Changes of state and specific latent heat

Changing state

Jonny Nelson introduces an animated explanation of latent heat

Adding or removing energy from a material can change the state. Heating a solid material will cause it to melt from a solid to a liquid. Continued heating will cause the liquid to boil or evaporate to form a gas. In some instances when heating the solid material, it can go straight to being a gas without being a liquid, this process is called sublimation.

Cooling a gas will cause it to condense from a gas to a liquid and cooling it further will cause it to then freeze from a liquid to a solid.

Flow chart showing processes between solid, liquid and gas, using water, ice and steam from a kettle as an example. Labels show all the processes in how one can change to another.Water changing state

Boiling is an active process. People actively apply energy to a liquid to turn it into a gas using a heater such as a kettle.

Evaporation on the other hand is a passive process. The liquid will slowly absorb energy from the surrounding area so that some of its particles will gain enough energy to escape the liquid.

Throughout all of these changes the number of particles has not changed, just their spacing and arrangement. As a result the total mass has not changed. It does not matter if a substance melts, freezes, boils, evaporates, condenses or sublimates, the mass does not change.

These changes in state are called physical changes because the processes can be reversed (eg cooling instead of heating). This is different to the changes seen in a chemical reaction when the changes cannot be reversed so easily.

Specific latent heat

Changing the internal energy of a material will cause it to change temperature or change state:

curriculum-key-fact
Specific latent heat is the amount of energy required to change the state of 1 kg of a material without changing its temperature.

As there are two boundaries, solid/liquid and liquid/gas, each material has two specific latent heats:

  • latent heat of fusion - the amount of energy needed to melt the material at its melting point
  • latent heat of vaporisation - the amount of energy needed to evaporate the material at its boiling point

Some typical values for specific latent heat include:

SubstanceSpecific latent heat of fusion (J/kg)Specific latent heat of vaporisation (J/kg)
Water334,0002,260,000
Lead2,400855,000
Oxygen13,900213,000

An input of 334,000 joules (J) of energy is needed to change 1 kg of ice into 1 kg of water. The same amount of energy needs to be taken out of the liquid to freeze it.

Calculating thermal energy changes

The amount of thermal energy stored or released as the temperature of a system changes can be calculated using the equation:

energy to cause a change in state = mass × specific latent heat

\Delta E_t = m \times l

This is when:

  • energy to cause a change of state ( \Delta E_t) is measured in joules (J)
  • mass (m) is measured in kilograms (kg)
  • specific latent heat (l) is measured in joules per kilogram (J/kg)
Question

How much energy is needed to freeze 500 grams (g) of water from 0°C?

E_t = m~l

E_t = 0.5 \times 334,000

E_t = 167,000~J

Measuring latent heat

Latent heat can be measured from a heating or cooling curve line graph. If a heater of known power is used, such as a 60 W immersion heater that provides 60 J/s, the temperature of a known mass of ice can be monitored each second. This will generate a graph that looks like this.

Graph measuring time against temperature, looking at the temperature changes between solid, liquid and gas for ice, water and steam.

The graph is horizontal at two places. These are the places where the energy is not being used to increase the speed of the particles, increasing temperature, but is being used to break the bonds between the particles to change the state.

The longer the horizontal line, the more energy has been used to cause the change of state. The amount of energy represented by these horizontal lines is equal to the latent heat.

Example

If a horizontal line that shows boiling on a heating curve is one hour three minutes long, how much energy has a 60 watts (W) heater provided to the water?

  • 63 minutes = 3,780 s
  • 60 W means 60 J of energy is supplied every second
  • energy = power × time
  • energy = 60 × 3,780
  • energy = 226,800 J

Example 2

If this energy had been applied to 100 g of water, what is the latent heat of vaporisation of water?

226,800 J for 100 g is equivalent to 2,268,000 J for 1 kg. The latent heat of vaporisation of water is 2,268,000 J/kg