Physics, Chemistry & Space

Most liquids shrink when they become solid. Water is different. When it freezes, its particles lock into an open pattern with gaps. So ice takes more space than the same water. Ice is lighter (less dense) than water and floats. Water pipes can burst on very cold nights for this reason.

Besides solid, liquid and gas, matter can be plasma — the glowing gas inside stars and neon signs — or a Bose–Einstein condensate, a very cold state named after the Indian scientist Satyendra Nath Bose and Albert Einstein.

Evaporating particles take heat from their surroundings. So the place they leave becomes cooler. Sweat cools the body, and water in an earthen pot (ghara) stays cool. Evaporation is faster with a larger surface, higher temperature, dry air and wind.

Common salt (sodium chloride) with a very small amount of potassium iodide (or potassium iodate) mixed in. The two do not react; they are only mixed. So iodised salt is a mixture. The iodine prevents goitre.

Soda water (an aerated drink) is carbon dioxide gas dissolved in water under pressure. So it is a gas-in-liquid solution: carbon dioxide is the solute and water is the solvent. When the bottle is opened, the pressure falls and the gas bubbles out.

• Water expands on freezing; that is why ice floats.
• Gas → liquid is condensation; solid → gas is sublimation.
• Diamond is an element (carbon), not a mixture. Air, soil and sea water are mixtures.
• Iodised salt is a mixture with potassium iodide, not a compound, and not 'molecular iodine'.
• Nitrogen is 78% of air by volume, not by mass.
• In soda water, CO2 is the solute and water the solvent.
• Milk and fog are colloids, not true solutions.

Convert 27 °C to kelvin, and 373 K to °C.

• Solid: fixed shape and volume; gas: neither
• Ice is lighter than water and floats
• Sublimes: camphor, naphthalene, dry ice, ammonium chloride
• Air: N2 78%, O2 21%, Ar 0.93%, CO2 0.04% by volume
• Mixtures: air, soil, sea water, iodised salt, brass
• Soda water: CO2 dissolved in water
• K = °C + 273

A body moving in a circle at constant speed keeps changing direction. So its velocity changes, and the motion is accelerated. The force that keeps it on the circle points to the centre. It is called the centripetal force. The Moon going round the Earth is an example.

On a distance–time graph, the slope gives the speed. On a velocity–time graph, the slope gives the acceleration and the area under the line gives the distance. A vehicle's odometer records distance; its speedometer shows speed.

Inertia is a body's tendency to resist any change in its rest or motion. Mass is the measure of inertia: a loaded truck is harder to start or stop than a bicycle. When a bus starts suddenly, standing passengers fall backward (inertia of rest). When it stops suddenly, they fall forward (inertia of motion).

Momentum (p) = mass × velocity. Its unit is kg m/s. If no outside force acts, the total momentum stays the same: the law of conservation of momentum. When a gun fires, the bullet goes forward and the gun moves back with equal and opposite momentum. This backward kick is the recoil.

Every two objects in the universe pull each other. The force grows with their masses and falls with the square of the distance between them: F = G m₁m₂ / d². Double the distance, and the force becomes one-fourth. G is the universal gravitational constant, 6.67 × 10⁻¹¹ N m²/kg², the same everywhere.

Near the Earth's surface every freely falling body speeds up at about 9.8 m/s², whatever its mass. In a vacuum a feather and a coin fall together. g is a little more at the poles than at the equator. It falls as we go up, and also as we go down into the Earth. At the centre of the Earth, g is zero.

• Free fall: acceleration is constant; velocity and speed are not.
• g (9.8 m/s², changes from place to place) is not G (6.67 × 10⁻¹¹ N m²/kg², same everywhere).
• Least weight: the centre of the Earth (zero). On the surface: the equator.
• Rocket and gun recoil: Newton's third law — not Kepler, not Einstein.
• Bus starts: fall backward (inertia of rest). Bus stops: fall forward (inertia of motion).
• Uniform circular motion is accelerated motion, though the speed is constant.

A car starts from rest and reaches 20 m/s in 5 s. What is its acceleration?

A person has a mass of 60 kg. What is the weight on Earth (g = 10 m/s²) and on the Moon?

• Distance scalar; displacement vector
• km/h × 5/18 = m/s
• v = u + at; s = ut + ½at²; v² − u² = 2as
• First law inertia; second F = ma; third action–reaction
• p = mv; momentum is conserved; rocket and recoil
• g = 9.8 m/s²; more at poles; zero at Earth's centre
• Weight = mg, in newtons; Moon weight about 1/6

The SI unit of work, named after James Prescott Joule. 1 joule is the work done when a force of 1 newton moves an object through 1 metre along the line of the force. A larger unit is the kilojoule: 1 kJ = 1000 J.

To lift a mass m through a height h, the work done is W = m × g × h. A porter who lifts a 15 kg bag onto his head 1.5 m above the ground does 15 × 10 × 1.5 = 225 J of work, taking g = 10 m/s². Carrying it along the level platform afterwards adds no work against gravity.

The energy an object has because of its motion: KE = ½mv², where m is mass and v is speed. Because speed is squared, doubling the speed makes the kinetic energy four times, while doubling the mass only doubles it. An object of mass 15 kg moving at 4 m/s has KE = ½ × 15 × 4 × 4 = 120 J.

The energy stored in an object because of its position or shape. An object raised to a height h has gravitational potential energy PE = mgh. It depends only on the height reached, not on the path taken to get there. A 10 kg object kept 6 m above the ground has PE = 10 × 10 × 6 = 600 J, taking g = 10 m/s². A stretched rubber band, a wound spring of a toy car and a bent bow also store potential energy.

Energy can neither be created nor destroyed; it can only be changed from one form to another. The total energy before and after any change remains the same.

The rate of doing work, or the rate at which energy is used: P = W / t. Its SI unit is the watt (W), named after James Watt. 1 W = 1 J/s. Two people may do the same work, but the one who finishes it faster has more power. An agent that does 1200 J of work in 60 s has a power of 1200 ÷ 60 = 20 W.

1 kWh is the energy used in 1 hour at a rate of 1000 W, that is 1000 J every second. In 1 hour there are 3600 seconds, so 1 kWh = 1000 × 3600 J = 3.6 × 10⁶ J. One 'unit' of electricity on a household bill means 1 kWh.

Coal, petroleum and natural gas formed from the remains of plants and animals buried over millions of years. Burning them releases oxides of carbon, nitrogen and sulphur. The oxides of sulphur and nitrogen are acidic and cause acid rain; carbon dioxide is a greenhouse gas.

Water stored behind a high dam has potential energy. It is let down through pipes to turbines at the bottom of the dam, and the falling water turns them to make electricity. Hydro power is renewable, because the reservoir is filled again whenever it rains.

Large dams submerge farmland and villages, displace people, and destroy ecosystems. Plants left under the water rot without oxygen and give off methane, a greenhouse gas. The Tehri dam in Uttarakhand and the Sardar Sarovar dam on the Narmada both faced protests over such problems.

Cow dung, plant waste and sewage are mixed with water into a slurry and kept in a sealed digester with no oxygen. Anaerobic micro-organisms break them down and give biogas, which contains up to 75% methane. It burns without smoke, leaves no residue and gives a lot of heat. The slurry left behind is a manure rich in nitrogen and phosphorus. Biogas is also called gobar gas.

When wood is burnt in a limited supply of oxygen, water and volatile matter escape and charcoal is left. Charcoal burns without flames, gives almost no smoke and produces more heat than wood.

Moving air has kinetic energy. Windmills once used it to lift water and grind grain; today the turning blades of a wind turbine drive a generator. Many turbines in one area form a wind energy farm. The wind should blow for most of the year at a speed above 15 km/h. Drawbacks: it needs a large area of land, the turbines need regular maintenance, and no electricity is made when the wind drops.

Ethanol is a biofuel made by fermenting the sugar of sugarcane juice or molasses. India mixes it with petrol. Wood, gobar gas and coal all come from living things (coal from ancient plants), but nuclear energy does not: it comes from splitting uranium atoms.

A box painted black inside, because a black surface absorbs more heat than a white or shiny one. A glass sheet on top lets sunlight in but traps the heat, and a mirror reflects extra sunlight into the box. It saves fuel and causes no pollution, but cannot be used at night or on cloudy days and cooks slowly. Solar water heaters work on the same idea.

A device that changes sunlight directly into electricity. Solar cells are made mainly of silicon. A typical cell gives a voltage of 0.5–1 V and about 0.7 W of electricity in sunlight, so many cells are joined into a solar panel. They have no moving parts and need little maintenance. The special-grade silicon is limited and costly, and silver used to connect the cells adds to the cost.

Solar panels power artificial satellites and space probes, traffic signals, calculators, and radio and TV relay stations in remote areas.

India's biggest tidal energy potential is in Gujarat: the Gulf of Khambhat (Cambay), then the Gulf of Kutch. The Sundarbans delta in West Bengal has a smaller potential.

The fission of one uranium atom gives about ten million times the energy released by burning one carbon atom of coal. But used fuel stays radioactive and is hard to store and dispose of safely, leaks of radiation are dangerous, plants are costly to build, and uranium is limited — so nuclear energy is non-renewable.

• Holding a heavy load still, or carrying it on level ground, is zero work against gravity — even though you feel tired.
• Doubling the speed makes kinetic energy four times, not two times.
• The kilowatt hour is a unit of energy, not power. The watt and the horsepower are units of power.
• Nuclear reactors and the atom bomb use fission; the Sun and the hydrogen bomb use fusion.
• A motor turns electrical energy into mechanical energy; a generator does the reverse.
• Biogas is mostly methane; LPG is mostly butane and propane.

A 60 W bulb glows for 6 hours a day. How much electrical energy does it use in a day, and how many units in 30 days?

A girl of mass 50 kg climbs a staircase 6 m high in 20 s. Find the work she does against gravity and her power. Take g = 10 m/s².

• W = F × s; unit joule
• Zero work: no displacement, or force at right angles
• KE = ½mv²; PE = mgh
• Energy is neither created nor destroyed
• P = W / t; 1 W = 1 J/s; 1 hp = 746 W
• 1 kWh = 1 unit = 3.6 × 10⁶ J
• Biogas: methane; solar cell: silicon
• Fission in reactors; fusion in the Sun

A mole is a fixed count of particles: 6.022 × 10²³, the Avogadro number — just as a dozen means 12. One mole of a substance weighs its formula mass in grams. One mole of water (H2O, 18 u) weighs 18 g.

The three isotopes of hydrogen. Mineral water carries minerals such as calcium, magnesium and potassium — never tritium.

Some atoms are unstable. They break down on their own and give out rays — this is radioactivity, found by Henri Becquerel in 1896 from uranium salts. Living things take in a little radioactive carbon-14. After death no new carbon-14 comes in, and the old amount halves every 5,730 years. Measuring what is left tells the age of bones, wood and other remains of once-living things. This is radiocarbon dating.

The four families asked most often

• Conservation of mass: Lavoisier, not Boyle or Dalton.
• Thomson: electron; Rutherford: nucleus; Chadwick: neutron; Bohr: shells; Becquerel: radioactivity.
• Tritium is a radioactive isotope of hydrogen, not a mineral.
• Carbon dating is for things that were once alive — not rocks or soil.
• H2 has a covalent bond; NaCl has an ionic bond.
• Mercury is a liquid metal but not an alkali metal; bromine is the liquid non-metal.
• Mendeleev used atomic mass; the modern table uses atomic number.

An atom has 11 protons and 12 neutrons. Find its atomic number, mass number and the element.

• Lavoisier: conservation of mass; Proust: constant proportions
• Electron 1897 Thomson; neutron 1932 Chadwick
• Z = protons; A = protons + neutrons
• Hydrogen isotopes: protium, deuterium, tritium
• Carbon-14 half-life about 5,730 years
• Group 1 alkali metals; 17 halogens; 18 noble gases
• Transition metal compounds are coloured

Humans speak with the larynx, at the upper end of the windpipe. Two vocal cords are stretched across it, leaving a narrow slit. When the lungs force air through the slit, the vocal cords vibrate and produce sound. Muscles make the cords tighter or looser to change the voice. The vocal cords of men are about 20 mm long, those of women about 5 mm shorter, and those of children very short — which is why their voices differ.

Sound travels through solids, liquids and gases, but not through a vacuum. Put a ringing electric bell in an airtight glass jar and pump the air out: the sound grows fainter and fainter, though the bell keeps vibrating. On the Moon, which has no air, astronauts cannot hear each other directly and talk by radio.

As a vibrating object moves forward it pushes the air in front of it together, making a region of high pressure and density — a compression. As it moves back it leaves a region of low pressure and density — a rarefaction. A series of compressions and rarefactions travels outward as the sound wave.

Speed = frequency × wavelength. A sound of frequency 2000 Hz and wavelength 0.17 m travels at 2000 × 0.17 = 340 m/s. In a given medium the speed of sound stays the same, so a higher frequency means a shorter wavelength.

Loudness is proportional to the square of the amplitude: if the amplitude doubles, the loudness becomes 4 times. Loudness is expressed in decibels (dB).

Temperature: warmer air carries sound faster. Humidity: moist air is lighter than dry air, so sound is faster in humid air. Pressure: at a fixed temperature, changing the pressure changes the density in the same ratio, so the speed does not change.

Sound bounces off hard surfaces, obeying the same laws of reflection as light. The reflected sound heard after the original is an echo. The sensation of a sound stays in the brain for about 0.1 s, so the echo must arrive at least 0.1 s later to be heard separately. At 22 °C sound travels 344 m/s; in 0.1 s it covers 34.4 m — there and back — so the reflecting surface must be at least 17.2 m away. The rolling of thunder is due to repeated reflections of sound from clouds and the land.

In a big hall, sound is reflected again and again from the walls, ceiling and floor, and lingers after the source has stopped. This persistence is reverberation; too much of it makes speech and music unclear. Halls are made to sound right by covering the roof and walls with sound-absorbing materials such as compressed fibreboard, rough plaster or heavy curtains, and by choosing seats that absorb sound.

SOund Navigation And Ranging. A transmitter on a ship sends out pulses of ultrasound; they reflect from the seabed or an underwater object, and a detector picks up the echo. If the echo returns after time t and the speed of sound in sea water is v, the distance is d = v × t ÷ 2. SONAR finds the depth of the sea and locates submarines, icebergs, sunken ships, and underwater hills and valleys.

RADAR uses radio waves, not ultrasound; SONAR uses ultrasound under water. Besides bats and dolphins, dogs and some whales (the toothed whales) also hear ultrasound.

The stirrup (stapes) of the middle ear is the smallest bone in the human body. The three ear bones are also called malleus (hammer), incus (anvil) and stapes (stirrup).

Unpleasant sound is noise; pleasant sound is music. The presence of excessive or unwanted sound in the surroundings is noise pollution.

Fit silencers to aircraft engines, vehicles, industrial machines and home appliances; keep noisy industries away from homes; use horns as little as possible; keep TV and music at low volume; and plant trees along roads and around buildings to absorb sound.

• Pitch depends on frequency; loudness depends on amplitude. Do not swap them.
• The least distance for an echo is 17.2 m, not 34.4 m — 34.4 m is the distance there and back.
• Sound is fastest in solids and slowest in gases — the opposite of what many students guess.
• Sound in air is a longitudinal wave; light is transverse and needs no medium.
• Bats and dolphins use ultrasound; elephants, whales and rhinoceroses use infrasound.
• In SONAR the echo time is for the round trip, so divide v × t by 2.

A person claps near a cliff and hears the echo after 2 s. If the speed of sound is 346 m/s, how far away is the cliff?

A ship's SONAR receives the echo from the seabed 3.42 s after sending the pulse. If the speed of sound in sea water is 1531 m/s, how deep is the sea?

• Sound comes from vibration; no sound in a vacuum
• Longitudinal: compressions and rarefactions
• v = νλ; 1 Hz = 1 oscillation per second
• Pitch: frequency; loudness: amplitude, in dB
• Audible 20 Hz to 20 kHz; below is infrasound, above is ultrasound
• Speed: solids, then liquids, then gases
• Echo: 0.1 s and at least 17.2 m
• Ear: hammer, anvil, stirrup; cochlea to brain

Signs that a reaction has taken place: a change of colour, a gas given off, a change of temperature, or an insoluble solid (precipitate) forming. Equations are balanced because mass is conserved: 2H2 + O2 → 2H2O.

Oxidation in daily life

Soda water is water with carbon dioxide dissolved in it under pressure. A little of the gas forms the weak carbonic acid, which gives the drink its slight sour bite. When the bottle is opened, the extra gas escapes as bubbles.

• Oxidation is loss of electrons, not gain. Gain of electrons is reduction.
• Temperature goes up = exothermic; goes down = endothermic.
• Ant sting is formic (methanoic) acid, not oxalic.
• Lemon: citric; milk and curd: lactic; vitamin C: ascorbic; vinegar: acetic.
• Acids have pH less than 7; a lower pH means a stronger acid.
• Baking soda is NaHCO3 (sodium bicarbonate); washing soda is Na2CO3·10H2O.
• Kidney stones: calcium oxalate, not just 'calcium'.

An ant bites you. What should you apply, and why?

• Combination, decomposition, displacement, double displacement
• Lime + water: combination and exothermic
• OIL RIG: oxidation is loss, reduction is gain
• Acid turns blue litmus red; base turns red litmus blue
• pH 7 neutral; blood 7.4; gastric juice 1.2
• Acid + base → salt + water
• Plaster of Paris CaSO4·½H2O; gypsum CaSO4·2H2O

Metals listed from most to least reactive. Potassium and sodium at the top react violently with water. Gold and silver at the bottom hardly react, so they are found free in nature and used for jewellery.

Metals at work in kitchens and in living things

Carbon has 4 outer electrons, which it shares to make covalent bonds (valency 4). Carbon atoms also join one another in long chains, branches and rings — this is catenation. Most carbon compounds are poor conductors and have low melting and boiling points.

• Brittle describes non-metals, not metals.
• Galvanising = zinc, not tin, lead or chromium.
• Vulcanisation is for rubber (with sulphur), not for iron.
• Rusting is a chemical change; salt water speeds it up.
• Chlorophyll has magnesium; haemoglobin has iron.
• Coal is not an allotrope of carbon; graphene is.
• Allotropes ≠ isotopes. '-ol' = alcohol; '-ane' = alkane.

Why are electric wires made of copper and covered with plastic?

• Liquid metal: mercury; liquid non-metal: bromine
• Li, Na, K: soft, cut with a knife, kept in kerosene
• Reactivity: K > Na > Ca > Mg > Al > Zn > Fe > Pb > Cu > Ag > Au
• Bauxite: aluminium; haematite: iron; galena: lead
• Rust needs air + water; zinc coat = galvanising
• Diamond hardest; graphite conducts; coal is not an allotrope
• Soap fails in hard water; detergent works

First law: the angle of incidence is equal to the angle of reflection. Second law: the incident ray, the reflected ray and the normal at the point of incidence all lie in the same plane. Both angles are measured from the normal, not from the mirror surface. These laws hold for every reflecting surface, flat or curved.

Two plane mirrors at an angle θ form 360/θ − 1 images of an object between them: at 90° you see 3 images, and parallel mirrors give endless images. A kaleidoscope uses mirror strips set at an angle to make repeating patterns, and a periscope uses two plane mirrors to see over obstacles.

A spherical mirror is part of a hollow sphere. Its centre is the pole (P); the centre of the sphere is the centre of curvature (C) and its radius is the radius of curvature (R). Rays parallel to the principal axis meet, or appear to meet, at the principal focus (F). The distance PF is the focal length, and for small mirrors f = R/2.

1/v + 1/u = 1/f, where u is the object distance, v the image distance and f the focal length. All distances are measured from the pole; distances in the direction of the incident light are positive and those against it are negative. So the focal length of a concave mirror is negative and that of a convex mirror is positive. Magnification m = −v/u; a negative m means a real, inverted image.

Large concave mirrors concentrate sunlight to produce heat in solar furnaces. A dentist uses a concave mirror to see a large image of the teeth, and the reflector behind a torch bulb or a headlight is concave, so that light from a bulb placed at its focus comes out as a strong parallel beam.

The refractive index of a medium tells how much light slows down in it: n = speed of light in vacuum ÷ speed of light in the medium. It has no unit. A medium with a higher refractive index is optically denser. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media; this is Snell's law.

The power of a lens is its ability to converge or diverge light: P = 1/f, with f in metres. The SI unit is the dioptre (D); 1 D is the power of a lens of focal length 1 m. A lens of +2.0 D is a convex lens with f = 0.5 m, and one of −2.0 D is a concave lens with f = −0.5 m. The powers of lenses placed in contact simply add up.

When light passes from one medium into another, its speed and wavelength change, but its frequency stays the same. Frequency is fixed by the source.

For a convex lens, an object at 2F gives a real, inverted image of the same size at 2F on the other side. An object between F and the lens gives a virtual, erect, enlarged image: this is the magnifying glass.

For lenses, 1/v − 1/u = 1/f, and magnification m = v/u. Distances are measured from the optical centre. The focal length of a convex lens is positive and that of a concave lens is negative. Note the minus sign: the mirror formula has a plus sign.

The ability of the eye lens to change its focal length. When the ciliary muscles relax, the lens becomes thin and we see distant objects; when they contract, the lens becomes thicker and we see nearby objects. The closest point at which a normal eye sees clearly without strain is the near point, about 25 cm, also called the least distance of distinct vision. The far point of a normal eye is at infinity.

The retina has two kinds of light-sensitive cells: rods respond to the intensity of light and help in dim light, while cones respond to colour and work in bright light. A person whose cones do not work properly cannot tell some colours apart; this is colour blindness.

The splitting of white light into its seven colours by a glass prism. Each colour bends through a different angle: red deviates the least and violet the most. The band of colours is the spectrum. Isaac Newton was the first to obtain the spectrum of sunlight with a glass prism, and he showed that a second, inverted prism recombines the colours into white light.

VIBGYOR: Violet, Indigo, Blue, Green, Yellow, Orange, Red. Violet is at the bottom of the spectrum because it bends the most; red is at the top and has the longest wavelength of visible light.

When light travels from a denser medium towards a rarer one and the angle of incidence is greater than a certain critical angle, no light passes out: it is all reflected back into the denser medium. It explains the sparkle of a diamond, whose very small critical angle traps light inside; optical fibres, which carry light along bent glass threads for telephone and internet signals and for endoscopy; and the mirage of water seen on hot roads and in deserts, where the air near the ground is hotter and rarer.

Uses of optical fibres: long-distance telephone and internet links, endoscopy (seeing inside the body), sensors that read the temperature inside jet engines, and pipes that carry sunlight from a roof into rooms of a building.

• A plane mirror reverses left and right, not top and bottom; its image is virtual, never real.
• Focal length is half the radius of curvature: f = R/2, not 2R.
• Convex mirror diverges, but convex lens converges.
• In P = 1/f the focal length must be in metres; a concave lens has negative power.
• Myopia means you see NEAR things clearly; it needs a concave lens.
• Danger signals are red because red is scattered the LEAST, not the most.
• Stars twinkle because of atmospheric refraction, not scattering; planets do not twinkle.

An optician prescribes a lens of power −2.5 D. What kind of lens is it, and what is its focal length?

Why do stars twinkle while planets do not?

• Speed of light in vacuum: 3 × 10⁸ m/s
• Angle of incidence = angle of reflection
• f = R/2; mirror: 1/v + 1/u = 1/f
• Concave mirror: headlights, shaving, dentist; convex: rear-view
• P = 1/f in metres; unit dioptre
• Myopia: concave; hypermetropia: convex; presbyopia: bifocal; astigmatism: cylindrical
• VIBGYOR: red bends least, violet most
• Blue sky and red sunset: scattering; twinkling: atmospheric refraction

Dead plants buried deep under the earth, at high temperature and pressure, slowly turned into coal. This is carbonisation. Because coal came from living things, it is a fossil fuel. Petroleum and natural gas formed in a similar way from tiny sea organisms.

The lowest temperature at which a substance catches fire. A paper cup of water does not burn over a flame, because the water takes the heat away. Substances that catch fire very easily — petrol, alcohol, LPG — are inflammable.

Incomplete burning gives carbon monoxide, a deadly gas — never sleep in a closed room with a coal fire. Extra carbon dioxide adds to global warming. Sulphur and nitrogen oxides dissolve in rain and cause acid rain.

'Poly' means many and 'mer' means part. Small units called monomers join into long chains. Polythene is made of thousands of ethene units. Natural polymers exist too: cotton is cellulose, and proteins are polymers of amino acids.

• CNG comes from gas wells, not from refining crude oil; LPG comes from refining.
• Cooking gas = butane + propane; marsh gas, gobar gas, CNG = methane.
• Mine explosions: methane + air, not hydrogen + oxygen.
• Combustion turns chemical energy into heat.
• The bright yellow zone is not the hottest — the outer blue zone is.
• PVC = polyvinyl chloride, not carbonate.
• Aspartame is a sweetener, not a preservative.

Why does a paper cup full of water not catch fire over a candle?

• Coal products: coke, coal tar, coal gas
• Petroleum = crude oil = black gold
• CNG methane, from gas wells; burns cleanly
• Fire needs fuel, air, heat; CO2 for oil and electrical fires
• Highest calorific value: hydrogen, 150,000 kJ/kg
• Rayon artificial silk; acrylic artificial wool; nylon fully synthetic
• Thermosetting: bakelite, melamine; thermoplastic: polythene, PVC

Current is the rate of flow of charge: I = Q/t. In a metal wire, electrons carry the charge. A cell keeps a potential difference (voltage) across the wire. This push drives the charge round the circuit. By custom, current flows from the + end to the − end, opposite to the electrons.

The voltage across a metal wire is directly proportional to the current in it, if its temperature stays the same: V = IR. R is the resistance, the wire's opposition to current. Double the voltage and the current doubles. Double the resistance and the current halves.

Resistance grows with the length of a wire and falls with its thickness: R = ρl/A. ρ is the resistivity of the material, in Ω m. A long, thin wire resists more than a short, thick one. Resistance also changes with temperature.

A capacitor is two metal plates with an insulator between them. It stores charge and gives it back when needed, as in a camera flash. A resistor controls current. A transistor switches or boosts signals. An ammeter only measures current.

A current I in a resistance R for time t makes heat H = I²Rt. Double the current and the heat becomes four times. Irons, toasters, kettles, heaters, bulbs and the fuse all use this effect.