Understanding density, internal energy, and how substances change state.
Density tells us how much mass is packed into a certain volume. It depends on the particle arrangement and the mass of the individual particles.
Real-world Anchor: A brick sinks in water because it is denser, but a giant cruise ship floats because its average density is lower than water.
$$ \rho = \frac{m}{V} $$
What it calculates: Density ($\rho$) in $kg/m^3$ or $g/cm^3$.
When it applies: To any pure substance or uniform object.
⚠️ Exam Tip: $1 \, g/cm^3 = 1000 \, kg/m^3$. Always check which unit the examiner wants.
Q1: A block has a mass of 200g and a volume of 50 $cm^3$. Calculate its density.
$$ \rho = 200 / 50 = 4 \, g/cm^3 $$
Q2: Why is ice less dense than liquid water?
The water molecules in ice are arranged in a regular, spaced-out structure, taking up more volume for the same mass.
Internal energy is the total kinetic energy (due to motion) and potential energy (due to bonds/position) of all particles in a system.
Backward Link: When we "heat" a substance (Topic 2), we are increasing its internal energy.
During a change of state, energy increases potential energy without increasing temperature. When temperature increases, the state remains the same.
Q1: Define 'sublimation'.
The direct change of state from solid to gas without becoming a liquid.
Q2: Is a change of state a physical or chemical change?
It is a physical change because the substance recovers its original properties if the change is reversed.
Different materials require different amounts of energy to raise their temperature.
Real-world Anchor: A metal spoon gets hot instantly in tea, but the water takes much longer because water has a very high specific heat capacity.
$$ \Delta E = m \times c \times \Delta\theta $$
What it calculates: Change in thermal energy ($\Delta E$).
When it applies: Only when the substance is changing temperature, NOT during a change of state.
Common misuse: Using the wrong mass unit (must be in kg if $c$ is in $J/kg^\circ C$).
Q1: How much energy is needed to heat 2kg of water ($c = 4200 \, J/kg^\circ C$) by $10^\circ C$?
$$ \Delta E = 2 \times 4200 \times 10 = 84,000 \, J \, (84 \, kJ) $$
During a change of state, the temperature stays constant because energy is being used to break intermolecular bonds, not to move particles faster.
$$ E = m \times L $$
What it calculates: Energy needed for a state change.
When it applies: Only at the melting or boiling point.
Common misuse: Forgetting that $L$ is different for fusion (solid $\leftrightarrow$ liquid) vs vaporisation (liquid $\leftrightarrow$ gas).
Q1: Why does the temperature of a glass of ice water stay at $0^\circ C$ until all the ice has melted?
The energy being absorbed is used as Latent Heat to break bonds between ice particles, not to increase their kinetic energy.
Gas pressure is caused by particles colliding with the walls of their container. Each collision exerts a tiny force over an area.
Forward Link: This relates to Topic 1 where $P = F/A$.
Rule: Increasing temperature increases the speed of particles, leading to more frequent and more energetic collisions.
Q1: If you decrease the volume of a gas (at constant temp), what happens to the pressure?
Pressure increases because particles are more crowded and collide with the walls more frequently.
1. Don't assume mass changes during a state change; it is conserved!
2. Don't use $mc\Delta\theta$ on a flat part of a heating graph.
3. Don't forget that gas pressure acts at right angles to the container walls.