4.3 Particle model of matter — 8463 spec coverage

4.3.1.1

Density of materials

Density is mass per unit volume: $\rho=m/V$ , with SI unit $\text{kg/m}^3$ .
Measure a regular solid's dimensions to calculate its volume, find an irregular solid's volume by displacement, and find a liquid's mass by subtracting the empty container's mass.
In the particle model, solids and liquids are usually denser than gases because their particles are much closer together; density also depends on particle mass and arrangement.
A common error is to mix units such as grams and cubic metres; convert both mass and volume into a compatible unit system before dividing.

Tier 1 · Easy

2 marks

ORIGINAL

A sample has mass $0.54\,\text{kg}$ and volume $2.0\times10^{-4}\,\text{m}^3$ . Calculate its density.

Tier 2 · Standard

4 marks

ORIGINAL

An irregular mineral has mass $0.390\,\text{kg}$ . When fully submerged, it displaces $1.50\times10^2\,\text{cm}^3$ of water. Calculate its density in $\text{kg/m}^3$ .

Tier 3 · Hard

6 marks

ORIGINAL

Describe how to determine the densities of a rectangular metal block, a small irregular stone and a liquid. Name suitable apparatus and state the calculation used in each case.

4.3.1.2

Changes of state

The state changes are melting, freezing, boiling, evaporation, condensation and sublimation.
Use particle arrangements and motion to describe the change, while keeping the number and type of particles unchanged.
Mass is conserved during a change of state in a closed system because no particles are created or destroyed.
A common error is to describe a state change as a chemical reaction; it is physical because reversing it restores the material's original properties.

Tier 1 · Easy

2 marks

ORIGINAL

Name the changes of state from gas to liquid and from solid directly to gas.

Tier 2 · Standard

3 marks

ORIGINAL

A sealed container holds $75.0\,\text{g}$ of ice. The ice melts completely. State the mass of water formed and explain why it is unchanged.

Tier 3 · Hard

4 marks

ORIGINAL

A solid air freshener gradually forms a gas and later deposits as solid crystals on a cold surface. Explain why these are physical changes and describe the particle arrangement before and after each change.

4.3.2.1

Internal energy

Internal energy is the total kinetic energy and potential energy of all the particles in a system.
When a system is heated, track whether the supplied energy raises particle kinetic energy and temperature or changes particle potential energy during a state change.
Within one state, a higher temperature means a greater average particle kinetic energy and therefore usually a greater internal energy for the same sample.
A common error is to say that temperature always rises when internal energy increases; during a change of state, internal energy changes while temperature stays constant.

Tier 1 · Easy

2 marks

ORIGINAL

Define the internal energy of a system.

Tier 2 · Standard

3 marks

ORIGINAL

A solid is heated but does not melt. Explain how its particles and internal energy change.

Tier 3 · Hard

5 marks

ORIGINAL

A pure solid is heated at a steady rate. Its temperature rises, remains constant while it melts, then rises again. Explain the changes in kinetic energy, potential energy and internal energy during all three stages.

4.3.2.2

Temperature changes in a system and specific heat capacity

For a temperature change without a change of state, $\Delta E=mc\Delta\theta$ links energy change, mass, specific heat capacity and temperature change.
Calculate $\Delta\theta=\theta_{\text{final}}-\theta_{\text{initial}}$ , convert mass to kilograms and rearrange the equation algebraically before inserting values.
For the same energy input, a larger mass or larger specific heat capacity gives a smaller temperature rise.
A common error is to confuse specific heat capacity in $\text{J/(kg}\,{}^\circ\text{C)}$ with specific latent heat in $\text{J/kg}$ ; the former applies when temperature changes.

Tier 1 · Easy

2 marks

ORIGINAL

State the meaning of specific heat capacity and give its unit.

Tier 2 · Standard

2 marks

ORIGINAL

A $2.0\,\text{kg}$ metal block warms by $35\,{}^\circ\text{C}$ . Its specific heat capacity is $450\,\text{J/(kg}\,{}^\circ\text{C)}$ . Calculate the increase in its thermal energy store.

Tier 3 · Hard

5 marks

ORIGINAL

Two insulated blocks each receive $54\,\text{kJ}$ . Block A has mass $1.5\,\text{kg}$ and specific heat capacity $900\,\text{J/(kg}\,{}^\circ\text{C)}$ . Block B has mass $0.75\,\text{kg}$ and specific heat capacity $450\,\text{J/(kg}\,{}^\circ\text{C)}$ . Calculate both temperature rises and explain the difference.

4.3.2.3

Changes of state and specific latent heat

Specific latent heat is the energy needed to change the state of $1\,\text{kg}$ of a substance with no temperature change, using $E=mL$ .
Use specific latent heat of fusion for solid-liquid changes and specific latent heat of vaporisation for liquid-vapour changes.
A flat section on a heating or cooling graph marks a state change: energy changes particle potential energy while average kinetic energy and temperature remain constant.
A common error is to apply $E=mc\Delta\theta$ across a state-change plateau; use $E=mL$ for that stage and calculate any temperature-changing stages separately.

Tier 1 · Easy

2 marks

ORIGINAL

Define specific latent heat.

Tier 2 · Standard

2 marks

ORIGINAL

A $0.28\,\text{kg}$ frozen material is already at its melting point. Calculate the transfer required to melt it completely, given $L_f=3.10\times10^5\,\text{J/kg}$ .

Tier 3 · Hard

5 marks

ORIGINAL

A $0.15\,\text{kg}$ sample of water is heated from $20\,{}^\circ\text{C}$ to $100\,{}^\circ\text{C}$ and then completely vaporised at $100\,{}^\circ\text{C}$ . Calculate the total energy supplied. Use $c=4200\,\text{J/(kg}\,{}^\circ\text{C)}$ and $L_v=2.26\times10^6\,\text{J/kg}$ .

4.3.3.1

Particle motion in gases

Gas molecules are in constant random motion, and gas temperature is related to their average kinetic energy.
Explain gas pressure through molecules colliding with container walls and changing momentum, which exerts a force on the walls.
At constant volume, heating increases average molecular speed, making collisions more frequent and harder, so pressure increases.
A common error is to say that heating creates more particles or makes each particle larger; the same molecules move faster unless gas enters or leaves.

Tier 1 · Easy

1 mark

ORIGINAL

State how the average kinetic energy of gas molecules changes when the gas temperature increases.

Tier 2 · Standard

4 marks

ORIGINAL

A sealed rigid flask of gas is heated. Explain why the gas pressure increases.

Tier 3 · Hard

5 marks

ORIGINAL

Two identical sealed rigid containers hold the same number of molecules of the same gas. Gas A is at a higher temperature than gas B. Compare the molecular motion and pressures, and explain why the comparison would be less certain if the containers had different volumes.

4.3.3.2

Pressure in gases (physics only)

Gas pressure produces a net force at right angles to a container wall or any other surface.
For a fixed mass of gas at constant temperature, use $pV=\text{constant}$ , so $p_1V_1=p_2V_2$ .
Increasing volume at constant temperature makes wall collisions less frequent per unit area, so pressure decreases.
A common error is to use $p_1/V_1=p_2/V_2$ ; pressure and volume are inversely proportional, so their product stays constant.

Tier 1 · Easy

2 marks

ORIGINAL

A fixed mass of gas is kept at constant temperature while its volume doubles. State what happens to its pressure.

Tier 2 · Standard

3 marks

ORIGINAL

A gas occupies $4.0\times10^{-3}\,\text{m}^3$ at a pressure of $1.2\times10^5\,\text{Pa}$ . It is compressed at constant temperature to $1.5\times10^{-3}\,\text{m}^3$ . Calculate the new pressure.

Tier 3 · Hard

5 marks

ORIGINAL

A syringe contains $3.20\times10^2\,\text{cm}^3$ of gas at $2.40\times10^2\,\text{kPa}$ . The outlet is sealed and the gas remains at constant temperature while the pressure rises to $3.60\times10^2\,\text{kPa}$ . Calculate the final volume and the decrease in volume. Explain the pressure rise using particles.

4.3.3.3

Increasing the pressure of a gas (physics only) (HT only)

Work is an energy transfer by a force; doing work on an enclosed gas transfers energy to its internal energy store.
Identify the force and displacement during compression, calculate work with $W=Fs$ when appropriate, and account for any energy transferred to the surroundings.
Rapid compression can raise gas temperature because increased internal energy gives the molecules greater average kinetic energy.
A common error is to attribute warming only to friction in the pump; compression itself involves work being done on the gas.

Tier 1 · Easy

2 marks

ORIGINAL

Explain why the air in a sealed bicycle pump can become warmer when the handle is pushed in quickly.

Tier 2 · Standard

3 marks

ORIGINAL

$180\,\text{J}$ of work is done on an enclosed gas, with negligible energy transfer to the surroundings. State the change in internal energy and explain the likely temperature change.

Tier 3 · Hard

4 marks

ORIGINAL

A piston exerts a constant force of $250\,\text{N}$ while moving $0.18\,\text{m}$ into a sealed cylinder. During compression, $12\,\text{J}$ is transferred from the gas to the surroundings. Calculate the increase in the gas's internal energy and explain the effect on its temperature.