Thermal expansion

Most substances expand when heated. The particles do not get bigger: they move or vibrate more, so they take up more space.

Everyday examples

• Gaps in bridges and railway tracks leave room for the metal to expand on hot days without buckling.
• Overhead power cables are hung slack so they don’t snap when they contract in cold weather.
• Liquid-in-glass thermometers: the liquid expands up a narrow tube as temperature rises.
• Loosening a tight metal lid by running it under hot water: the metal lid expands more than the glass jar.

Specific heat capacity

• Heating an object increases its internal energy (the total energy of its particles), which raises its temperature.
• Different materials need different amounts of energy to warm up by the same amount. Water needs a lot; metals need much less.

Supplement Definition and equation

Specific heat capacity (c) is the energy needed to raise the temperature of 1 kg of a substance by 1 °C.

Measuring specific heat capacity

Melting, boiling and evaporation

• While a substance is melting or boiling, energy is still going in but its temperature stays the same. The energy is used to overcome the forces between particles, not to speed them up.
• For pure water at standard atmospheric pressure: melting point 0 °C, boiling point 100 °C.
• Condensation (gas → liquid) and solidification (liquid → solid): particles lose energy, slow down and the attractive forces pull them closer together.
• Evaporation happens at the surface of a liquid at any temperature. Only the more energetic particles near the surface have enough energy to escape.
• Evaporation causes cooling: the fastest particles leave, so the average kinetic energy of those left behind is lower, and temperature measures average kinetic energy.

Supplement Boiling vs evaporation

Supplement What makes evaporation faster

• Higher temperature: more particles have enough energy to escape.
• Larger surface area: more particles are at the surface.
• Air moving over the surface (wind, a fan): escaped particles are carried away before they can fall back in.

Cooling something by evaporation: when a liquid evaporates from an object (sweat on skin, water on a clay pot), the liquid cools, and energy flows from the warmer object into the liquid. The object cools down.

Conduction

Conduction is the transfer of thermal energy through a material, mainly solids, without the material itself moving.

• Good thermal conductors: metals (copper, aluminium, iron).
• Poor conductors (insulators): plastic, wood, glass, air, wool. Materials that trap air, such as foam and fleece, are especially good insulators.
• Liquids and gases are poor conductors because their particles are far apart.

Showing which material conducts best

Attach a pin to the end of equal-sized rods of different metals with wax, then heat the other ends equally. The pin falls first from the best conductor.

Supplement How conduction works

• Lattice vibrations (all solids): particles at the hot end vibrate more strongly and pass this vibration on to their neighbours, one by one. This is slow.
• Free (delocalised) electrons (metals only): electrons at the hot end gain kinetic energy and move quickly through the metal, colliding with particles further away and transferring energy. This is much faster, which is why metals are the best conductors.

Convection

Convection is the transfer of thermal energy by the movement of a liquid or gas (a fluid). It cannot happen in solids.

Showing convection: drop a crystal of potassium manganate(VII) at the bottom edge of a beaker of water and heat gently below it. The purple colour rises above the flame, moves across the top and sinks on the far side.

Thermal radiation

• Thermal radiation is infrared electromagnetic radiation. All objects emit it, and hotter objects emit more.
• It needs no medium, so it can travel through a vacuum. That is how energy reaches us from the Sun.

Comparing surfaces

Fill identical cans painted different colours (or a Leslie cube with four different faces) with the same volume of hot water. Measure the infrared from each surface with an infrared detector at the same distance, or record how fast each can cools. The dull black surface emits most and cools fastest.

Supplement Rate of radiation and the Earth’s temperature

• The rate at which an object emits radiation increases with its surface temperature and its surface area.
• An object stays at a constant temperature when it absorbs energy at the same rate as it emits it. If it absorbs faster, it warms up; if it emits faster, it cools down.
• The Earth absorbs radiation from the Sun and emits infrared back into space. Its temperature depends on the balance. Greenhouse gases in the atmosphere absorb some of the outgoing infrared and re-emit some back towards the Earth. More greenhouse gas means less energy escapes, so the balance is reached at a higher temperature. On a cloudy night, clouds trap more infrared, so it stays warmer than on a clear night.

Consequences of thermal energy transfer

What a wave does

Waves transfer energy from one place to another without transferring matter. The particles of the medium vibrate about fixed positions; they don’t travel with the wave.

Transverse and longitudinal waves

Reflection, refraction and diffraction

A ripple tank shows these effects with water waves. A light above it projects the wavefronts onto a screen below.

• Reflection: waves bounce off a flat barrier. The angle of reflection equals the angle of incidence, and the wavelength stays the same.
• Refraction: waves change speed when they move into a different medium (in a ripple tank, into shallower water where they slow down). The wavelength gets shorter and, if the waves arrive at an angle, they change direction.
• Diffraction: waves spread out when they pass through a gap or round the edge of an obstacle. The wavelength stays the same.

Supplement How much do waves diffract?

• Diffraction is greatest when the gap is about the same size as the wavelength. A gap much wider than the wavelength gives only a little spreading at the edges.
• Longer wavelengths diffract more round obstacles. That is why you can hear someone round a corner (sound wavelengths are around a metre) but can’t see them (light wavelengths are less than a millionth of a metre).

Key words

Reflection in a plane mirror

Law of reflection: angle of incidence = angle of reflection.

The image in a plane mirror is:

• the same size as the object
• the same distance behind the mirror as the object is in front
• virtual (it can’t be shown on a screen, because the light only appears to come from it)
• upright, and laterally inverted (left and right swapped)

Supplement Drawing the image in a plane mirror

Refraction

Light changes speed when it passes from one material into another. If it hits the boundary at an angle, this makes it change direction: this is refraction.

• Air → glass or water: light slows down and bends towards the normal (r is smaller than i).
• Glass or water → air: light speeds up and bends away from the normal.
• A ray that hits the boundary along the normal (i = 0) changes speed but does not change direction.

Investigating refraction with a glass block

Draw round a rectangular block on paper. Shine a narrow ray from a ray box into one side, mark the ray going in and coming out with crosses, then remove the block and join the points. Draw the normal and measure i and r with a protractor. Repeat for several angles of incidence.

Supplement Refractive index

The refractive index (n) of a material tells you how much it bends (and slows) light. It has no units, and the larger it is, the more the light bends. Glass is about 1.5; water is about 1.33.

Here i is the angle in air and r is the angle in the material.

Total internal reflection

• When light travels from glass (or water) towards air, some is refracted out and some is reflected back.
• As the angle of incidence increases, the refracted ray bends further from the normal. At the critical angle (c), the refracted ray travels along the boundary (angle of refraction = 90°).
• If the angle of incidence is greater than the critical angle, all the light is reflected back inside: total internal reflection (TIR).

Supplement Critical angle and optical fibres

Optical fibres are thin, flexible strands of very clear glass. Light entering one end hits the inside surface at an angle greater than the critical angle, so it is totally internally reflected again and again and comes out of the far end with very little loss.

• Communications: carrying telephone, cable TV and broadband signals as pulses of light or infrared.
• Medicine: an endoscope uses bundles of fibres to carry light into the body and an image back out, so doctors can look inside without major surgery.

Converging and diverging lenses

Ray diagrams for a converging lens

To find where the image of the top of an object is, draw two of these rays from it:

The top of the image is where the rays cross.

• A real image is formed where light rays actually meet. It can be projected onto a screen and is upside down (inverted).
• Describe an image with three words: real or virtual, upright or inverted, enlarged, same size or diminished.

Supplement Virtual images and the magnifying glass

• When the object is closer to the lens than F, the rays leaving the lens spread apart and never meet. Extend them backwards with dashed lines: they appear to meet behind the object. That is where the virtual image is.
• A virtual image can’t be projected on a screen. A magnifying glass uses a converging lens this way to give an upright, enlarged image.

Supplement Correcting eyesight

Dispersion of light

• When white light passes through a glass prism, it is refracted and splits into a spectrum of colours: this is dispersion.
• Each colour refracts by a slightly different amount: violet bends the most, red the least.
• The seven colours, in order: red, orange, yellow, green, blue, indigo, violet (“ROY G BIV”).

Supplement Colour, frequency and wavelength

• From red to violet, frequency increases and wavelength decreases. Red has the longest wavelength of visible light; violet has the shortest.
• Monochromatic light has a single frequency (one colour), e.g. light from a laser.

Properties all EM waves share

• They are all transverse waves.
• They can all travel through a vacuum.
• They all travel at the same speed in a vacuum: 3.0 × 10⁸ m/s (about the same in air).
• They all transfer energy, and can be reflected and refracted.

Uses

Harmful effects

EM waves in communication

• Microwaves: mobile phones, wireless internet and satellite communication. They pass easily through the atmosphere to and from satellites.
• Radio waves: Bluetooth and radio broadcasting. Longer radio waves diffract around hills and buildings, so they reach areas without a direct line of sight.
• Visible light and infrared: optical fibres for cable TV and high-speed broadband, because the glass is very transparent to them and they can carry a lot of data.

Supplement Analogue and digital signals

• An analogue signal varies continuously and can take any value (like the sound wave from your voice).
• A digital signal has only two values: on and off (1 and 0).
• Sound can be sent as either. To send it digitally, the analogue signal is converted into a code of 1s and 0s.

Benefits of digital signals:

• As any signal travels, it gets weaker and picks up noise (random unwanted changes). A digital signal can be regenerated: it only has to be recognised as a 1 or a 0, so the noise is removed and a clean copy is sent on. When an analogue signal is amplified, the noise is amplified with it.
• This means digital signals can travel longer distances with no loss of quality, and data can be sent faster.

How sound is made and travels

• Sound is produced by vibrating objects (a guitar string, a loudspeaker cone, your vocal cords).
• Sound is a longitudinal wave: the particles of the medium vibrate back and forth parallel to the direction the wave travels.
• It travels as a series of compressions (particles squashed together, higher pressure) and rarefactions (particles spread out, lower pressure).
• Sound needs a medium (solid, liquid or gas) and cannot travel through a vacuum. If air is pumped out of a jar containing a ringing bell, the sound fades even though you can still see the bell vibrating.

Hearing, pitch and loudness

• The range of human hearing is about 20 Hz to 20 000 Hz (20 kHz).
• Higher frequency = higher pitch.
• Larger amplitude = louder sound.
• An echo is a reflected sound wave.

The speed of sound

• In air, the speed of sound is about 330–350 m/s.
• Sound travels fastest in solids, slower in liquids and slowest in gases.

Measuring the speed of sound in air (echo method)

Another method: two people stand a measured distance apart. One makes a loud sound with a visible action (bangs two blocks together) and the other starts a stopwatch on seeing it and stops it on hearing it. Light arrives almost instantly, so speed = distance ÷ time.

Supplement Ultrasound

Ultrasound is sound with a frequency above 20 kHz, too high for humans to hear. It partly reflects at boundaries between different materials, and the time taken for the echo to return shows how deep the boundary is.

• Non-destructive testing: finding cracks or flaws inside metal parts (such as aircraft wings or rail tracks) without damaging them. A crack reflects some ultrasound back early.
• Medical scanning of soft tissue: e.g. scanning an unborn baby. Unlike X-rays, ultrasound is not ionising, so it is safe.
• Sonar: ships send pulses of ultrasound down and time the echo from the sea bed or a shoal of fish to find the depth.

The structure of the atom

• An atom has a tiny, dense, positively charged nucleus at its centre, made of protons and neutrons.
• Electrons (negatively charged) orbit the nucleus. Most of the atom is empty space.
• An atom has equal numbers of protons and electrons, so it is neutral overall.
• An atom that loses electrons becomes a positive ion; one that gains electrons becomes a negative ion.

Supplement Evidence: the alpha-particle scattering experiment

Rutherford’s team fired alpha particles (small, positive) at a very thin sheet of gold foil and recorded where they went.

The nucleus and nuclide notation

A nuclide is written as ^A_ZX, for example ¹⁴₆C: carbon-14 has 6 protons and 14 − 6 = 8 neutrons.

Supplement What A and Z tell you

• The proton number is also the relative charge of the nucleus (each proton is +1, neutrons are 0).
• The nucleon number is the relative mass of the nucleus (protons and neutrons each have a relative mass of 1).

Isotopes

Isotopes are atoms of the same element (same number of protons) with different numbers of neutrons, so different nucleon numbers. Example: carbon-12 (6 neutrons) and carbon-14 (8 neutrons). Some isotopes are unstable and radioactive.

Nuclear fission and fusion

Detecting radiation and background radiation

• Ionising nuclear radiation is measured with a detector such as a Geiger–Müller (GM) tube connected to a counter. The count rate is given in counts per second or counts per minute.
• Background radiation is the low level of radiation around us all the time. Its sources include:
  • radon gas in the air (from rocks and soil)
  • rocks and buildings
  • food and drink
  • cosmic rays from space

Supplement Correcting for background

Measure the background count rate with no source present, then subtract it from every reading taken with the source. This gives the corrected count rate due to the source alone.

The three types of radiation

• Radioactive decay is spontaneous (nothing triggers it) and random (you can’t predict which nucleus will decay next, or when).
• It happens because the nucleus is unstable. Emitting radiation makes it more stable.

Supplement Deflection in electric and magnetic fields

• Alpha and beta are charged, so they are deflected by electric and magnetic fields, in opposite directions.
• Beta is deflected more than alpha because a beta particle has a much smaller mass.
• Gamma is uncharged, so it is not deflected.
• In an electric field, alpha bends towards the negative plate and beta towards the positive plate.

Supplement Why their ionising effects differ

Ionisation happens when radiation knocks electrons off atoms. Alpha particles have a large charge (+2) and are relatively large and slow, so they interact strongly with nearly every atom they pass. They lose all their energy quickly and travel only a short distance. Beta particles have less charge and move faster, so they ionise less. Gamma rays have no charge and rarely interact, so they ionise least and penetrate furthest.

Radioactive decay equations

• In alpha and beta decay the number of protons changes, so the nucleus becomes a different element.
• Gamma emission does not change the proton or nucleon number. The nucleus just loses energy.

Supplement Why isotopes decay and what happens in beta decay

• Isotopes can be unstable because they have too many neutrons (or too few), or because the nucleus is too heavy.
• In beta decay, a neutron changes into a proton and an electron. The proton stays in the nucleus and the electron is emitted as the beta particle. That is why Z goes up by 1 but A stays the same.

Half-life

The half-life of a radioactive isotope is the time taken for half the nuclei in a sample to decay. Equivalently, it is the time taken for the count rate (activity) to fall to half its value.

Uses of radioactive isotopes

The best isotope for a job depends on the type of radiation (how penetrating it is) and its half-life.

Safety

• Ionising radiation can kill cells, cause mutations (damage to DNA) and lead to cancer.
• Keep exposure as low as possible:
  • Reduce exposure time: use the source for as short a time as possible.
  • Increase distance: handle sources with long tongs and never point them at people.
  • Use shielding: store sources in lead-lined boxes and use lead or concrete barriers.

Supplement Explaining the safety precautions

• Shorter time: fewer particles or rays reach the body, so less ionisation and lower risk.
• Greater distance: radiation spreads out (and alpha and beta are absorbed by air), so less reaches the body.
• Shielding: dense materials like lead absorb the radiation before it reaches people.
• Alpha sources are most dangerous inside the body (if swallowed or breathed in), because alpha is so strongly ionising. Outside the body, skin stops it.

The Earth, the Sun and the Moon

Seasons

The Earth’s axis is tilted (by about 23°) and always points the same way in space as the Earth orbits the Sun. When your hemisphere is tilted towards the Sun, it is summer: the Sun is higher in the sky, its energy is more concentrated on each square metre of ground and the days are longer. Six months later your hemisphere is tilted away from the Sun and it is winter.

Phases of the Moon

• The Moon gives out no light of its own. We see it because it reflects sunlight.
• The half of the Moon facing the Sun is always lit. As the Moon orbits the Earth, we see different amounts of that lit half.
• New Moon: the Moon is between the Earth and the Sun, so its lit side faces away from us and we see almost nothing.
• Full Moon: the Earth is between the Sun and the Moon, so we see the whole lit half.
• The cycle from new Moon to full Moon and back takes about a month, showing that the Moon orbits the Earth once a month.

What is in the Solar System

• One star: the Sun.
• Eight planets orbiting the Sun. In order from the Sun: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.
• Minor planets orbiting the Sun, including dwarf planets such as Pluto, and asteroids in the asteroid belt between Mars and Jupiter.
• Moons (natural satellites), which orbit planets.
• Smaller bodies, including comets: lumps of ice and dust with very stretched (elliptical) orbits.

Inner and outer planets

How the Solar System formed (the accretion model)

Light travelling across the Solar System

Distances in space are so large that even light takes time to cross them. Use speed = distance ÷ time with the speed of light, 3.0 × 10⁸ m/s.

Gravity and orbits

• The gravitational attraction of the Sun is the force that keeps the planets, minor planets and comets in orbit.
• Planets, minor planets and comets move in elliptical orbits (stretched circles). Most planets’ orbits are very nearly circular; comets’ are very stretched.

Using planetary data

Exam questions often give a table of data about the planets (distance from the Sun, orbital time, density, surface temperature, gravitational field strength) and ask you to spot patterns. Look for:

• The further a planet is from the Sun, the longer its orbit takes and (generally) the colder its surface. Venus is the exception for temperature: its thick carbon dioxide atmosphere traps energy.
• The inner rocky planets have higher densities than the outer gas giants.
• Planets with more mass have a stronger gravitational field at their surface (Jupiter’s is the strongest).

Supplement Gravitational fields

• The gravitational field strength at the surface of a planet depends on the planet’s mass.
• The field around a planet (or the Sun) gets weaker as the distance increases.
• The Sun contains most of the mass of the Solar System (over 99%). This is why everything orbits the Sun.
• Further from the Sun, its gravitational field is weaker, so the planets’ orbital speeds are lower and their orbits take much longer.

Supplement Orbital speed

2πr is the distance round a circular orbit, so this is just speed = distance ÷ time.

Supplement Speed in an elliptical orbit

• An object in an elliptical orbit (such as a comet) moves fastest when it is closest to the Sun and slowest when it is furthest away.
• Why (conservation of energy): as the comet moves towards the Sun, it loses gravitational potential energy, which is converted to kinetic energy, so it speeds up. As it moves away, kinetic energy is converted back to gravitational potential energy, so it slows down. The total energy stays the same.
• In a circular orbit the distance from the Sun stays the same, so the speed is constant, but the velocity changes all the time because the direction of motion keeps changing.

The Sun

• The Sun is a star of medium size.
• It is made mostly of hydrogen and helium.
• It radiates most of its energy as infrared, visible light and ultraviolet. Visible light is the peak; infrared has longer wavelengths and ultraviolet shorter.
• Stars are powered by nuclear reactions that release energy. In stable stars like the Sun, the reaction is the fusion of hydrogen nuclei into helium.

Galaxies and the light-year

• A galaxy is made up of many billions of stars.
• The Sun is one of the stars in our galaxy, the Milky Way.
• Other stars in the Milky Way are much further from Earth than any planet. The nearest, Proxima Centauri, is about 4 light-years away.
• The Milky Way is one of many billions of galaxies in the Universe. Its diameter is about 100 000 light-years.

A light-year is the distance light travels through space in one year: about 9.5 × 10¹⁵ m.

Supplement The life cycle of a star

The expanding Universe and redshift

• Redshift is an increase in the observed wavelength of electromagnetic radiation from stars and galaxies that are moving away from us. The light is shifted towards the red end of the spectrum.
• Light from distant galaxies is redshifted compared with light from the same elements on Earth. So the galaxies are moving away from us.
• This shows the Universe is expanding and supports the Big Bang Theory: the Universe began from a single point a long time ago and has been expanding ever since.

Supplement Cosmic microwave background radiation (CMBR)

• The CMBR is microwave radiation of a specific frequency that is detected coming from every direction in space.
• It was produced shortly after the Universe formed, when the Universe was extremely hot. As the Universe expanded, the wavelength of this radiation was stretched until it reached the microwave region.
• It is further evidence for the Big Bang.

Supplement The Hubble constant and the age of the Universe

• The speed v at which a galaxy is moving away is found from the change in wavelength of its light (its redshift).
• The distance d to a far galaxy can be found from the brightness of a supernova in it: supernovae of a particular type all have about the same true brightness, so a dimmer one is further away.
• The further away a galaxy is, the faster it is moving away. The ratio is the Hubble constant, H₀, currently estimated at about 2.2 × 10⁻¹⁸ per second.

On a graph of speed (y-axis) against distance (x-axis) for galaxies, the gradient is H₀.

Why: if a galaxy has always moved away at speed v, then d ÷ v is the time it has taken to travel distance d from the point where everything started. Because d ÷ v is the same for every galaxy, everything was together at a single point at that time. This is evidence that the Universe expanded from a single point.

Numbers to remember