Your revision route
What you’ll learn
- Use particle arrangements to compare the three states and account for their density differences.
- Calculate density and plan measurements for regular solids, irregular solids and liquids.
- Describe state changes as reversible physical changes in which mass is conserved.
- Explain internal energy and distinguish specific heat capacity from specific latent heat.
- Interpret heating and cooling graphs and use ΔE = mcΔθ and E = mL.
- Explain gas temperature and pressure using random molecular motion and collisions.
- Separate Physics: relate gas pressure to a resultant force normal to the wall and use pV = constant for a fixed gas mass at constant temperature.
- Separate Physics Higher: link compression work on a trapped gas to a possible temperature rise.
Build the big picture
Key ideas
Density asks how crowded the mass is
Two equal boxes can hide very different masses because density measures mass per unit volume, not mass or volume alone.
- Use ρ = m/V. The SI units are kg/m³, but g/cm³ is valid when mass and volume use that matching pair.
- Solids and liquids usually have closely packed particles; gas particles are far apart, so gases are usually much less dense.
- Particle diagrams for one substance keep particle size the same and change arrangement and separation.
- For a state change in a closed system, mass is conserved even though volume and density may change.
The punchline: Choose compatible units before dividing mass by volume.
Volume is easy only when shape cooperates
A cuboid yields to a ruler; an irregular stone makes water do the geometry.
- Measure a regular solid's dimensions with a suitable ruler, micrometer or Vernier callipers and calculate its volume.
- For an irregular solid, measure water displacement in a measuring cylinder or displacement can.
- For a liquid, weigh the empty measuring cylinder, add a measured volume and reweigh it; subtract the empty mass, or tare the cylinder before filling.
- Density uncertainty is reduced by zeroing instruments, using a large sample and repeating measurements.
The punchline: Measure mass once, choose the right volume method, then divide.
Same substance, different particle choreography
State changes alter arrangement, motion and separation without creating a new substance. The mass stays with the same particles.
- SolidParticles are close in a regular arrangement and vibrate about fixed positions.
- LiquidParticles stay close but move around one another, so the liquid flows and keeps nearly fixed volume.
- GasParticles are far apart and move rapidly in random directions, so the gas is compressible.
State changes rearrange; reactions rebuild
Melting, freezing, boiling, evaporation, condensation and sublimation change physical state without forming a new substance.
- A reversed physical change restores the material's original properties; a chemical change produces new substances.
- Melting and freezing connect solid and liquid; boiling, evaporation and condensation connect liquid and gas.
- Sublimation is the direct change from solid to gas; the reverse change is deposition.
- In a closed system, the same particles remain present, so mass is conserved.
The punchline: Change the arrangement, not the identity, in a physical state change.
Internal energy counts motion and separation together
To find a system's internal energy, add the kinetic energy associated with particle motion to the potential energy associated with their arrangement.
- Heating transfers energy into the system and can raise particle kinetic energy, potential energy or both.
- When temperature rises without a state change, use ΔE = mcΔθ.
- Specific heat capacity tells you the joules transferred per kilogram for each 1 °C temperature rise.
- For the same mass and energy input, a larger specific heat capacity produces a smaller temperature rise.
The punchline: Use temperature change, not final temperature, in the specific-heat calculation.
Make the model move
Interactive checkpoint
Touch the science. Change a state, build a route or test a relationship.
Let the ratio decide
Explore mass, volume and density
Vary mass and volume independently and watch their ratio set density.
ρ = m / V
Density8 kg/m³
Vary mass and volume independently to explore ρ = m/V. For a uniform material at fixed conditions, a larger sample increases both together, so density stays constant. Use kg and m³ for kg/m³, or g and cm³.
Follow the energy
Trace every section of heating and cooling curves
Explore all ten sections; follow the tabs from left to right. For each one, track energy direction, temperature, average kinetic energy, potential energy and state.
Energy transfers into the solid, so internal energy, temperature and average kinetic energy rise. It remains solid; potential energy is treated as unchanged in this idealised slope.
1 of 10 states explored
Heating: solid warms → melts → liquid warms → boils → gas warms. Cooling reverses this order. Slopes change temperature and average kinetic energy; plateaux change state and potential energy at constant temperature.
Name the fixed condition
Match each gas change to its mechanism
Pair each change with its distinguishing mechanism. The fixed condition is part of the physics.
All routes: pressure comes from wall collisions, and heating a sealed fixed-volume sample changes collision speed. Separate Physics: at fixed mass and temperature, volume changes collision frequency.
A flat temperature line can conceal busy particles
During a state change, energy enters or leaves while temperature stays constant because particle potential energy is changing.
- Specific latent heat tells you the joules transferred per kilogram while a substance changes state at constant temperature.
- Use E = mL. Latent heat of fusion refers to solid ↔ liquid; vaporisation refers to liquid ↔ gas.
- Graph slopes show temperature change; plateaux show melting or boiling on heating and condensation or freezing on cooling. Energy leaves during cooling as internal energy falls.
- Do not use specific heat capacity on a flat state-change section or latent heat on a sloping temperature-change section.
The punchline: Slope means kinetic-energy change; plateau means state and potential-energy change.
Gas pressure is a storm of tiny impacts
One collision is negligible; countless molecular momentum changes create steady gas pressure. Separate Physics: their forces combine into a resultant directed normal to the container wall.
- Gas molecules travel continually in random directions. The gas's temperature tracks their average kinetic energy.
- In a sealed, rigid container, gas mass and volume are fixed; heating makes molecules faster, so collisions are more frequent and harder and pressure rises.
- Separate Physics: the many collision forces combine into a resultant perpendicular to the surface.
- State every fixed quantity before explaining a pressure change.
The punchline: Link molecular speed and collision rate to force on the wall.
Read slopes and plateaux on heating and cooling curves
Each graph plots temperature vertically against time horizontally. Follow every labelled stage from left to right; a plateau is a horizontal section, not a gap.
Pressure is a wall receiving momentum
Gas molecules rebound from a container wall and change momentum; the barrage creates pressure. Separate Physics: adding those collision forces gives a resultant directed normal to the wall.
- Random motionGas molecules move constantly in all directions.
- Wall collisionA molecule rebounds and changes momentum, exerting a force on the wall.
- Many impactsThe total force per unit area is the gas pressure.
- Change conditionsAll routes: heating a fixed gas mass in a rigid container intensifies impacts. Separate Physics: expansion at fixed mass and temperature makes wall collisions less frequent.
Separate Physics: give a gas more room and impacts thin out
For a fixed gas mass at constant temperature, pressure and volume trade inversely so their product remains constant.
- Increasing volume makes wall collisions less frequent, so pressure falls when temperature remains constant.
- Use p₁V₁ = p₂V₂, with the same pressure unit on both sides and the same volume unit on both sides.
- Use this relationship only while both the amount of gas and its temperature stay fixed; it cannot describe simultaneous heating.
The punchline: Before using pV = constant, write ‘fixed mass, constant temperature’.
Separate Physics Higher: a bicycle pump warms by work
Rapid compression lets a force transfer energy into the enclosed gas before much energy escapes to the surroundings.
- Work is energy transferred by a force. A moving piston does work on the gas during compression.
- That transfer raises the gas's internal energy and can raise its temperature.
- This is not simply ‘particles have less room’; include the energy transfer by work.
The punchline: Force moves piston → work is done on gas → internal energy rises → temperature can rise.
Words worth knowing
Key definitions
- density
- Mass per unit volume, measured in kg/m³ in SI units.
- internal energy
- Add the energy of particle motion to the energy stored in their arrangement; that sum is the system's internal energy.
- specific heat capacity
- Energy transferred per kilogram for each 1 °C rise in a substance's temperature.
- specific latent heat
- Energy transferred per kilogram during a state change that occurs at constant temperature.
- latent heat of fusion
- The per-kilogram energy for moving between solid and liquid at constant temperature.
- latent heat of vaporisation
- The per-kilogram energy for moving between liquid and gas at constant temperature.
- gas pressure
- Force per unit area on a surface caused by gas-particle collisions.
- sublimation
- The direct physical change from solid to gas without passing through the liquid state.
Calculate with confidence
Equations
Density
ρ = m / V
Density equals mass divided by volume.
| Symbol | Meaning | Unit |
|---|---|---|
| ρ | density | kg/m³ |
| m | mass | kg |
| V | volume | m³ |
Exam tip: Recall this equation and keep mass-volume unit pairs compatible.
Change in thermal energy
ΔE = m × c × Δθ
Energy transferred during a temperature change without a change of state.
| Symbol | Meaning | Unit |
|---|---|---|
| ΔE | change in thermal energy | J |
| m | mass | kg |
| c | specific heat capacity | J/(kg °C) |
| Δθ | temperature change | °C |
Exam tip: This equation is given; calculate final temperature minus initial temperature.
Energy for a state change
E = m × L
Energy for a state change equals mass multiplied by specific latent heat.
| Symbol | Meaning | Unit |
|---|---|---|
| E | energy for the state change | J |
| m | mass | kg |
| L | specific latent heat | J/kg |
Exam tip: This equation is given; choose fusion or vaporisation to match the state change.
Separate Physics: pressure and volume
p₁V₁ = p₂V₂
Hold gas mass and temperature steady: the product of pressure and volume stays constant.
| Symbol | Meaning | Unit |
|---|---|---|
| p₁, p₂ | initial and final pressure | Pa |
| V₁, V₂ | initial and final volume | m³ |
Exam tip: This equation is given; state fixed mass and constant temperature before using it.
Follow it step by step
Processes to remember
How to choose the thermal equation
- Ask whether the temperature changes or the state changes.
- For a temperature change with no state change, use ΔE = mcΔθ.
- For a state change at constant temperature, use E = mL.
- If both occur, split the journey into separate stages and add their energies.
Exam tip: A heating curve tells you where one equation stops and the other begins.
How to explain a gas-pressure change
- State every fixed condition: heating at fixed volume also needs a fixed gas mass or sealed sample; pV comparisons need fixed mass and temperature.
- Describe any change in molecular average kinetic energy and speed.
- Describe the change in collision frequency or momentum change at the walls.
- Link the changed force per unit area to pressure.
Exam tip: ‘Particles collide more’ needs a reason and a link to force on the wall.
See the thinking
Worked example
Worked example: warm, then melt
A 0.50 kg solid has specific heat capacity 900 J/(kg °C) and latent heat of fusion 200,000 J/kg. Find the energy to warm it by 20 °C and then melt it completely.
- Warm the solid: ΔE = mcΔθ.
- Substitute: ΔE = 0.50 × 900 × 20 = 9,000 J.
- Melt it: E = mL.
- Substitute: E = 0.50 × 200,000 = 100,000 J.
- Add the stages: 9,000 + 100,000 = 109,000 J.
Answer: The total energy required is 109,000 J, or 109 kJ.
Temperature rises during the first stage, so specific heat capacity applies. Temperature stays constant during melting, so latent heat applies. The full journey requires both energies.
Protect the marks
Common mistakes
Watch out: Drawing larger particles in a gas than in the liquid.
Do this instead: For one substance, particle size stays the same; spacing and arrangement change.
Watch out: Using mass divided by density for density itself.
Do this instead: Density is mass divided by volume: ρ = m/V.
Watch out: Saying particles expand when a substance is heated.
Do this instead: Particles move or vibrate more and may become farther apart; the particles themselves do not swell.
Watch out: Saying temperature rises while a pure substance melts.
Do this instead: During the state change, energy changes particle potential energy while temperature stays constant.
Watch out: Using final temperature instead of temperature change.
Do this instead: Use Δθ = final temperature − initial temperature.
Watch out: Separate Physics: using pV = constant while the gas is being heated.
Do this instead: Separate Physics: both the amount of gas and its temperature must remain fixed.
Plan it like the exam
Required practicals
Determine densities of solids and liquids
Combined Science and separate Physics
Aim: Measure mass and volume with appropriate apparatus to determine the density of regular solids, irregular solids and liquids.
Method
- Zero a balance and measure each solid's mass. For a liquid, weigh the empty measuring cylinder, add the liquid and reweigh it; subtract, or tare the empty cylinder before filling.
- For a regular solid, measure every needed dimension with suitable equipment—Vernier callipers, a micrometer or a ruler—then calculate volume.
- For an irregular solid, record the initial water volume, submerge it fully and find volume from the rise or displaced water.
- For a liquid, read a measured volume at eye level from the appropriate meniscus.
- Calculate density = mass ÷ volume using a consistent unit pair, then repeat measurements where practical.
Variables
- Independent
- material or sample being measured
- Dependent
- calculated density
- Controls
- temperature
- volume-reading method
- sample dryness for solid measurements
Analysis: Calculate density for each repeat and compare a mean. Check units before comparing with reference values; explain whether uncertainty comes mainly from dimensions, the meniscus or trapped air.
Safety
- Lower irregular objects gently so they do not crack the measuring cylinder or splash water.
- Keep water away from the balance and wipe spills promptly.
- Handle glassware and dense or sharp-edged samples carefully under teacher instructions.
Improvements
- Use callipers or a micrometer when they suit the dimension better than a ruler.
- Measure larger volumes or dimensions to reduce percentage uncertainty.
- Remove trapped air bubbles and dry a solid before reweighing it.
- Repeat readings and calculate a mean after checking anomalies.
Try it before you move on
Quick check
Say your answer first, then open the card to check it.
A 240 g block has volume 80 cm³. What is its density?
Answer: 3.0 g/cm³
ρ = m/V = 240 g ÷ 80 cm³ = 3.0 g/cm³.
Why is a gas usually much less dense than the same substance as a liquid?
Answer: Gas particles are much farther apart, so the same volume contains far less mass.
The particles do not shrink; their separation changes.
What does a high specific heat capacity mean?
Answer: More energy is needed to raise the temperature of each kilogram by 1 °C.
For fixed mass and energy input, a higher specific heat capacity gives a smaller temperature rise.
Why can energy enter a melting substance while its temperature stays constant?
Answer: The energy changes particle separation and potential energy rather than average kinetic energy.
The supplied energy is latent heat for the state change.
A complete heating curve has three rising slopes separated by melting and boiling plateaux. What changes on each kind of section?
Answer: On slopes, temperature and average kinetic energy rise. On plateaux, they stay constant while particle arrangement and potential energy change.
Energy enters throughout: slopes warm one state, while plateaux supply latent heat for a state change. A cooling curve reverses the sequence and energy direction.
A sealed gas sample is heated in a rigid container, so its mass and volume stay fixed. Why does its pressure increase?
Answer: Faster molecules hit the walls more often and with larger momentum changes.
Because no gas escapes and volume cannot change, those impacts increase the total force per unit area on the walls.
Separate Physics: a sealed gas sample stays at one temperature while its volume doubles. What happens to its pressure?
Answer: It halves.
For fixed mass and constant temperature, pV is constant.
Good questions, clear answers
Frequently asked questions
Do particles expand when matter is heated?
The particles themselves are not drawn larger. Their motion becomes more energetic and their average separation can increase, causing the material to expand.
Why does temperature stay constant during melting?
Supplied energy changes particle arrangement and potential energy rather than average kinetic energy. Temperature rises again after the state change is complete.
How are specific heat capacity and latent heat different?
Specific heat capacity links energy to a temperature change. Specific latent heat links energy to a state change with no temperature change.
Separate Physics: why is the force from gas pressure normal to a wall?
Separate Physics: molecules rebound from the wall, changing the component of momentum normal to it. Their combined impacts exert a net normal force.
Which content is Separate Physics only?
Separate Physics at both tiers includes the resultant wall force being normal to the surface and the pressure–volume relationship. Higher Tier also links compression work on a trapped gas to a possible temperature rise.
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