# 9.1 Specific Heat Capacity & Latent Heat

## Specific Heat Capacity

• Specific heat capacity is defined as:

the energy required to raise the temperature of one kilogram of a substance by one kelvin

• The increase in temperature of an object depends on:
• The amount of heat energy transferred
• The mass of the object
• The specific heat capacity of the material from which the object is made

Explanation of Heat Energy

• The energy input is in the form of heat energy
• The amount of heat energy needed is given by the equation:

ΔEmcΔθ

• Where:
• ΔE = change in heat energy, in joules (J)
• m = mass, in kilograms (kg)
• c = specific heat capacity, in joules per kilogram per degree Kelvin (J/kg K or J/kg °C)
• Δθ = change in temperature, in Kelvin or Celsius
• (The symbol Δ in Maths is used to denote a change in value)

Examples of heat energy

• The thermodynamic Kelvin temperature scale is defined as:

An absolute temperature scale where each degree is the same size as those on the Celsius scale

• Different materials:
• Have different specific heat capacities because of their molecular structure
• Have different rises in temperature for the same change in heat energy

• Specific heat capacity is mainly used for liquids and solids
• Good electrical conductors, such as copper and lead, are excellent conductors of heat due to their low specific heat capacity
• On the other hand, water has a very high specific heat capacity, making it ideal for heating homes as the water remains hot in a radiator for a long time
• The specific heat capacity of different substances determines how useful they would be for a specific purpose eg. choosing the best material for kitchen appliances

Low v high specific heat capacity

• The specific heat capacity of some substances are given in the table below as examples:

Table of values of specific heat capacity for various substances

#### Worked example

Water of mass 0.48 kg is increased in temperature by 0.7 K. The specific heat capacity of water is 4200 J kg-1 K-1. Calculate the amount of energy transferred to the water.

Step 1: Write down the known quantities

• Mass, m = 0.48 kg
• Change in temperature, Δθ = 0.7 K
• Specific heat capacity, c = 4200 J kg-1 K-1

Step 2: Write down the relevant equation

ΔE = mcΔθ

Step 3: Calculate the energy transferred by substituting in the values

ΔE = (0.48) × (4200) × (0.7) = 1411.2

Step 4: Round the answer to 2 significant figures

ΔE = 1400 J

#### Exam Tip

You will always be given the specific heat capacity of a substance, so you do not need to memorise any values. Make sure that Δθ is the change in temperature, therefore, it can be in K or °C.

## Specific Latent Heat

• Energy is required to change the state of substance
• Examples of changes of state are:
• Melting = solid to liquid
• Evaporation/vaporisation/boiling = liquid to gas
• Sublimation = solid to gas
• Freezing = liquid to solid
• Condensation = gas to liquid

The example of changes of state between solids, liquids and gases

• When a substance changes state, there is no temperature change
• The energy supplied to change the state is called the latent heat and is defined as:

The thermal energy required to change the state of one kilogram of a substance without any change of temperature

• There are two types of latent heat:
• Specific latent heat of fusion (melting)
• Specific latent heat of vaporisation (boiling)

The changes of state with heat supplied against temperature. There is no change in temperature during changes of state

• The specific latent heat of fusion is defined as:

The thermal energy required to convert one kilogram of solid to liquid with no change in temperature

• This is used when melting a solid or freezing a liquid

• The specific latent heat of vaporisation is defined as:

The thermal energy required to convert one kilogram of liquid to gas with no change in temperature

• This is used when vaporising a liquid or condensing a gas

#### Calculating Specific Latent Heat

• The amount of energy ΔE required to melt or vaporise a mass of m with latent heat L is:

ΔE = LΔm

• Where:
• ΔE =  amount of heat energy to change the state (J)
• L = latent heat of fusion or vaporisation (J kg-1)
• Δm = change in mass of the substance changing state (kg)

• The values of latent heat for water are:
• Specific latent heat of fusion = 330 kJ kg-1
• Specific latent heat of vaporisation = 2.26 MJ kg-1
• Therefore, evaporating 1 kg of water requires roughly seven times more energy than melting the same amount of ice to form water
• The reason for this is to do with intermolecular forces:
• When ice melts: energy is required to just increase the molecular separation until molecules can flow freely over each other
• When water boils: energy is required to completely separate the molecules until there are no longer forces of attraction between them, hence this requires much more energy

#### Worked example

The energy needed to boil a mass of 530 g of a liquid is 0.6 MJ. Calculate the specific latent heat of the liquid and state whether it is the latent heat of vaporisation or fusion.

Step 1: Substitute in the values

= 530 g = 530 × 10-3 kg

= 0.6 MJ = 0.6 × 106 J

L is the latent heat of vaporisation because the change in state is from liquid to gas (boiling)

#### Exam Tip

Use these reminders to help you remember which type of latent heat is being referred to:

• Latent heat of fusion = imagine ‘fusing’ the liquid molecules together to become a solid
• Latent heat of vaporisation = “water vapour” is steam, so imagine vaporising the liquid molecules into a gas

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