Particle model of matter

Explanation

• 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.

Explanation

• 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.
• The particles gain or lose energy as their arrangement changes.
• 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.

Explanation

• 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.

Explanation

• 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.
• Quote the final energy in joules.
• 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.

Explanation

• 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.

Explanation

• 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.
• This increases force per unit area.
• 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.

Explanation

• 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.
• Use consistent pressure and volume units on both sides of the equation, though the units need not be SI if they match.
• 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.

Explanation

• 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.