Specific Heat Capacity & Latent Heat (Edexcel International A Level Physics)

• 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:

ΔE = mcΔθ

• 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

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

• 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

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)