Specific latent heat Revision Notes for AQA A-Level Physics

Specific latent heat

What is specific latent heat?

When you heat a substance, you might expect its temperature to always increase. However, this isn't always the case. When a substance undergoes a change of state (also called a phase change), such as melting from solid to liquid or boiling from liquid to gas, the temperature remains constant even though energy is still being supplied.

During a change of state, the energy supplied doesn't increase the temperature. Instead, it does work against the forces holding the particles together. In a solid or liquid, particles are held in place by attractive forces. To separate these particles and change the state of the substance, energy must be supplied to overcome these attractive forces. This increases the potential energy component of the substance's internal energy, while the kinetic energy of the particles (which determines temperature) remains constant.

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When a substance changes from liquid to gas, it expands significantly. Energy is therefore needed to do work against atmospheric pressure as the substance expands. For example, when water turns to steam, approximately 7% of the energy supplied is used to do work against atmospheric pressure, while the rest overcomes the attractive forces between water molecules.

Specific latent heat of vaporisation

The specific latent heat of vaporisation (symbol: $l_v$ ) of a substance is the energy required to change 1 kg of a liquid into 1 kg of gas with no change in temperature. It is measured in joules per kilogram (J kg⁻¹).

This property tells you how much energy you need to supply to completely convert a liquid at its boiling point into a gas at the same temperature. Different substances require different amounts of energy for this process, which is why they have different values of specific latent heat of vaporisation.

Specific latent heat of fusion

The specific latent heat of fusion (symbol: $l_f$ ) of a substance is the energy required to change 1 kg of a solid into 1 kg of liquid with no change in temperature. It is measured in joules per kilogram (J kg⁻¹).

This tells you how much energy is needed to completely melt a solid at its melting point into a liquid at the same temperature. The word "fusion" here refers to the melting process - the solid particles gain enough energy to break free from their fixed positions and move more freely as a liquid.

The energy transfer equation

When a substance changes state, the energy transferred is given by:

$Q = ml$

where:

$Q$ is the energy transferred (J)
$m$ is the mass of the substance (kg)
$l$ is the specific latent heat (J kg⁻¹) - either of vaporisation or fusion depending on the change of state

This equation can be rearranged to find the specific latent heat:

$l = \frac{Q}{m}$

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This simple relationship shows that the energy needed is directly proportional to the mass of substance changing state. Double the mass, and you need double the energy.

Values of specific latent heat

Different substances have different values of specific latent heat because the strength of the forces between particles varies. Here are some typical values:

Material	Specific latent heat of vaporisation (kJ kg⁻¹)	Specific latent heat of fusion (kJ kg⁻¹)
Water	2260	334
Oxygen	243	14
Helium	25	5
Mercury	290	11
Iron	6339	276
Lead	854	25

Notice that the specific latent heat of vaporisation is always much larger than the specific latent heat of fusion for the same substance. This is because:

Converting liquid to gas requires completely separating particles against strong attractive forces
Converting solid to liquid only requires loosening the particle arrangement, not completely separating them
Energy is also needed to do work against atmospheric pressure during vaporisation

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Water has a particularly high specific latent heat of vaporisation (2260 kJ kg⁻¹), which makes it very effective for cooling applications. This is why water is commonly used in power station cooling towers and why sweating is such an effective cooling mechanism for the human body.

Temperature behavior during phase changes

When you supply energy to a substance at a constant rate, its temperature changes in a characteristic way:

Solid phase: Temperature increases steadily as energy is supplied. The particles vibrate more vigorously, increasing their kinetic energy.
Melting (fusion): When the melting point is reached, temperature remains constant even though energy continues to be supplied. This is because the energy is being used to break bonds and increase potential energy, not kinetic energy. This continues until all the solid has turned into liquid.
Liquid phase: Temperature increases steadily again as more energy is supplied. The liquid particles move faster and the temperature rises.
Boiling (vaporisation): At the boiling point, temperature again remains constant while energy is supplied. The energy separates the particles completely and does work against atmospheric pressure. This continues until all the liquid has turned into gas.
Gas phase: Once all the substance is in gas form, the temperature increases steadily again with further energy input.

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On a temperature versus energy graph, the horizontal sections represent the phase changes. The length of these horizontal sections depends on the specific latent heat - a larger specific latent heat means more energy is needed, creating a longer horizontal section.

Internal energy changes during phase changes

Understanding what happens to internal energy during a phase change is important:

Internal energy has two components:

Kinetic energy of the particles (related to their random motion)
Potential energy of the particles (related to their positions and the forces between them)

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During a phase change:

The temperature remains constant, so the average kinetic energy of the particles does not change
The internal energy increases because the potential energy component increases
The particles are doing work against the attractive forces holding them together, increasing their potential energy

This is why heating a substance during a phase change doesn't make it hotter - the energy is stored as potential energy rather than kinetic energy.

Worked example: heating water to steam

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Worked Example: Heating Water to Steam

An electric kettle is used to raise the temperature of 1.1 kg of water from 18.5°C to 100°C. The kettle continues to heat the water until 10% of the water has been converted to steam before switching off. The kettle was switched on for 275 s. We can calculate:

Part a: Total energy supplied to raise the water temperature and vaporise 10%

First, calculate the energy needed to heat the water to 100°C:

$Q_1 = mc\Delta\theta = 1.1 \times 4190 \times (100 - 18.5)$

$Q_1 = 3.756 \times 10^5 \text{ J}$

Next, calculate the energy needed to vaporise 10% of the water ( $0.1 \times 1.1 = 0.11$ kg):

$Q_2 = ml = 0.11 \times 2.26 \times 10^6 = 2.486 \times 10^5 \text{ J}$

Total energy supplied:

$Q_{\text{total}} = Q_1 + Q_2 = 6.242 \times 10^5 \text{ J} \approx :success[6.2 × 10⁵ J]$

Part b: Energy transferred to surroundings

If the kettle has a power rating of 2.5 kW, the total energy supplied by the heating element is:

$\text{Power} \times \text{time} = 2500 \times 275 = 6.875 \times 10^5 \text{ J}$

Energy transferred to surroundings:

$6.875 \times 10^5 - 6.242 \times 10^5 = 0.633 \times 10^5 \text{ J} = :success[6.3 × 10⁴ J]$

This calculation shows that not all the electrical energy supplied goes into heating and vaporising the water - some is transferred to the surroundings through the kettle body.

Worked example: evaporation for cooling

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Worked Example: Evaporation for Cooling

The evaporation of sweat is an important cooling mechanism for the human body. A typical person loses about 0.5 litre (0.5 kg) of sweat per day through evaporation. We can calculate the average power of this energy transfer.

The energy needed to evaporate 0.5 litre of sweat is:

$Q = ml$

where $m$ is the mass of 0.5 litre of water (0.5 kg) and $l$ is the specific latent heat of vaporisation of water ( $2.260 \times 10^6$ J kg⁻¹).

$Q = 0.5 \times 2.260 \times 10^6 = 1.13 \times 10^6 \text{ J}$

If this is transferred over 24 hours (86400 s), then:

$\text{Average power} = \frac{1.13 \times 10^6}{86400} = :success[13 W]$

This shows that evaporation provides a continuous cooling effect of about 13 W, helping to regulate body temperature.

Experimental investigation of phase changes

Phase changes can be investigated experimentally using a temperature sensor and data logging equipment. A common experiment involves heating a substance at a constant rate and monitoring its temperature over time.

Experimental setup:

A substance (such as stearic acid) is placed in a boiling tube
A temperature sensor is inserted into the substance
The boiling tube is heated in a water bath using a Bunsen burner
A data logger connected to a computer records temperature every few seconds (e.g., every 2 s, giving a sampling rate of 0.5 Hz)
The substance is heated at a constant rate

What happens during the experiment:

When heating begins, the solid substance warms up and its temperature rises steadily. When it reaches its melting point, the temperature stays approximately constant while the solid changes to liquid. Once melting is complete, the temperature of the liquid rises until it reaches the boiling point, where it remains constant again during vaporisation.

The resulting temperature-time graph shows:

Upward sloping sections where temperature increases (solid warming, liquid warming)
Horizontal or nearly horizontal sections where phase changes occur (melting, boiling)
The gradient of the upward sloping sections relates to the rate of temperature change

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Cooling curve:

If the substance is then removed from the heat source and allowed to cool, the cooling curve shows similar features but in reverse. However, the cooling rate depends on the temperature difference between the object and its surroundings. The larger this difference, the faster the cooling. This is why the cooling curve is not simply a mirror image of the heating curve.

During cooling:

The gas cools down steadily
At the boiling point, condensation occurs at constant temperature
The liquid cools down steadily
At the melting point, solidification occurs at constant temperature
The solid continues to cool down

Dissipation and practical applications

The energy needed to change the state of a substance has practical applications in energy transfer systems. When a substance changes state, it can absorb or release large amounts of energy without changing temperature, making phase changes useful for thermal energy transfer.

Dissipation refers to the spreading out of energy in a way that cannot easily be reversed. During thermal energy transfer, energy becomes randomly spread out and is said to be dissipated to the surroundings. This dissipated energy cannot easily be recovered for useful work.

Examples of using latent heat for cooling include:

Cooling towers in power stations: Water is heated in the power station and then transferred to cooling towers. As the water evaporates, it removes thermal energy from the system, cooling the remaining water. The large specific latent heat of vaporisation of water makes this process very effective. The thermal energy is dissipated to the surroundings through the evaporated water vapor.
Evaporative cooling in the human body: When we sweat, water evaporates from our skin surface. The energy required for this evaporation (the latent heat of vaporisation) is taken from our body, cooling us down. On average, this provides a continuous cooling effect of about 13 W.
Refrigeration systems: Refrigerators use the evaporation and condensation of a refrigerant to transfer thermal energy. The refrigerant evaporates inside the refrigerator, absorbing energy (and cooling the interior). It then condenses outside the refrigerator, releasing this energy to the surroundings. By evaporating liquid at a smaller scale, we transfer excess thermal energy through this phase change process.

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Key Points to Remember:

Specific latent heat is the energy required to change the state of 1 kg of a substance with no temperature change
Specific latent heat of vaporisation (liquid → gas) is always much larger than specific latent heat of fusion (solid → liquid) for the same substance
The energy equation for phase changes is $Q = ml$ , where $Q$ is energy, $m$ is mass, and $l$ is specific latent heat
During a phase change, temperature remains constant while internal energy increases - the potential energy component increases but the kinetic energy component stays the same
Temperature-time graphs show horizontal sections during phase changes, with the length of these sections depending on the specific latent heat value
Water has a particularly high specific latent heat of vaporisation (2260 kJ kg⁻¹), making it excellent for cooling applications

Specific latent heat (AQA A-Level Physics): Revision Notes