# 5.1.7 Specific Latent Heat

## Specific Latent Heat of Fusion & Vaporisation

• 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 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)

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 used when a solid is melting or a liquid is freezing
• It is defined as:

The thermal energy required to convert 1 kg of solid to liquid with no change in temperature

• The specific latent heat of vaporisation is used when a liquid is vapourising or a gas is condensing
• It is defined as:

The thermal energy required to convert 1 kg of liquid to gas with no change in temperature

## Determining Specific Latent Heat

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

E = mL

• Where:
• E = 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)
• Specific latent heat of fusion is represented by Lf
• Specific latent heat of vaporisation is represented by Lv
• The values of latent heat for water are:
• Specific latent heat of fusion = 330 kJ kg1
• Specific latent heat of vaporisation = 2.26 M J kg1

• 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 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,
• 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: State the known values

• Mass, m = 530 g = 0.53 kg
• Energy supplied = 0.6 MJ = 0.6 × 106 J

Step 2: State the specific latent heat equation

E = mL

Step 3: Rearrange for latent heat

Step 4: Substitute in the values

Step 5: State whether the value is the specific latent heat of vaporisation or fusion

• 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

## Procedures to Determine Specific Latent Heat

#### Determining the Specific Latent Heat of Fusion, Lf

Equipment List

• Crushed ice
• Two funnels with filter paper
• Three retort stands
• Two thermometers
• Two electric balances
• An appropriate heater (e.g., an immersion heater)
• A power source
• A voltmeter, ammeter and stop-clock

Method

• Place a beaker on each balance
• Leaving the beaker on the balance, zero the scale
• Arrange a funnel, clamped above each beaker
• Set up an immersion heater
• Connect to the power source
• Add an ammeter in series and a voltmeter in parallel
• Place the immersion heater in one of the funnels
• Measure out 50-100g of ice
• Add the same mass of ice to each beaker
• Record this value
• Turn on the immersion heater and start the stop watch
• Record the potential difference and current
• After a suitable period of time (around 5-10 minutes) remove the funnels, stop the stop watch and turn off the heater
• Record the mass of water in the beaker

Analysis

• The energy supplied to the ice can be calculated using the equation:

energy = current x potential difference x time

• Using the values for current, potential difference and time, calculate the energy supplied
• The specific latent heat of fusion can be calculated using the equation:

energy = mass x specific latent heat

• The change mass is equal to the mass of water collected
• To take into account melting due to heat transfer from the surroundings find the difference in mass between the two beakers of water
• This gives the change in mass due to the energy supplied by the heater
• Calculate the mass of the melted ice and convert it into kg
• Δm = m- mB
• Mass in g ÷ 1000 = Mass in kg
• Calculate the specific latent heat of fusion of ice to water using the equation for specific latent heat

Evaluation

• Errors may be introduced due to precision of the instruments
• Water may be absorbed by the filter paper
• This will reduce the mass and therefore give a higher value for specific latent heat

#### Determining the Specific Latent Heat of Vaporisation, Lv

Equipment List

• A double-walled glass vessel with an inner flask containing water
• An appropriate electric heater (e.g., an immersion heater)
• A condenser with a collecting flask
• A power source
• A voltmeter, ammeter and stop-clock
• An electric balance

Method

• Connect the double-walled glass vessel to the condenser
• Place the collecting flask at the end of the condenser
• Set up an immersion heater
• Connect to the power source
• Add an ammeter in series and a voltmeter in parallel
• Place the immersion heater in the fluid
• Turn on the immersion heater and start the stop watch
• Record the potential difference and current
• After a suitable period of time (around 5-10 minutes), stop the stop watch and turn off the heater
• Record the mass of water collected in the conical flask

Analysis

• The energy supplied to the water can be calculated using the equation:

energy = current x potential difference x time

• Using the values for current, potential difference and time, calculate the energy supplied
• The specific latent heat of vaporisation can be calculated using
• The mass of water collected
• The energy supplied calculated
• The equation:

energy = mass x specific latent heat

Evaluation

• Errors may be introduced due to precision of the instruments
• Not all of the vapour which enters the condenser may make it to the beaker

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