§ 2.1 Kinetic particle model of matter
Key ideas
- Solids: particles closely packed in a regular pattern, vibrating about fixed positions; fixed shape and volume.
- Liquids: particles close but irregular, able to slide past one another; fixed volume, takes the container's shape.
- Gases: particles far apart, moving quickly in all directions; a gas fills its container and is easily compressed.
- Brownian motion is the random, jerky movement of smoke or pollen grains in a fluid, caused by uneven collisions with fast-moving molecules; evidence that matter is made of tiny particles in constant motion.
- Gas pressure comes from particles colliding with the container walls; heating the gas at constant volume makes the collisions faster and more frequent, so pressure rises.
- Absolute zero, -273 °C = 0 K, is the lowest possible temperature: particles have their minimum kinetic energy.
- Extended: for a fixed mass of gas at constant temperature, pressure × volume stays constant (Boyle's law).
Equations
T = θ + 273kelvin temperature from Celsius temperatureK
p1 V1 = p2 V2fixed mass of gas at constant temperature (Extended)Pa, m³
Fig. 1 · The particle model: spacing and freedom of movement increase from solid to liquid to gas; the particles themselves never change size.
Fig. 2 · Gas pressure: every collision with a wall exerts a tiny outward force; faster particles mean harder, more frequent collisions and a higher pressure.
Fig. 3 · Boyle's law: squeeze a fixed mass of gas to half the volume at constant temperature and the pressure doubles; p × V is the same at every point on the curve.
Watch out: gas-law reasoning needs kelvin. Going from 20 °C to 40 °C is not "doubling the temperature": it is 293 K to 313 K, a rise of only 7%.
§ 2.2 Thermal properties and temperature
Key ideas
- Heating makes particles vibrate more energetically, so their average separation grows: solids expand a little, liquids more, gases most. The particles themselves do not get bigger.
- Expansion must be allowed for (gaps in bridges and rails) and can be used (bimetallic strips in thermostats).
- Extended: specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Water's is unusually high, so it warms and cools slowly.
- Ice melts at 0 °C and water boils at 100 °C. During a change of state the temperature stays constant: the energy rearranges the particles instead of speeding them up.
- Evaporation happens at any temperature and only at the surface: the most energetic molecules escape, so the liquid left behind cools.
- Evaporation is faster with a higher temperature, a larger surface area, and a draught across the surface.
Equations
c = ΔE / (m Δθ)specific heat capacity = energy ÷ (mass × temperature change) (Extended)J/(kg °C)
Fig. 4 · A heating curve for water: the flat steps show melting at 0 °C and boiling at 100 °C, where the energy supplied changes the state, not the temperature.
Fig. 5 · Evaporation: only the most energetic surface molecules can escape, so the average energy of those remaining falls and the liquid cools.
Watch out: in c = ΔE / (mΔθ), Δθ is the temperature change, never the final temperature. Heating water from 20 °C to 70 °C means Δθ = 50 °C.
§ 2.3 Transfer of thermal energy
Key ideas
- Conduction: energy is passed from particle to particle by lattice vibrations; in metals, free electrons also carry energy quickly, which is why metals conduct best.
- Liquids and gases are poor conductors because their particles are further apart; trapped air makes wool and foam good insulators.
- Convection happens only in liquids and gases: heated fluid expands, becomes less dense and rises, while cooler denser fluid sinks, setting up a convection current.
- Radiation is energy carried by infrared waves; it is the only transfer that works through a vacuum, which is how the Sun's energy reaches the Earth.
- Dull black surfaces are the best absorbers and emitters of radiation; shiny light surfaces are the worst (they are good reflectors).
- Extended: the rate of emission rises with surface temperature and surface area. The Earth keeps a steady temperature when the energy it absorbs from the Sun balances the energy it radiates back to space.
Fig. 6 · The three transfer mechanisms: conduction needs particles in contact, convection needs a fluid that can flow, radiation needs nothing at all.
Watch out: a surface that is a good absorber is also a good emitter. Dull black is best at both; shiny silver is poor at both. Being good at one never makes a surface bad at the other.