Specific heat capacity

Definition

Specific heat capacity

Specific heat capacity is the energy needed to raise the temperature of one kilogram of a substance by one degree Celsius.

Different materials need different amounts of energy to warm up by the same number of degrees, and specific heat capacity is the quantity that measures that difference.
Its symbol is $c$ and its unit is joules per kilogram per degree Celsius, written $∘C\text{J/kg}\,^\circ\text{C}$ .
The word specific means the value is quoted for one kilogram, so the mass has already been divided out and the value belongs to the material rather than to a particular object.
Water has an unusually high value of about $∘C4200\ \text{J/kg}\,^\circ\text{C}$ , while aluminium is about $∘C900\ \text{J/kg}\,^\circ\text{C}$ and copper about $∘C385\ \text{J/kg}\,^\circ\text{C}$ .
A high specific heat capacity means the material warms up slowly for a given energy input, and it also cools down slowly.
A low specific heat capacity means the material heats up quickly, which is why a copper pan base reaches cooking temperature much faster than the water inside it.
Water is used to carry energy around a central heating system because its high value lets each kilogram carry a large amount of energy for a modest temperature change.
The same property explains why the sea warms up and cools down far more slowly than the land around it.
Ice, liquid water and steam each have their own specific heat capacity, because the arrangement of the molecules is different in each state.

Specific latent heat

Definition

Specific latent heat

Specific latent heat is the energy needed to change the state of one kilogram of a substance without changing its temperature.

Definition

Specific latent heat of fusion

Specific latent heat of fusion is the energy needed to melt one kilogram of a substance at its melting point without changing its temperature.

Definition

Specific latent heat of vaporisation

Specific latent heat of vaporisation is the energy needed to boil one kilogram of a substance at its boiling point without changing its temperature.

Energy is still needed to change the state of a substance even though its temperature does not change, and specific latent heat measures how much energy each kilogram needs.
Its symbol is $L$ and its unit is joules per kilogram, written $J/kg\text{J/kg}$ .
There is no temperature in the unit, because the temperature is constant throughout the change of state.
Fusion refers to the change between solid and liquid, so it covers both melting and freezing.
Vaporisation refers to the change between liquid and gas, so it covers both boiling and condensing.
For water the specific latent heat of fusion is about $J/kg3.34\times10^{5}\ \text{J/kg}$ and the specific latent heat of vaporisation is about $J/kg2.26\times10^{6}\ \text{J/kg}$ .
Vaporisation always needs more energy than fusion for the same substance, because melting only frees the particles from their fixed positions while boiling separates them completely.
The value works in both directions, so freezing one kilogram of water releases the same energy that melting one kilogram of ice absorbs.

Comparing the two quantities

Both quantities are quoted per kilogram, so both tell you the energy involved for a $kg1\ \text{kg}$ sample of the substance.
Specific heat capacity applies while the substance stays in one state and its temperature is changing.
Specific latent heat applies while the substance is changing state and its temperature is constant.
The energy in the specific heat capacity case changes the average kinetic energy of the particles, so the temperature moves.
The energy in the specific latent heat case changes the arrangement of the particles and overcomes the forces between them, so the temperature holds still.
The units separate the two: a temperature appears in $∘C\text{J/kg}\,^\circ\text{C}$ but not in $J/kg\text{J/kg}$ .
One substance has a specific heat capacity for each of its states, but only two specific latent heats, one for fusion and one for vaporisation.
Specific latent heat values are usually far larger than the energy needed to warm the same mass by a few degrees, which is why melting and boiling stages dominate the energy needed to take a substance through a wide temperature range.

Example

Choosing the right quantity at each stage

Ice at $∘C-5\,^\circ\text{C}$ is warmed to $∘C0\,^\circ\text{C}$ , which is a temperature change within one state, so the specific heat capacity of ice applies.
The ice at $∘C0\,^\circ\text{C}$ then melts into water at $∘C0\,^\circ\text{C}$ , which is a change of state, so the specific latent heat of fusion applies.
The water is warmed from $∘C0\,^\circ\text{C}$ to $∘C100\,^\circ\text{C}$ , so the specific heat capacity of liquid water applies to that stage.
The water at $∘C100\,^\circ\text{C}$ then boils into steam at $∘C100\,^\circ\text{C}$ , so the specific latent heat of vaporisation applies.
Each kilogram needs about $J3.34\times10^{5}\ \text{J}$ for the melting stage and about $J2.26\times10^{6}\ \text{J}$ for the boiling stage.
The boiling stage therefore needs by far the most energy of the four stages, even though it produces no change in temperature at all.

Exam technique

Writing the two definitions

Include the energy, the mass of one kilogram and the temperature rise of one degree Celsius in a definition of specific heat capacity, because all three are needed for full marks.
Include the energy, the mass of one kilogram and the phrase without a change in temperature in a definition of specific latent heat.
Name the change of state you mean, because fusion and vaporisation have different values for the same substance.
Quote the units carefully, since the presence or absence of the degree Celsius is often the mark that separates the two quantities.
Give a matching statement about each quantity in a compare question, so the examiner can see the two sides of the difference.
Mention the particles when you are asked to explain the difference, since the arrangement changing rather than the speed changing is the real distinction.

Common Mistake

Do not leave the mass out of a definition, because both quantities are defined for one kilogram of the substance.
Do not write that specific latent heat produces a temperature rise, because the temperature is constant while the state changes.
Do not use one latent heat value for both melting and boiling, because the two values differ by roughly a factor of seven for water.
Do not treat latent heat as a temperature or as a store of heat, because it is an energy per kilogram.
Do not assume a substance with a high specific heat capacity also has a high melting point, because the two properties are unrelated.

Self review

Define specific heat capacity and give its unit.
Define specific latent heat and give its unit.
State the difference between the specific latent heat of fusion and the specific latent heat of vaporisation.
Explain why the unit of specific latent heat contains no temperature.
Explain what a high specific heat capacity tells you about how a material warms and cools.
Explain why boiling water needs more energy per kilogram than melting ice.

Specific heat capacity

Definition

Specific heat capacity

Specific heat capacity is the energy needed to raise the temperature of one kilogram of a substance by one degree Celsius.

Different materials need different amounts of energy to warm up by the same number of degrees, and specific heat capacity is the quantity that measures that difference.
Its symbol is $c$ and its unit is joules per kilogram per degree Celsius, written $∘C\text{J/kg}\,^\circ\text{C}$ .
The word specific means the value is quoted for one kilogram, so the mass has already been divided out and the value belongs to the material rather than to a particular object.
Water has an unusually high value of about $∘C4200\ \text{J/kg}\,^\circ\text{C}$ , while aluminium is about $∘C900\ \text{J/kg}\,^\circ\text{C}$ and copper about $∘C385\ \text{J/kg}\,^\circ\text{C}$ .
A high specific heat capacity means the material warms up slowly for a given energy input, and it also cools down slowly.
A low specific heat capacity means the material heats up quickly, which is why a copper pan base reaches cooking temperature much faster than the water inside it.
Water is used to carry energy around a central heating system because its high value lets each kilogram carry a large amount of energy for a modest temperature change.
The same property explains why the sea warms up and cools down far more slowly than the land around it.
Ice, liquid water and steam each have their own specific heat capacity, because the arrangement of the molecules is different in each state.

Specific latent heat

Definition

Specific latent heat

Specific latent heat is the energy needed to change the state of one kilogram of a substance without changing its temperature.

Definition

Specific latent heat of fusion

Specific latent heat of fusion is the energy needed to melt one kilogram of a substance at its melting point without changing its temperature.

Definition

Specific latent heat of vaporisation

Specific latent heat of vaporisation is the energy needed to boil one kilogram of a substance at its boiling point without changing its temperature.

Energy is still needed to change the state of a substance even though its temperature does not change, and specific latent heat measures how much energy each kilogram needs.
Its symbol is $L$ and its unit is joules per kilogram, written $J/kg\text{J/kg}$ .
There is no temperature in the unit, because the temperature is constant throughout the change of state.
Fusion refers to the change between solid and liquid, so it covers both melting and freezing.
Vaporisation refers to the change between liquid and gas, so it covers both boiling and condensing.
For water the specific latent heat of fusion is about $J/kg3.34\times10^{5}\ \text{J/kg}$ and the specific latent heat of vaporisation is about $J/kg2.26\times10^{6}\ \text{J/kg}$ .
Vaporisation always needs more energy than fusion for the same substance, because melting only frees the particles from their fixed positions while boiling separates them completely.
The value works in both directions, so freezing one kilogram of water releases the same energy that melting one kilogram of ice absorbs.

Comparing the two quantities

Both quantities are quoted per kilogram, so both tell you the energy involved for a $kg1\ \text{kg}$ sample of the substance.
Specific heat capacity applies while the substance stays in one state and its temperature is changing.
Specific latent heat applies while the substance is changing state and its temperature is constant.
The energy in the specific heat capacity case changes the average kinetic energy of the particles, so the temperature moves.
The energy in the specific latent heat case changes the arrangement of the particles and overcomes the forces between them, so the temperature holds still.
The units separate the two: a temperature appears in $∘C\text{J/kg}\,^\circ\text{C}$ but not in $J/kg\text{J/kg}$ .
One substance has a specific heat capacity for each of its states, but only two specific latent heats, one for fusion and one for vaporisation.
Specific latent heat values are usually far larger than the energy needed to warm the same mass by a few degrees, which is why melting and boiling stages dominate the energy needed to take a substance through a wide temperature range.

Example

Choosing the right quantity at each stage

Ice at $∘C-5\,^\circ\text{C}$ is warmed to $∘C0\,^\circ\text{C}$ , which is a temperature change within one state, so the specific heat capacity of ice applies.
The ice at $∘C0\,^\circ\text{C}$ then melts into water at $∘C0\,^\circ\text{C}$ , which is a change of state, so the specific latent heat of fusion applies.
The water is warmed from $∘C0\,^\circ\text{C}$ to $∘C100\,^\circ\text{C}$ , so the specific heat capacity of liquid water applies to that stage.
The water at $∘C100\,^\circ\text{C}$ then boils into steam at $∘C100\,^\circ\text{C}$ , so the specific latent heat of vaporisation applies.
Each kilogram needs about $J3.34\times10^{5}\ \text{J}$ for the melting stage and about $J2.26\times10^{6}\ \text{J}$ for the boiling stage.
The boiling stage therefore needs by far the most energy of the four stages, even though it produces no change in temperature at all.

Exam technique

Writing the two definitions

Include the energy, the mass of one kilogram and the temperature rise of one degree Celsius in a definition of specific heat capacity, because all three are needed for full marks.
Include the energy, the mass of one kilogram and the phrase without a change in temperature in a definition of specific latent heat.
Name the change of state you mean, because fusion and vaporisation have different values for the same substance.
Quote the units carefully, since the presence or absence of the degree Celsius is often the mark that separates the two quantities.
Give a matching statement about each quantity in a compare question, so the examiner can see the two sides of the difference.
Mention the particles when you are asked to explain the difference, since the arrangement changing rather than the speed changing is the real distinction.

Common Mistake

Do not leave the mass out of a definition, because both quantities are defined for one kilogram of the substance.
Do not write that specific latent heat produces a temperature rise, because the temperature is constant while the state changes.
Do not use one latent heat value for both melting and boiling, because the two values differ by roughly a factor of seven for water.
Do not treat latent heat as a temperature or as a store of heat, because it is an energy per kilogram.
Do not assume a substance with a high specific heat capacity also has a high melting point, because the two properties are unrelated.

Self review

Define specific heat capacity and give its unit.
Define specific latent heat and give its unit.
State the difference between the specific latent heat of fusion and the specific latent heat of vaporisation.
Explain why the unit of specific latent heat contains no temperature.
Explain what a high specific heat capacity tells you about how a material warms and cools.
Explain why boiling water needs more energy per kilogram than melting ice.

14.2.2 Specific heat capacity and specific latent heat

Specific heat capacity

Specific latent heat

Comparing the two quantities

Choosing the right quantity at each stage

Writing the two definitions

Review 14.2.2 Specific heat capacity and specific latent heat by teaching Genie

14.2.2 Specific heat capacity and specific latent heat

Specific heat capacity

Specific latent heat

Comparing the two quantities

Choosing the right quantity at each stage

Writing the two definitions

Review 14.2.2 Specific heat capacity and specific latent heat by teaching Genie

14.2.2 Specific heat capacity and specific latent heat

Specific heat capacity

Specific latent heat

Comparing the two quantities

Choosing the right quantity at each stage

Writing the two definitions

Review 14.2.2 Specific heat capacity and specific latent heat by teaching Genie

14.2.2 Specific heat capacity and specific latent heat Revision Guide

14.2.2 Specific heat capacity and specific latent heat

Specific heat capacity

Specific latent heat

Comparing the two quantities

Choosing the right quantity at each stage

Writing the two definitions

Review 14.2.2 Specific heat capacity and specific latent heat by teaching Genie

14.2.2 Specific heat capacity and specific latent heat Revision Guide