Physics Revision Manual: Topics 6.1 to 6.4

6.1.1 Energy changes in a system

Systems and energy stores

• System: an object or group of objects. When a system changes, the way its energy is stored changes.
• Energy stores: kinetic (moving objects), thermal (all objects), chemical (anything that can release energy in a reaction), elastic potential (stretched things), gravitational potential (raised objects), electrostatic (attracting or repelling charges), magnetic (attracting or repelling magnets), nuclear (the nucleus of an atom).
• Energy is transferred mechanically (a force does work), electrically (moving charge does work), or by heating (from a hotter to a colder object).

Calculating energy changes

• Rearranged: m = 2E_k ÷ v² and v = √(2E_k ÷ m). m = E_p ÷ gh, h = E_p ÷ mg, g = E_p ÷ mh. e = √(2E_e ÷ k) and k = 2E_e ÷ e². m = ΔE ÷ cΔθ, c = ΔE ÷ mΔθ, Δθ = ΔE ÷ mc.
• Energy in a system changes by heating (ΔE = mcΔθ), work done by forces (W = F × s, see Source notes) or work done when a current flows (E = QV or E = Pt, see 6.2.4).
• Redistribution: total energy stays the same, so a loss in one store equals the gain in others. For a falling object with no air resistance: loss in E_p = gain in E_k.

Specific heat capacity

• Specific heat capacity: the energy needed to raise the temperature of 1 kg of a material by 1°C. Materials differ: some need more energy than others to warm up.
• Required practical 14 (independent: material; dependent: specific heat capacity; control: insulating layer, starting temperature, time taken):

1. Measure the mass of the metal block in kg, then wrap it in insulation.
2. Put the heater in the large hole and a drop of water plus the thermometer in the small hole.
3. Connect the power pack with an ammeter in series and a voltmeter across the power pack. Set 12 V.
4. Switch on and start the clock. Record the temperature every minute for 10 minutes. The voltmeter and ammeter readings should not change.
5. Calculate the energy transferred (work done) at each time and plot energy against temperature.

Power

• Power: the rate at which energy is transferred or work is done. 1 W = 1 joule per second.
• If motors A and B do the same work, the one that does it faster is more powerful.
• Worked example: a 60 W bulb on for 2 minutes: E = Pt = 60 × 120 = 7200 J. Rearranged: t = E ÷ P.

6.1.2 Conservation and dissipation of energy

Conservation and dissipation

• Conservation of energy: energy can be transferred usefully, stored or dissipated, but never created or destroyed.
• In a closed system the total energy is the same before and after any change.
• Dissipated: energy ends up stored in less useful ways, usually as thermal energy in the surroundings. This is often called ‘wasted’. Example: friction in a moving object transfers energy to the surroundings.

Reducing unwanted transfers

• Lubrication: oil between moving surfaces reduces friction, so less energy is lost as heat.
• Thermal insulation: thick walls; loft insulation (reduces convection); cavity walls (reduce conduction and convection); double glazing (reduces conduction).
• Conduction: in a heated solid the particles vibrate more and collide, passing the energy on.
• Convection: a heated liquid or gas becomes less dense and rises above cooler fluid, forming a convection current.
• Thermal conductivity: the higher it is, the faster energy is conducted through a material. A building with thick walls of low thermal conductivity cools slowly; thin metal walls lose heat quickly.

Efficiency

• Efficiency = useful output energy transfer ÷ total input energy transfer. Also = useful power output ÷ total power input. Give as a decimal or × 100 for a percentage.
• Rearranged: useful output = efficiency × total input; total input = useful output ÷ efficiency.
• Nothing is 100% efficient because some energy is always wasted.
• HT Increasing efficiency: reduce waste output (lubrication, insulation) or recycle waste output (e.g. absorb waste thermal energy and reuse it as input).

6.1.3 National and global energy resources

• Non-renewable: fossil fuels (coal, oil, gas) and nuclear fuel. They run out. Fossil fuels give large amounts of energy per kilogram, so they supply most large-scale energy.
• Renewable: replenished as they are used and will never run out: biofuel, wind, hydroelectricity, geothermal, tidal, solar, water waves.
• Main uses: transport, electricity generation and heating.

• Reliability: solar fails at night and in bad weather, wind is intermittent. Geothermal, tidal and fossil fuels are reliable.
• Environmental impact: extracting fossil fuels destroys landscapes; using them releases harmful emissions. Solar and wind create electricity with no emissions.
• Trends: fossil fuels became important in the Industrial Revolution because they were easy to mine and gave a lot of energy. Renewables only became suitable recently as technology developed. The UK now has renewable targets, and electric and hybrid cars are on sale, but they cost money and some people oppose plants near them.
• Why science cannot always solve the issues: political, social, ethical and economic factors, such as cost and public opposition.

6.2.1 Current, potential difference and resistance

Circuit symbols

Charge, current and resistance

• For charge to flow: the circuit must be closed (no open switch) and contain a source of potential difference (cell or battery).
• Current: the flow of electrical charge. A bigger current means a greater rate of flow of charge. In a single closed loop, the current is the same at every point.
• Potential difference (voltage): the push that drives the charge. Resistance: slows the flow.
• Q = I t (charge in coulombs C, current in amperes A, time in s). Rearranged: I = Q ÷ t, t = Q ÷ I.
• V = I R (volts V, amperes A, ohms Ω). Rearranged: I = V ÷ R, R = V ÷ I. More resistance → less current for the same pd.

I–V characteristics and components

• Ohmic conductor (constant temperature): current is directly proportional to pd, giving a straight line through the origin. Resistance stays constant as current changes.
• Filament lamp: as current rises the filament heats up, so its resistance increases and the line becomes less steep.
• Diode: current flows in one direction only. In the reverse direction its resistance is very high, so almost no current flows.
• Why resistance rises with heating: electrons collide with the atoms, transferring energy, so the atoms vibrate more and it is harder for charge to flow.
• Thermistor: resistance falls as temperature rises. Used in temperature detectors and thermostats: the circuit responds to temperature.
• LDR: resistance falls as light intensity rises (highest in the dark). Used in automatic night lights and burglar detectors.
• Measuring resistance: put an ammeter in series with the component and a voltmeter across it (in parallel), then R = V ÷ I. A variable resistor changes the current.

6.2.2 Series and parallel circuits

• Why series resistance adds: the charge has to push through every resistor in turn.
• Why parallel resistance falls: the charge has more than one branch to take, so only part of the current flows along each.
• Equivalent resistance: replace the resistors with one resistor of the same total resistance, then use V = IR on the whole circuit.

6.2.3 Domestic uses and safety

• The pd between the live wire and earth is 230 V.
• Danger: touching a live wire lets current flow through your body to earth, causing an electric shock. A live wire can be dangerous even with a switch open, because the wire up to the switch is still at 230 V.
• If the live wire touches a metal casing, the casing becomes live. The earth wire, connected to the casing and the ground, carries the current away.
• Cables have three wires covered in plastic insulation for safety.

6.2.4 Energy transfers: power and the National Grid

Power and energy

• Rearrange as needed: I = P ÷ V, V = P ÷ I, I = √(P ÷ R), R = P ÷ I², t = E ÷ P, P = E ÷ t, Q = E ÷ V, V = E ÷ Q.
• Power rating (in watts) shows how much energy an appliance transfers each second, so a higher rating uses more energy. Energy transferred depends on power and time on.
• Appliances: energy is transferred from a battery or the mains to motors (kinetic) or heating devices (thermal, e.g. a kettle). A moving charge does work, and this equals the energy transferred.

The National Grid

• A system of cables and transformers that transfers electrical power from power stations to consumers. Power stations can change their output to meet demand (e.g. evenings).
• Step-up transformers increase the pd for transmission. Power is constant (P = VI), so a higher pd means a lower current, so less energy is lost as heat in the cables (power loss ∝ I²R).
• Step-down transformers decrease the pd to make it safe for consumers.
• This is efficient because transmission uses high voltage and low current.
• HT Transformer equation: V_p × I_p = V_s × I_s (primary and secondary coils; see Source notes). Example: 25 000 V at 80 A stepped up to 400 000 V → I_s = (25 000 × 80) ÷ 400 000 = 5 A.

6.3.1 Changes of state and the particle model

Density

• Density: how much mass is in a given volume. ρ = m ÷ V (kg/m³; kg; m³). Rearranged: m = ρV and V = m ÷ ρ.
• A denser material has more particles in the same volume.

The particle model

• Density differences: solids and liquids have similar densities because the particles are close together (usually a liquid is slightly less dense; water and ice are the exception). Gases have a far lower density because the particles are very far apart.

Required practical 17: measuring density

• Regular solid: measure the mass on a balance; measure length, width and height with a ruler; volume = l × w × h; density = m ÷ V.
• Irregular solid: measure the mass. Fill a eureka can with water, lower the object in, and collect the displaced water in a measuring cylinder. That volume equals the object’s volume. Then density = m ÷ V.
• Liquid: measure the mass of a measuring cylinder, add the liquid, measure again (mass of liquid = difference) and read its volume (see Source notes).

Changes of state

• Changes: melting (solid → liquid), freezing (liquid → solid), evaporating or boiling (liquid → gas), condensing (gas → liquid), sublimation (solid → gas).
• Mass is conserved: the number of particles does not change. 20 g of liquid that evaporates becomes 20 g of gas.
• Physical, not chemical: no new substance forms, and the substance returns to its original properties when the change is reversed.

6.3.2 Internal energy and energy transfers

Internal energy and temperature changes

• Internal energy: the total kinetic energy (particles vibrating or moving) plus potential energy (between the particles) of all the particles in a system.
• Heating increases the energy of the particles, so it increases the internal energy. This either raises the temperature or changes the state.
• What affects the temperature rise: the energy supplied, the mass, and the substance (its specific heat capacity).
• ΔE = m c Δθ, where c is the specific heat capacity (energy to raise 1 kg by 1°C, in J/kg°C).

Specific latent heat

• Specific latent heat (L): the energy needed to change 1 kg of a substance from one state to another without changing its temperature. It differs for different materials.
• Fusion = solid ↔ liquid. Vaporisation = liquid ↔ gas.
• E = m L (energy in J; mass in kg; L in J/kg).
• Melting and boiling: energy goes in and is used to break bonds, so the internal energy rises but the temperature stays the same. Condensing and freezing: bonds form, energy is released, internal energy falls, temperature stays the same.

• Reading the heating curve: A = solid heating up. B reaches the melting point. B to C is flat: melting, energy goes into breaking bonds. C to D = liquid heating up. D to E is flat: boiling (longer, because more energy is needed). E to F = gas heating up.

6.3.3 Particle model and pressure

• Gas motion: the molecules of a gas are in constant, random motion and collide with each other and the container walls.
• Temperature: related to the average kinetic energy of the molecules. The hotter the gas, the greater the average kinetic energy and the faster the molecules move.
• Pressure: each collision with a wall exerts a force. The total force from all the molecules on a unit area of the wall is the gas pressure.
• Temperature and pressure (constant volume): heating the gas → molecules move faster → they hit the walls more often and harder → pressure increases.

6.4.1 Atoms and isotopes

Structure of the atom

• Radius of an atom: about 1 × 10⁻¹⁰ m. The nucleus has a radius about 10 000 times smaller, but contains almost all of the atom’s mass.
• A positively charged nucleus (protons and neutrons) is surrounded by negatively charged electrons in different energy levels (shells) at different distances from the nucleus.
• Atoms have no overall charge because the number of electrons equals the number of protons.
• Absorbing EM radiation: an electron moves to a higher energy level (further from the nucleus). Emitting EM radiation: it falls to a lower level (closer to the nucleus).
• Positive ions: if an electron gains enough energy it leaves the atom, leaving a positive ion.

• Atomic (proton) number: number of protons. It defines the element.
• Mass number: protons + neutrons. Neutrons = mass number − atomic number.
• Isotopes: atoms of the same element (same protons) with different numbers of neutrons, so different mass numbers, e.g. carbon-12, carbon-13 and carbon-14.

Development of the model of the atom

• Alpha scattering results: most alpha particles went straight through → the atom is mostly empty space. Some were slightly deflected → the nucleus is positive (like charges repel). Very few were deflected by more than 90° → the nucleus is small and holds most of the mass.
• Plum pudding vs nuclear model: the plum pudding model had charge spread through the whole atom; the nuclear model has a tiny, dense, positive nucleus with mostly empty space around it.
• Later: the positive charge of the nucleus was found to be divided into smaller particles, each with the same charge, the protons. New experimental methods and Chadwick’s experiments then provided evidence for neutrons, completing the nuclear model.

6.4.2 Atoms and nuclear radiation

Radioactive decay

• Radioactive decay: unstable nuclei give out radiation to become more stable. It is a random process: you cannot predict which nucleus will decay next.
• Activity: the rate at which a source of unstable nuclei decays, measured in becquerels (Bq): 1 Bq = 1 decay per second.
• Count rate: the number of decays recorded by a detector (e.g. a Geiger–Müller tube) per second.

• Ionising radiation can knock electrons off atoms.
• Choosing a source: match penetration to the job. Alpha is the most dangerous inside the body (highly ionising) but is less dangerous outside as it cannot penetrate skin. Beta is less dangerous inside as some escapes, but more dangerous outside. Gamma is the least dangerous inside (most passes out) but more dangerous outside.
• Example, smoke alarm: americium (alpha emitter, half-life 432 years) ionises the air in the alarm. Alpha is weakly penetrating so it does not leave the alarm. When smoke enters, fewer alpha particles reach the detector and the alarm sounds. A long half-life means no need to replace it, and its weak activity is not harmful.

Nuclear equations

• Alpha decay: mass number falls by 4, atomic number by 2.
  23892U → 23490Th + 42He
• Beta decay: mass number unchanged, atomic number rises by 1 (charge of the nucleus increases).
  146C → 147N + 0−1e
• Gamma decay: no change to mass or charge.
• Balancing: the mass numbers must add up to the same total on both sides, and so must the atomic numbers.

Half-life

• Half-life: the time for the number of unstable nuclei in a sample to halve, or for the activity or count rate to fall to half.
• Decay is random, so you cannot predict one nucleus, but the half-life is a constant that predicts the behaviour of a very large number of nuclei.
• From data: count how many halvings have happened, then divide the time. Example: 80 → 40 → 20 is 2 half-lives in 10 min, so half-life = 5 min. From a graph, read the time for the activity to fall to half (the graph in your organiser gives a half-life of 2 days).
• Short half-life: very radioactive at first but dies away quickly (less long-term risk). Long half-life: stays weakly radioactive for a long time.
• HT Net decline: after n half-lives, 1 ÷ 2ⁿ of the original remains. Example: 800 Bq after 3 half-lives → 100 Bq, a decline in the ratio 8 : 1 (see Source notes).

Contamination and irradiation

• Irradiation can be useful: medical items are irradiated to kill bacteria on their surface without making them radioactive.
• Publishing studies on radiation and humans: results should be published and peer reviewed by other scientists, because if the first measurements were wrong, safety levels based on them could cause harm.

Coverage and source notes

Every checklist criterion for 6.1 to 6.4 is covered in the matching section, except where a gap is listed below. Content marked “Physics only” in the PMT notes is not on your Trilogy checklist, so it is left out (static electricity, electric fields, Boyle’s law, background radiation, uses of radiation, nuclear fission and fusion).

Gaps in the sources

• Work done by forces (6.1.1): neither source gives W = F × s. I used it as the standard equation, so check it against your Forces notes.
• Nuclear fuel (6.1.3): it is named as a non-renewable resource, but there are no advantages, disadvantages or environmental impacts for it in either source.
• Density of a liquid (6.3.1): the practical covers regular and irregular solids only. The liquid method is the standard one.
• Measuring resistance (6.2.1): ammeter in series and voltmeter in parallel is the standard set-up. The sources show it only in diagrams.
• Transformer equation (HT, 6.2.4): the sources say power is constant (P = VI) but do not write V_pI_p = V_sI_s.
• Net decline (HT, 6.4.2): the PMT formula did not extract legibly, so I used the standard remaining fraction 1 ÷ 2ⁿ.

Disagreements and errors in the sources

• Atomic model dates: the organiser gives Rutherford 1909, Bohr around 1911 and Chadwick around 1940. PMT gives Rutherford 1911, Bohr 1913 and Chadwick about 20 years after the nucleus was accepted. I used the PMT dates. Check which your teacher expects.
• Beta penetration: PMT says beta is stopped by “a sheet of paper”, but the organiser says aluminium (and paper stops alpha). I used the organiser.
• Series resistance: the PMT text shows “Total resistance = I₁ + I₂”, which is a typing error for R₁ + R₂.
• Gravitational field strength: PMT gives 9.8 N/kg; use the value given in the question.
• Numbering: the checklist uses 6.1 to 6.4 and required practicals 14 to 17; the PMT notes number the topics 1 to 4.