3 Heating, temperature and changes of state Revision Guide

1.2.3 Heating, temperature and changes of state

Energy stored in a system

Raising the temperature

Producing a change of state

Heating curves

Reading a heating curve

Recording the temperature of ice as it is heated

Explaining the flat sections

Review 1.2.3 Heating, temperature and changes of state by teaching Genie

1.2.3 Heating, temperature and changes of state Revision Guide