Objectives:

1. To understand that if a change of state happens; the energy needed for a substance to change state is called latent heat. When a change of state occurs, the energy supplied changes the energy stored (internal energy), but not the temperature
2. To be able to use the equation $E = mL$ and understand what each term represents and the units of each term
3. To be able to understand that the specific latent heat of a substance is the amount of energy required to change the state of one kilogram of the substance with no change in temperature
4. To appreciate the difference between the specific latent heat of fusion and the specific latent heat of vaporisation
5. To be able to interpret heating and cooling graphs that include changes of state.
6. You should be able to distinguish between specific heat capacity and specific latent heat

We have previously looked at a graph showing how the energy input to a system affects the temperature of it. When a substance is a solid, liquid or gas, the input energy goes into raising the temperature. When the system changes state, the input energy does not raise the temperature but instead goes into breaking (or creating) the intermolecular bonds between particles. Specific latent heat is the term used to describe the amount of energy required to change the state of a substance, there is no temperature change during a change of state.
What the energy required to heat a substance up depends on:

1. Which requires the most energy to change the state of a small amount of water or a large amount of water?The full glass requires the most energy, because there are more particles to boil and separate the bonds of and so more overall energy required. So the mass is important.
2. Which of the following, if both are at their own respective boiling points, requires the most energy to boil and separate the bonds of?Both substances require different amounts of energy, hopefully we can all agree on that? If not, do a home experiment and put a certain amount of water in a saucepan and when it reaches boiling point time how long it takes for it to boil dry, then do the same but with oil; you will notice that the oil will boil dry faster if the same heating filament is used. This is because oil and water have different intermolecular bonds between then, this property of a substance is called its latent heat value. Every substance has its own specific latent heat value.

# Putting this altogether:

The energy required to heat up a substance is (as was discussed above) dependent on the following two quantities:

• Mass
• The specific latent heat

These quantities can be put together to form the equation:

$E = mL$

where;
$E$ is the input energy given, measure in Joules, $J$
$m$ is the mass, measure in kilograms, $kg$
$L$ is the specific latent heat of a substance, measure in Joules per kilogram , $J/kg$

The definition for specific latent heat is the amount of energy required to change the state of $1 \ kg$ of a substance, the temperature does not change in this process.

The reason for using a mass of  $1 \ kg$ is simply for simplicity. The equation above can be rearranged for specific heat capacity as is;

$L = \frac{E}{m}$

The units for specific latent heat, as shown above, are something you will need to remember for you examinations. Personally I wouldn’t bother remembering the units but instead would remember how to find them; this is done by substituting the correct units into the equation for specific heat capacity;

$L = \frac{E}{m} \rightarrow \frac{J}{kg}$

As you can see from the graph above, there are two changes of state that can occur, one for between solids and liquids and the other between liquids and gases. The energy required to change these two states are different and therefore have different names.

• The name given to the energy required to change the state of a solid into a liquid is known as the specific latent heat of fusion.
• The same term is given to the change of state from a liquid to a solid, this is because the same bonds are involved but the process is just reversed
• The name given to the energy required to change the state of a liquid into a gas is known as the specific latent heat of vaporisation.
• The same as above, the same term is given to the change of state from a gas to a liquid, this is because the same bonds are involved but the process is just reversed.

Determining the specific heat capacity of a substance

1. How much energy is required to boil dry 1.5 kg of water initially at 100℃, which has a specific latent heat of vaporisation value of 2,260,000 J/kg?
2. How much energy is required to melt 15g of gold, when initially at its melting point, with a specific latent heat of fusion value of 62,800 J/kg?

1. $\Delta E = mL$
$\Delta E = 1.5 \times 2260000$
$\Delta E = 3,390,000 J$
2. $\Delta E = mL$
$\Delta E = 0.015 \times 62800$
$\Delta E = 942 J$

Putting the specific latent heat to use

The following is a list of substances and their appropriate specific latent heat value;Which, specific latent heat of fusion or specific latent heat of vaporisation, requires the most energy to change the state of 1 kg of a substance? Why is this?

Answer: the specific latent heat of vaporisation is greater than the specific latent heat of fusion because liquids require more energy to completely separate their particles than solids do to partially break their bonds.

Here is a quick revision video on specific latent heat: