Specific heat capacity

Definition

Specific heat capacity

The energy needed to raise the temperature of $kg1\ \text{kg}$ of a substance by $∘C1\ ^\circ\text{C}$ .

Different materials need different amounts of energy to warm up by the same number of degrees.
The specific heat capacity of a material is the energy needed to raise the temperature of $kg1\ \text{kg}$ of it by $∘C1\ ^\circ\text{C}$ .
Its symbol is $c$ , and its unit is the joule per kilogram per degree Celsius, $∘C\text{J/kg}\,^\circ\text{C}$ .
Water has a specific heat capacity of about $∘C4200\ \text{J/kg}\,^\circ\text{C}$ , so $J4200\ \text{J}$ is needed to warm $kg1\ \text{kg}$ of water by just $∘C1\ ^\circ\text{C}$ .
Aluminium has a specific heat capacity of about $∘C900\ \text{J/kg}\,^\circ\text{C}$ and copper about $∘C390\ \text{J/kg}\,^\circ\text{C}$ , so the same energy warms $kg1\ \text{kg}$ of copper by more than ten times as much as $kg1\ \text{kg}$ of water.
A material with a high specific heat capacity warms up slowly and cools down slowly, because it must gain or lose a lot of energy for each degree of temperature change.
A material with a low specific heat capacity warms up and cools down quickly.
On a sunny day at the beach, the dry sand becomes too hot to walk on barefoot while the sea stays cool, partly because sand has a much lower specific heat capacity than water.
Central heating systems pump hot water round the radiators because each kilogram of water carries a large amount of energy from the boiler to the rooms.
Specific heat capacity applies only while a substance stays in the same state, because the temperature does not change at all while the state is changing.

Specific latent heat

Definition

Specific latent heat

The energy needed to change the state of $kg1\ \text{kg}$ of a substance without any change in its temperature.

Definition

Specific latent heat of fusion

The energy needed to change $kg1\ \text{kg}$ of a substance from solid to liquid without any change in its temperature.

Definition

Specific latent heat of vaporisation

The energy needed to change $kg1\ \text{kg}$ of a substance from liquid to gas without any change in its temperature.

During a change of state, energy is transferred to or from a substance while its temperature stays constant.
That energy goes into or comes out of the potential energy stores of the particles as they move apart or closer together, rather than changing their kinetic energy.
The specific latent heat of a substance is the energy needed to change the state of $kg1\ \text{kg}$ of it without changing its temperature.
Its symbol is $L$ , and its unit is the joule per kilogram, $J/kg\text{J/kg}$ .
There is no degree Celsius in the unit, because the temperature does not change during a change of state.
The specific latent heat of fusion applies when a substance melts or freezes.
The specific latent heat of vaporisation applies when a substance boils or condenses.
For water, the specific latent heat of fusion is about $3.34 \times 10^{5}\ \text{J/kg}$ and the specific latent heat of vaporisation is about $2.26 \times 10^{6}\ \text{J/kg}$ .
The value for vaporisation is almost seven times larger, because turning a liquid into a gas means pulling the particles completely apart, whereas melting only frees them from their fixed positions.
The energy taken in when $kg1\ \text{kg}$ of a substance melts is given out again when $kg1\ \text{kg}$ of it freezes, and the same is true for boiling and condensing.
This is why a scald from steam at $∘C100\ ^\circ\text{C}$ is much worse than one from water at the same temperature, since the steam releases its latent heat of vaporisation as it condenses on the skin.

Comparing the two quantities

Both quantities describe the energy needed per kilogram of a substance, but they describe different things happening to it.
Specific heat capacity is about a change in temperature with no change of state.
Specific latent heat is about a change of state with no change in temperature.
During a temperature change, the energy transferred mainly increases the kinetic energy of the particles.
During a change of state, the energy transferred increases the potential energy of the particles.
The unit of specific heat capacity is $∘C\text{J/kg}\,^\circ\text{C}$ , while the unit of specific latent heat is $J/kg\text{J/kg}$ .
On a heating curve, specific heat capacity decides how steep the sloping sections are, and specific latent heat decides how long the flat sections last.

Practical

Specific heat capacity of a metal

Aim: to measure the energy supplied to a metal block and the rise in its temperature, and use them to find the specific heat capacity of the metal.
Apparatus: a $kg1\ \text{kg}$ aluminium block with two holes drilled in its top, a $V12\ \text{V}$ electric immersion heater, a low-voltage power supply, a joulemeter, a thermometer reading to $∘C0.5\ ^\circ\text{C}$ or a temperature probe and data logger, a pipette with a little water, insulating material such as foam lagging, a heatproof mat, a stopwatch and an electronic balance.
Method:
- Measure the mass of the block on the electronic balance and write it in kilograms.
- Stand the block on the heatproof mat and wrap its sides and top in insulation, leaving the two holes uncovered.
- Slide the heater into the larger hole and the thermometer into the smaller one, adding a few drops of water to the thermometer hole so the bulb makes good thermal contact with the metal.
- Connect the heater to the power supply through the joulemeter, and reset the joulemeter to zero.
- Record the starting temperature of the block once the reading is steady.
- Switch on and let the heater run for about $10$ minutes, recording the joulemeter reading and the temperature every minute.
- Switch off and keep watching the thermometer, recording the highest temperature reached, because energy carries on spreading from the hot heater into the block for a short time.
- Work out the temperature rise by subtracting the starting temperature from the highest temperature.
Variables: the energy supplied is the independent variable, the temperature rise is the dependent variable, and the block, its mass and its insulation stay the same.
Maths: the specific heat capacity is $\dfrac{\Delta E}{m\,\Delta\theta}$ , where $ΔE\Delta E$ is the joulemeter reading, $m$ is the mass of the block and $Δθ\Delta\theta$ is the temperature rise.
Graph: plotting temperature against energy supplied gives a straight line, and its gradient equals $c\dfrac{1}{m\,c}$ , so the result uses every reading rather than just the first and last.
Results: a typical class value for aluminium is about $∘C1000\ \text{J/kg}\,^\circ\text{C}$ , a little above the accepted value of about $∘C900\ \text{J/kg}\,^\circ\text{C}$ .
Watch out: some of the energy recorded by the joulemeter warms the heater, the thermometer and the surrounding air instead of the block, so the calculated value comes out too high, and a dry thermometer hole makes the reading lag behind the true temperature.
Safety: the heater and block become hot enough to burn, so leave them on the heatproof mat to cool before handling, and keep water away from the power supply.

Common Mistake

Do not mix up the two units, because specific heat capacity has a degree Celsius in its unit and specific latent heat does not.
Do not use specific latent heat for a temperature change, or specific heat capacity for a change of state.
Do not swap fusion and vaporisation, because fusion goes with melting and freezing while vaporisation goes with boiling and condensing.
Do not leave $kg1\ \text{kg}$ out of either definition, because both quantities are measured per kilogram.

Exam technique

Writing the definitions

A definition of specific heat capacity needs three ideas: the energy needed, $kg1\ \text{kg}$ of the substance, and a temperature rise of $∘C1\ ^\circ\text{C}$ .
A definition of specific latent heat needs the energy needed, $kg1\ \text{kg}$ of the substance, a change of state, and no change in temperature.
An answer such as the heat needed to make something hotter scores nothing, because it gives no mass and no size of temperature change.
When explaining the insulation in the practical, say that it reduces energy transfer to the surroundings so that more of the measured energy heats the block, rather than writing that it makes the result more accurate.
When explaining why the calculated value is too high, say that some energy was transferred to the surroundings, so the energy that heated the block was less than the joulemeter reading.

Self review

State the definition of specific heat capacity.
State the unit of specific latent heat and explain why it has no temperature in it.
Name the specific latent heat used when ice melts and the one used when steam condenses.
Explain why dry sand on a beach heats up much faster than the sea on a sunny day.
Explain why the specific heat capacity found for a metal block in the practical is usually higher than the accepted value.

Specific heat capacity

Definition

Specific heat capacity

The energy needed to raise the temperature of $kg1\ \text{kg}$ of a substance by $∘C1\ ^\circ\text{C}$ .

Different materials need different amounts of energy to warm up by the same number of degrees.
The specific heat capacity of a material is the energy needed to raise the temperature of $kg1\ \text{kg}$ of it by $∘C1\ ^\circ\text{C}$ .
Its symbol is $c$ , and its unit is the joule per kilogram per degree Celsius, $∘C\text{J/kg}\,^\circ\text{C}$ .
Water has a specific heat capacity of about $∘C4200\ \text{J/kg}\,^\circ\text{C}$ , so $J4200\ \text{J}$ is needed to warm $kg1\ \text{kg}$ of water by just $∘C1\ ^\circ\text{C}$ .
Aluminium has a specific heat capacity of about $∘C900\ \text{J/kg}\,^\circ\text{C}$ and copper about $∘C390\ \text{J/kg}\,^\circ\text{C}$ , so the same energy warms $kg1\ \text{kg}$ of copper by more than ten times as much as $kg1\ \text{kg}$ of water.
A material with a high specific heat capacity warms up slowly and cools down slowly, because it must gain or lose a lot of energy for each degree of temperature change.
A material with a low specific heat capacity warms up and cools down quickly.
On a sunny day at the beach, the dry sand becomes too hot to walk on barefoot while the sea stays cool, partly because sand has a much lower specific heat capacity than water.
Central heating systems pump hot water round the radiators because each kilogram of water carries a large amount of energy from the boiler to the rooms.
Specific heat capacity applies only while a substance stays in the same state, because the temperature does not change at all while the state is changing.

Specific latent heat

Definition

Specific latent heat

The energy needed to change the state of $kg1\ \text{kg}$ of a substance without any change in its temperature.

Definition

Specific latent heat of fusion

The energy needed to change $kg1\ \text{kg}$ of a substance from solid to liquid without any change in its temperature.

Definition

Specific latent heat of vaporisation

The energy needed to change $kg1\ \text{kg}$ of a substance from liquid to gas without any change in its temperature.

During a change of state, energy is transferred to or from a substance while its temperature stays constant.
That energy goes into or comes out of the potential energy stores of the particles as they move apart or closer together, rather than changing their kinetic energy.
The specific latent heat of a substance is the energy needed to change the state of $kg1\ \text{kg}$ of it without changing its temperature.
Its symbol is $L$ , and its unit is the joule per kilogram, $J/kg\text{J/kg}$ .
There is no degree Celsius in the unit, because the temperature does not change during a change of state.
The specific latent heat of fusion applies when a substance melts or freezes.
The specific latent heat of vaporisation applies when a substance boils or condenses.
For water, the specific latent heat of fusion is about $3.34 \times 10^{5}\ \text{J/kg}$ and the specific latent heat of vaporisation is about $2.26 \times 10^{6}\ \text{J/kg}$ .
The value for vaporisation is almost seven times larger, because turning a liquid into a gas means pulling the particles completely apart, whereas melting only frees them from their fixed positions.
The energy taken in when $kg1\ \text{kg}$ of a substance melts is given out again when $kg1\ \text{kg}$ of it freezes, and the same is true for boiling and condensing.
This is why a scald from steam at $∘C100\ ^\circ\text{C}$ is much worse than one from water at the same temperature, since the steam releases its latent heat of vaporisation as it condenses on the skin.

Comparing the two quantities

Both quantities describe the energy needed per kilogram of a substance, but they describe different things happening to it.
Specific heat capacity is about a change in temperature with no change of state.
Specific latent heat is about a change of state with no change in temperature.
During a temperature change, the energy transferred mainly increases the kinetic energy of the particles.
During a change of state, the energy transferred increases the potential energy of the particles.
The unit of specific heat capacity is $∘C\text{J/kg}\,^\circ\text{C}$ , while the unit of specific latent heat is $J/kg\text{J/kg}$ .
On a heating curve, specific heat capacity decides how steep the sloping sections are, and specific latent heat decides how long the flat sections last.

Practical

Specific heat capacity of a metal

Aim: to measure the energy supplied to a metal block and the rise in its temperature, and use them to find the specific heat capacity of the metal.
Apparatus: a $kg1\ \text{kg}$ aluminium block with two holes drilled in its top, a $V12\ \text{V}$ electric immersion heater, a low-voltage power supply, a joulemeter, a thermometer reading to $∘C0.5\ ^\circ\text{C}$ or a temperature probe and data logger, a pipette with a little water, insulating material such as foam lagging, a heatproof mat, a stopwatch and an electronic balance.
Method:
- Measure the mass of the block on the electronic balance and write it in kilograms.
- Stand the block on the heatproof mat and wrap its sides and top in insulation, leaving the two holes uncovered.
- Slide the heater into the larger hole and the thermometer into the smaller one, adding a few drops of water to the thermometer hole so the bulb makes good thermal contact with the metal.
- Connect the heater to the power supply through the joulemeter, and reset the joulemeter to zero.
- Record the starting temperature of the block once the reading is steady.
- Switch on and let the heater run for about $10$ minutes, recording the joulemeter reading and the temperature every minute.
- Switch off and keep watching the thermometer, recording the highest temperature reached, because energy carries on spreading from the hot heater into the block for a short time.
- Work out the temperature rise by subtracting the starting temperature from the highest temperature.
Variables: the energy supplied is the independent variable, the temperature rise is the dependent variable, and the block, its mass and its insulation stay the same.
Maths: the specific heat capacity is $\dfrac{\Delta E}{m\,\Delta\theta}$ , where $ΔE\Delta E$ is the joulemeter reading, $m$ is the mass of the block and $Δθ\Delta\theta$ is the temperature rise.
Graph: plotting temperature against energy supplied gives a straight line, and its gradient equals $c\dfrac{1}{m\,c}$ , so the result uses every reading rather than just the first and last.
Results: a typical class value for aluminium is about $∘C1000\ \text{J/kg}\,^\circ\text{C}$ , a little above the accepted value of about $∘C900\ \text{J/kg}\,^\circ\text{C}$ .
Watch out: some of the energy recorded by the joulemeter warms the heater, the thermometer and the surrounding air instead of the block, so the calculated value comes out too high, and a dry thermometer hole makes the reading lag behind the true temperature.
Safety: the heater and block become hot enough to burn, so leave them on the heatproof mat to cool before handling, and keep water away from the power supply.

Common Mistake

Do not mix up the two units, because specific heat capacity has a degree Celsius in its unit and specific latent heat does not.
Do not use specific latent heat for a temperature change, or specific heat capacity for a change of state.
Do not swap fusion and vaporisation, because fusion goes with melting and freezing while vaporisation goes with boiling and condensing.
Do not leave $kg1\ \text{kg}$ out of either definition, because both quantities are measured per kilogram.

Exam technique

Writing the definitions

A definition of specific heat capacity needs three ideas: the energy needed, $kg1\ \text{kg}$ of the substance, and a temperature rise of $∘C1\ ^\circ\text{C}$ .
A definition of specific latent heat needs the energy needed, $kg1\ \text{kg}$ of the substance, a change of state, and no change in temperature.
An answer such as the heat needed to make something hotter scores nothing, because it gives no mass and no size of temperature change.
When explaining the insulation in the practical, say that it reduces energy transfer to the surroundings so that more of the measured energy heats the block, rather than writing that it makes the result more accurate.
When explaining why the calculated value is too high, say that some energy was transferred to the surroundings, so the energy that heated the block was less than the joulemeter reading.

Self review

State the definition of specific heat capacity.
State the unit of specific latent heat and explain why it has no temperature in it.
Name the specific latent heat used when ice melts and the one used when steam condenses.
Explain why dry sand on a beach heats up much faster than the sea on a sunny day.
Explain why the specific heat capacity found for a metal block in the practical is usually higher than the accepted value.

1.2.4 Specific heat capacity and specific latent heat

Specific heat capacity

Specific latent heat

Comparing the two quantities

Specific heat capacity of a metal

Writing the definitions

Review 1.2.4 Specific heat capacity and specific latent heat by teaching Genie

1.2.4 Specific heat capacity and specific latent heat

Specific heat capacity

Specific latent heat

Comparing the two quantities

Specific heat capacity of a metal

Writing the definitions

Review 1.2.4 Specific heat capacity and specific latent heat by teaching Genie

1.2.4 Specific heat capacity and specific latent heat

Specific heat capacity

Specific latent heat

Comparing the two quantities

Specific heat capacity of a metal

Writing the definitions

Review 1.2.4 Specific heat capacity and specific latent heat by teaching Genie

1.2.4 Specific heat capacity and specific latent heat Revision Guide

1.2.4 Specific heat capacity and specific latent heat

Specific heat capacity

Specific latent heat

Comparing the two quantities

Specific heat capacity of a metal

Writing the definitions

Review 1.2.4 Specific heat capacity and specific latent heat by teaching Genie

1.2.4 Specific heat capacity and specific latent heat Revision Guide