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Specific Latent Heat Capacity (CIE A Level Physics)

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Katie M

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Defining latent heat capacity

  • Energy is required to change the state of a 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

Changes of state

Changes of state diagram

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 specific latent heat and is defined as:

The thermal energy required to change the state of 1 kg of mass 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)
  • It is important to recognise the difference between latent heat and specific latent heat
    • latent heat is the energy required to change a materials state
    • specific latent heat is the energy required to change the state of 1 kg of a material

Types of latent heatLatent heat graph, downloadable AS & A Level Physics revision notes

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 1 kg 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 1 kg 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 Q required to melt or vaporise a mass of m with latent heat L is:

 Q space equals space L m

  • Where:
    • Q = amount of thermal energy to change the state (J)
    • L = latent heat of fusion or vaporisation (J kg-1)
    • m = 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 they 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 the molecules, 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:            Write the thermal energy required to change state equation

bold italic Q bold space bold equals bold space bold italic L bold italic m 

Step 2:            Rearrange for latent heat

bold italic L bold space bold equals bold space bold Q over bold m

Step 3:            Substitute in the values

m = 530 g = 530 × 10-3 kg

Q = 0.6 MJ = 0.6 × 106 J

bold italic L bold space bold equals bold space fraction numerator bold 0 bold. bold 6 bold space bold cross times bold 10 to the power of bold 6 over denominator bold 530 bold space bold cross times bold 10 to the power of bold minus bold 3 end exponent end fraction bold space bold equals bold space bold 1 bold. bold 132 bold space bold cross times bold 10 to the power of bold 6 bold space bold italic J bold space bold italic k bold italic g to the power of bold minus bold 1 end exponent bold space bold equals bold space bold 1 bold. bold 1 bold space bold italic M bold italic J bold space bold italic k bold italic g to the power of bold minus bold 1 end exponent bold space bold left parenthesis bold 2 bold space bold italic s bold. bold italic f bold. bold right parenthesis

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

Examiner 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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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.