Heating and internal energy (Topic 9A)

The specific heat capacity of a substance is defined as:

Specific heat capacity is a measure of how much a material resists changes in temperature.

Specific heat capacity is expressed in units of (joules per kilogram per Kelvin) or (joules per kilogram per degree Celsius) and is denoted by the symbol

Substances with low specific heat capacity:

• Heat up and cool down quickly.
• Examples: Metals such as copper and lead have low specific heat capacities, making them efficient conductors of heat.
• These materials are ideal for applications such as cooking utensils, where rapid heat transfer is crucial.

Substances with high specific heat capacity:

• Heat up and cool down slowly.
• Examples: Water has a very high specific heat capacity, making it excellent for storing and transporting heat.
• High value substances are useful in systems such as radiators or thermal insulators, where slow temperature changes are desirable.

Metals such as copper and lead are excellent heat conductors due to the presence of free electrons, which efficiently carry thermal energy. This ability to transfer heat quickly explains their low specific heat capacities.

Some practical applications of specific heat capacity:

Energy is required to change the state of a substance.

When a change of state occurs, energy is supplied to overcome intermolecular forces, not to increase temperature – the temperature remains constant.

The diagram below illustrates the key state changes to remember:

It is useful to note that there is an additional state of change called deposition, where a gas changes directly into a solid without passing through a liquid phase. However, knowledge of this change of state is not required for your exams.

An example of deposition is water vapour in the air depositing as a solid, crystalline frost on a window in cold conditions, bypassing the liquid water state.

Heating curves show how the temperature of a substance changes as heat is supplied.

Heating curves demonstrate how temperature remains constant during state changes.

When a substance is melting or boiling, all of the energy supplied is being used to change its state, not to raise its temperature, so the temperature remains constant.

While the temperature is constant, the latent heat equation applies:

allowing the latent heat to be determined.

Method for measuring the specific latent heat of fusion of ice:

1. Place ice cubes in a funnel with filter paper, above a beaker, to isolate the melted water from the ice block.
2. Use two beakers:
   1. Beaker A collects water from ice melted by the immersion heater and by the surrounding air.
   2. Beaker B collects water from naturally melting ice exclusively.
3. Heat the ice with an immersion heater and ensure the electrical circuit is set up for accurate ammeter and voltmeter readings.
4. Record the current voltage and heating time
5. After a set time, measure the mass of water in both beakers with an electronic balance.
6. Isolate the mass melted by the heater alone by calculating the difference in mass readings.
7. Calculate the specific latent heat fusion of ice:

Sources of error:

• Filter paper absorbs water: Use non-absorbent material if possible.
• Incomplete thermal equilibrium: If ice is not at some energy is used to raise its temperature before melting begins.

Method for measuring the specific latent heat of vaporisation of water:

1. Use a double-walled glass vessel to reduce heat loss and focus energy on vaporisation.
2. A condenser ensures the vapour is collected efficiently for mass measurements.
3. Collect condensed vapour: Ensure that the entire vapour from the liquid is condensed and collected to accurately measure its mass.

Sources of error:

• Heat loss in the condenser: If vapour escapes before condensing, the mass of collected water will be underestimated, resulting in a higher latent heat value
• Energy loss to surroundings: Not all energy from the heater goes into vaporisation; some heats the environment, causing overestimation of

The three main phases of matter are solids, liquids, and gases.

The solid phase is the most ordered, followed by the liquid phase, and the gas phase is the least ordered.

Solids have the following properties:

• The spacing between the particles is small.
• The particles are ordered, arranged in a regular structure.
• The particles vibrate about fixed positions.

The three main phases of matter are solids, liquids, and gases.

The solid phase is the most ordered, followed by the liquid phase, and the gas phase is the least ordered.

Solids have the following properties:

• The spacing between the particles is small.
• The particles are ordered, arranged in a regular structure.
• The particles vibrate about fixed positions.

Gases have the following properties:

• The spacing between the particles is large.
• The particles move at high speeds.

The kinetic model explains the phases of matter in terms of particle motion.

In a solid, particles experience strong electrostatic forces, so they can only vibrate about fixed positions and cannot move freely.

1. When a solid is heated, the particles gain kinetic energy and vibrate more strongly.
2. Once they have enough energy to overcome some of the attractive forces, the solid melts and becomes a liquid.

In a liquid, particles experience weaker electrostatic forces than in a solid, allowing them to move past each other while remaining close together.

Liquid particles, therefore, have greater kinetic energy than solid particles.

1. When a liquid is heated, the particles gain kinetic energy and move faster.
2. Evaporation occurs when particles on the surface gain sufficient energy to overcome intermolecular forces and escape, resulting in the formation of a gas.

It is important to note that evaporation is distinct from boiling:

• Evaporation is a surface phenomenon that occurs at any temperature, where high-energy particles escape into a gas.
• Boiling happens at a fixed temperature throughout the liquid, as particles gain enough energy to form gas bubbles.

In a gas, particles experience negligible intermolecular forces, except during collisions. As a result, gas particles move freely in random directions.

Gas particles have greater kinetic energy than liquid particles.

1. When a gas is cooled, the particles lose kinetic energy and move more slowly.
2. As the gas particles slow down, they come closer together, and the attractive intermolecular forces between them become more significant.
3. Once the particles are close enough, they begin to stick together, transitioning from a gas to a liquid. This process is called condensation.

In a liquid, particles experience weaker electrostatic forces than in a solid, allowing them to move past each other, while remaining close together.

1. When a liquid is cooled, the particles lose kinetic energy and move more slowly.
2. As their kinetic energy decreases, the particles are less able to overcome the attractive intermolecular forces.
3. Eventually, the particles become fixed in position, and the liquid freezes to form a solid.

Density is defined as mass per unit volume. According to the particle model, substances with particles that are further apart have a lower density. For most substances, the solid phase is denser than the liquid phase, which is denser than the gas phase.

Water is unusual because its solid phase, ice, is less dense than liquid water.

When water freezes, its volume increases because the ice crystal structure forms with more open space between the water molecules than in the liquid state.

The internal energy of a substance is the sum of the random distribution of kinetic and potential energies of its particles.

Particles in solids, liquids, and gases have potential energy due to the electrostatic attraction between the particles. This energy is negative because energy must be supplied to overcome the attractions.

Solids have the largest magnitude of negative potential energy, liquids have a lower magnitude, and gases have a negligible magnitude.

When a substance is heated, its internal energy increases.

• While a substance remains in the same phase, the heat energy supplied increases the average kinetic energy of its particles, causing the substance’s temperature to rise.
• When the substance reaches its melting point or boiling point, the heat energy is used to weaken intermolecular bonds, increasing the particles’ potential energy and changing the phase of the substance, without changing the temperature.

This can be seen on a temperature–heat graph, which shows temperature rising between phase changes and remaining constant during melting or boiling.

The transition of a substance from solid to liquid, and then to gas, involves changes in energy, bonding, and temperature:

1. Melting:

• At the melting point, the supplied energy does not increase the temperature.
• Instead, this energy is used to weaken the bonds within the solid structure.
• This process makes the potential energies less negative, allowing the solid to melt into a liquid.

2. Heating the liquid:

• Once melting is complete, continuous heating increases the liquid’s kinetic energy, causing its temperature to rise.

3. Vaporisation:

• At the boiling point, the temperature remains constant.
• The energy supplied weakens the intermolecular bonds.
• The particle’s potential energies become less negative, and the liquid evaporates into a gas.

4. Heating the gas:

• After all the liquid has vaporised, further heating increases the gas’s kinetic energy, resulting in a temperature rise.

As a substance cools, internal energy decreases. Phase changes occur at the freezing or condensation points. Removing energy strengthens bonds, making potential energies more negative, reducing internal energy.

After the phase change, further cooling lowers the kinetic energy, resulting in a drop in temperature.

As a substance is cooled, the average kinetic energy of its particles decreases. The temperature at which the average kinetic energy is zero is known as absolute zero, the lowest theoretical temperature.

The absolute (thermodynamic) scale starts at this point, so it has no negative values. The standard unit of temperature is the kelvin , one of the seven SI base units. The increment is the same as Celsius.

On the absolute scale, temperature is directly proportional to the average kinetic energy of the particles in a substance. Therefore, doubling the absolute temperature doubles the average kinetic energy, regardless of the material. This is why the scale is independent of any particular substance.