Energy Changes in a System, and The Ways Energy is Stored Before and After such Changes

A system is the object — or group of objects — you have decided to focus on. Energy is a property of a system, not a substance that flows around like water. When something changes, we describe it by saying which stores within the system fill up and which empty.

Think of energy stores like accounts at a bank. Each account (store) holds some amount of energy (joules). When something happens, money moves from one account to another, but the total stays the same — this is conservation of energy.

A closed system is one in which no energy enters or leaves. The total energy of a closed system never changes — although energy can be redistributed between stores, and some may be wasted into thermal stores.

Worked example — choosing a system. A skydiver falls from a plane.

• If the system is just the skydiver: gravitational potential energy enters from outside (the Earth). The kinetic store and thermal store of the skydiver both grow.
• If the system is the skydiver + Earth: this is closed. The gravitational PE store of the skydiver–Earth pair empties; kinetic and thermal stores of the skydiver and air fill.

The second view is cleaner because conservation of energy applies neatly.

AQA's specification names exactly eight energy stores. Memorise them.

Store	What fills it	Real-world example
Kinetic	An object moving	A football kicked across the pitch
Gravitational potential	An object raised in a gravity field	A book on a high shelf
Elastic potential	A spring, elastic band or rubber stretched/compressed	A drawn bow
Thermal (internal)	Particles vibrating faster (warmer object)	A cup of hot tea
Chemical	Bonds within fuel, food or batteries	A battery in your phone
Magnetic	Two magnets held apart against attraction or pushed together against repulsion	Two N poles pinched together
Electrostatic	Two charged objects held against the electrical force between them	A charged balloon stuck to a wall
Nuclear	Energy held in atomic nuclei	A uranium-235 nucleus

Notice what is NOT a store: heat, light, sound, electrical, kinetic-electrical. Heat, sound and light are transfers, not places where energy resides.

When energy moves between stores, it always uses one of four pathways.

1. Mechanically — a force acts through a distance (work is done). Example: pushing a trolley fills the trolley's kinetic store from your chemical store.
2. Electrically — a current does work in a circuit. Example: a battery transfers from its chemical store to the kinetic store of motor blades via an electrical pathway.
3. By heating — energy flows from hotter to cooler particles (via conduction, convection or contact). Example: hot tea transfers to the cool surroundings by heating.
4. By radiation — electromagnetic waves (e.g. light, infrared, microwaves) or sound waves carry energy through space. Example: the Sun's radiation pathway fills the thermal store of your skin.

Worked example — a phone playing music. Trace the energy.

• Chemical store of the battery (in the phone) empties.
• Electrical transfer pathway carries energy to the speaker.
• Kinetic store of the speaker cone fills momentarily.
• Sound radiation pathway carries energy to your ear and to thermal stores of the air.
• Thermal store of the speaker also fills (waste).

Every Paper 1 'describe the energy transfers' question follows this template: name the starting store, the pathway, the ending store(s) — including any waste thermal store of the surroundings.

In every real change, some energy is wasted — usually dissipated to the thermal store of the surroundings. This happens because of friction, air resistance and electrical resistance.

For an electric drill:

• Useful: kinetic store of the drill bit.
• Wasted: thermal store of the bearings and gears (friction), thermal store of the wire (resistive heating), and sound radiation into the room.

The total of useful + wasted always equals the input (conservation of energy). We can quantify this as efficiency (covered in spec 4.1.2.2).

For a kettle boiling water:

• Input: 100 % electrical (from chemical store of the National Grid → chemical store of fuel at the power station, conceptually).
• Useful output: thermal store of the water.
• Wasted: thermal stores of the kettle body, lid, surrounding air, and a tiny amount of sound radiation.

Every moving object has a kinetic store that contains energy:

$E_k = \frac{1}{2}\,m\,v^2$

• $E_k$ in joules (J)
• $m$ in kilograms (kg)
• $v$ in metres per second (m/s)

The $v^2$ is the key feature. Doubling the speed quadruples the kinetic energy. Tripling it multiplies it by nine. This is why:

• Crash forces grow rapidly with speed.
• A car at 60 mph carries four times the kinetic energy of one at 30 mph.
• Braking distance scales with $v^2$, not $v$.

Worked example. A 1200 kg car moves at 25 m/s on a UK motorway.

$E_k = \tfrac{1}{2} \times 1200 \times 25^2 = 600 \times 625 = 375{,}000\,\text{J} = 375\,\text{kJ}$

Rearranging for speed. Given $E_k$, $v = \sqrt{2E_k/m}$. This appears in 'estimate the speed of impact' questions.

When an object of mass $m$ is raised a vertical height $h$:

$E_p = m\,g\,h$

• $g = 9.8\,\text{N/kg}$ on Earth (printed on AQA's 2026 data sheet).
• $h$ is the vertical height gained, not the distance along a slope.

Worked example. A 65 kg student climbs a 12 m staircase.

$E_p = 65 \times 9.8 \times 12 = 7644\,\text{J} \approx 7.6\,\text{kJ}$

Slopes — use vertical height only. If a 20 kg suitcase is pushed 5 m up a slope that rises 2 m vertically, use $h = 2\,\text{m}$, not 5 m:

$E_p = 20 \times 9.8 \times 2 = 392\,\text{J}$

The slope length matters for work done against friction (covered in 4.5.2), not for gravitational PE.

Connecting $E_p$ to $E_k$. When a dropped object falls without air resistance, gravitational PE → kinetic. Setting $mgh = \tfrac{1}{2}mv^2$ gives $v = \sqrt{2gh}$ — a 5 m fall reaches $v = \sqrt{2 \times 9.8 \times 5} = 9.9\,\text{m/s}$.

When a spring of constant $k$ is stretched (or compressed) by extension $e$:

$E_e = \tfrac{1}{2}\,k\,e^2$

• $k$ in N/m (stiffness).
• $e$ in m — the change in length (final length − natural length).
• Equation is on the AQA equation sheet.

The equation assumes the spring is within its limit of proportionality (so it obeys Hooke's law $F = ke$).

Worked example. A spring with $k = 250$ N/m is stretched by 4 cm.

• Convert: $e = 0.04\,\text{m}$.
• $E_e = \tfrac{1}{2} \times 250 \times 0.04^2 = 125 \times 0.0016 = 0.20\,\text{J}$.

Worked example (rearranging). A toy gun stores 2.0 J in a spring of $k = 400$ N/m. Find the extension.

$e = \sqrt{\frac{2E_e}{k}} = \sqrt{\frac{2 \times 2.0}{400}} = \sqrt{0.01} = 0.10\,\text{m} = 10\,\text{cm}$

Set the two energies equal:

$mgh = \tfrac{1}{2}mv^2 \quad \Longrightarrow \quad v = \sqrt{2gh}$

Mass cancels — every object falls and gains the same speed (in the absence of air resistance). This is why Galileo's hammer-and-feather demo on the Moon famously showed both hitting the surface together.

Worked example. A pencil falls 0.80 m from a desk. With what speed does it hit the floor?

$v = \sqrt{2 \times 9.8 \times 0.80} = \sqrt{15.68} \approx 4.0\,\text{m/s}$

Skateboard ramp example. A 50 kg skater starts at rest 2.5 m above the bottom of a smooth ramp.

• Gravitational PE: $E_p = 50 \times 9.8 \times 2.5 = 1225\,\text{J}$.
• At the bottom (smooth — no friction): all 1225 J is in the kinetic store.
• $v = \sqrt{2 \times 9.8 \times 2.5} = 7.0\,\text{m/s}$.

If friction acts, less than $mgh$ ends up as kinetic — the rest fills the thermal store of the ramp and the wheels.

In AQA GCSE Physics, energy is treated as a property of a system — a chosen part of the world we're studying. A system might be a single object (a moving car), a pair of objects (a ball and the Earth), or something more complex (a kettle, water and surroundings).

A store is a place where energy can be held. The AQA specification lists eight stores you need to recognise by name:

Store	Filled when …	Everyday example
Kinetic	An object is moving	Moving train
Gravitational potential	An object is raised above the ground	Apple on a shelf
Elastic potential	A spring or elastic band is stretched/compressed	Stretched bungee cord
Thermal (internal)	Particles in an object speed up	Hot mug of tea
Chemical	Energy stored in bonds	Battery, food, fuel
Magnetic	Two magnets pushed/pulled apart	Two N poles held close
Electrostatic	Two charged objects held against attraction/repulsion	Charged balloon
Nuclear	Stored in the nucleus	Uranium-235 nucleus

Describing an event using stores. Almost every exam question on this topic asks you to write a before-and-after sentence:

"Energy is transferred from the [store A] store of the [object] to the [store B] store of the [object/surroundings]."

Always name both the store and the object that owns the store. AQA examiner reports (2022–2024) flag answers like "kinetic energy is lost" as too vague — the mark scheme awards credit for which object's store is being filled or emptied.

Worked example. A child slides down a slide.

• Before: gravitational potential store of the child–Earth system is filled.
• During: that store empties; the kinetic store of the child fills.
• After arriving at the bottom: the kinetic store also partially empties because friction has filled the thermal stores of the slide and the child's clothing (you can feel it warming).

There are only four ways to transfer energy between stores:

1. Mechanically — a force moves through a distance (work done).
2. Electrically — a current does work on a circuit component.
3. By heating — energy moves from hotter to cooler particles.
4. By radiation — light, infrared or sound waves carry energy from a source.

These four "transfer pathways" appear on every series of Paper 1.

AQA tip. Don't write "heat energy" or "sound energy" in an answer — the spec is strict: heat is a transfer pathway, not a store; sound is a transfer pathway (radiation), not a store. The store you actually mean is thermal (also called internal energy).

Kinetic energy of a moving object:

$E_k = \frac{1}{2}\,m\,v^2$

• $E_k$ — kinetic energy, joules (J).
• $m$ — mass, kilograms (kg).
• $v$ — speed, metres per second (m/s).

Notice the $v^2$ — doubling the speed quadruples the kinetic energy. This is why braking distance grows so dramatically with speed, and why crashes at higher speeds are so much more dangerous.

Worked example 1. A 60 kg cyclist moves at 8 m/s. Find her kinetic energy.

$E_k = \tfrac{1}{2} \times 60 \times 8^2 = 30 \times 64 = 1920\,\text{J}$

Gravitational potential energy stored when an object is raised:

$E_p = m\,g\,h$

• $g = 9.8\,\text{N/kg}$ on Earth (this value is on the AQA data sheet; some legacy textbooks use 10 — use 9.8 in the exam unless told otherwise).
• $h$ — height gained, metres.

Worked example 2. A 1.5 kg book is lifted from the floor to a shelf 1.8 m high.

$E_p = 1.5 \times 9.8 \times 1.8 = 26.46\,\text{J}$

Round to a sensible number of significant figures (here, 26 J).

Elastic potential energy stored in a stretched or compressed spring:

$E_e = \frac{1}{2}\,k\,e^2$

• $k$ — spring constant, N/m (a stiff spring has a bigger $k$).
• $e$ — extension, m (not the natural length — only the change).

This equation is on AQA's equation sheet (provided in 2026 exams). You don't need to recall the equation, but you must be able to use it confidently.

Worked example 3. A spring with $k = 200$ N/m is stretched by 0.05 m. How much energy is stored?

$E_e = \tfrac{1}{2} \times 200 \times 0.05^2 = 100 \times 0.0025 = 0.25\,\text{J}$

Conservation of energy in motion problems. When an object falls (and air resistance is small), the gravitational store empties at the same rate the kinetic store fills. So:

$\tfrac{1}{2}mv^2 = mgh \quad \Longrightarrow \quad v = \sqrt{2gh}$

This is a hidden formula on AQA papers — they won't give it, but you can derive it on the spot for falling-object questions.

When energy is transferred to an object's thermal store, its temperature rises (provided the substance does not change state at the time). The exact relationship is:

$\Delta E = m \, c \, \Delta\theta$

• $\Delta E$ — change in thermal energy, joules (J).
• $m$ — mass, kilograms (kg).
• $c$ — specific heat capacity (SHC), J/kg°C.
• $\Delta\theta$ — change in temperature, °C (Greek 'theta' is AQA's symbol).

Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Some values to remember (or to expect on a data sheet):

Substance	SHC (J/kg°C)
Water	4200
Aluminium	900
Copper	385
Iron	450
Oil	~2000

Water's SHC is unusually large — this is why oceans buffer climate, why cooling systems use water, and why coastal regions of the UK have milder winters than central regions.

Worked example. How much energy is needed to heat 0.5 kg of water from 20 °C to 100 °C?

• $m = 0.5\,\text{kg}$, $c = 4200\,\text{J/kg°C}$, $\Delta\theta = 100 - 20 = 80\,\text{°C}$.

$\Delta E = 0.5 \times 4200 \times 80 = 168{,}000\,\text{J} = 168\,\text{kJ}$

Worked example (rearranging for SHC). A 0.20 kg metal block warms from 22 °C to 38 °C when 1280 J of energy is supplied. Find the SHC.

$c = \frac{\Delta E}{m \, \Delta\theta} = \frac{1280}{0.20 \times 16} = \frac{1280}{3.2} = 400\,\text{J/kg°C}$

This value is close to iron (450) — so the block is probably iron (or similar).

AQA's Required Practical 1 — investigating SHC. Mark schemes test this method every year. Memorise the apparatus and the sources of error.

Apparatus: mass of block (kg), insulating jacket, electric heater (joulemeter or known V and I, with stopwatch), thermometer, two holes drilled in the block (one for the heater, one for the thermometer with oil for good thermal contact).

Method (short version):

1. Measure mass on a balance.
2. Insulate the block.
3. Switch heater on; record initial temperature.
4. After a known time $t$ (e.g. 600 s), switch off, record peak temperature.
5. Energy supplied: $E = VIt$ (or read from joulemeter).
6. Rearrange $\Delta E = m c \Delta\theta$ to find $c$.

Sources of error:

• Heat lost to surroundings (insulation isn't perfect).
• Thermometer responds slowly — final temperature may still be rising.
• Heater itself takes some energy to warm up.
• Energy supplied calculation assumes 100 % goes to the block.

Reduce errors by insulating well, leaving the block to equilibrate after switching off, and starting from room temperature.

Power is defined as the rate of energy transfer (or, equivalently, the rate of work done):

$P = \frac{E}{t} \qquad \text{and} \qquad P = \frac{W}{t}$

• $P$ — power, watts (W).
• $E$ — energy transferred, joules.
• $W$ — work done, joules.
• $t$ — time, seconds.

One watt (1 W) = one joule per second (1 J/s). A device rated at 100 W transfers 100 J every second.

Worked example. A 60 W bulb is left on for 30 minutes. How much energy does it transfer?

• $t = 30 \times 60 = 1800\,\text{s}$
• $E = P \times t = 60 \times 1800 = 108{,}000\,\text{J} = 108\,\text{kJ}$

Worked example (comparing two devices). Device A transfers 6000 J in 30 s. Device B transfers 4000 J in 25 s. Which is more powerful?

• $P_A = 6000 / 30 = 200\,\text{W}$
• $P_B = 4000 / 25 = 160\,\text{W}$

A is more powerful — it transfers energy at a higher rate, even though B did the job in less time with less energy.

Typical power values to know (UK appliances):

Device	Typical power
LED bulb	6 – 10 W
Phone charger	5 – 20 W
Laptop	50 – 100 W
Fridge (running)	100 – 200 W
Toaster	800 – 1200 W
Kettle	2000 – 3000 W (2 – 3 kW)
Electric shower	7000 – 10500 W (7 – 10.5 kW)

AQA exam tip. Foundation Tier candidates often see questions asking you to compare power values and explain the meaning. State the value with its unit, then add a sentence explaining what the number physically represents ("3000 J of energy is transferred every second"). Examiner reports note that comparing in everyday terms ("about as bright as 200 LED bulbs") wins clarity marks.

Higher Tier extension. Combine $P = E/t$ with $\Delta E = m c \Delta\theta$ to find heating times. If a 2.5 kW kettle has to boil 0.4 kg of water from 20 °C to 100 °C:

1. Energy needed: $\Delta E = 0.4 \times 4200 \times 80 = 134{,}400\,\text{J}$
2. Time: $t = E/P = 134{,}400 / 2500 = 53.76\,\text{s}$ ≈ 54 s.

Real kettles take a bit longer because not all the electrical energy heats the water — some warms the kettle itself and the room.

Power measures how quickly energy is transferred (or, equivalently, work is done):

$P = \frac{E}{t} \qquad \text{and} \qquad P = \frac{W}{t}$

• $P$ in watts (W)
• $E$ in joules (J) — energy transferred
• $W$ in joules — work done (same as energy when transferred mechanically)
• $t$ in seconds (s)

1 watt = 1 joule per second.

A 100 W bulb transfers 100 J of energy every second it is on.

A 2 kW kettle transfers 2000 J per second to its thermal store.

Power vs energy — a key distinction. A 60 W bulb left on for 1 hour transfers more total energy than a 2400 W kettle boiling water for 30 seconds:

• Bulb: $E = 60 \times 3600 = 216{,}000\,\text{J}$.
• Kettle: $E = 2400 \times 30 = 72{,}000\,\text{J}$.

So the bulb (low power, long time) wastes more total energy than the kettle (high power, short time) — useful when discussing energy bills.

Worked example 1. A 1500 W vacuum cleaner runs for 8 minutes. How much energy does it transfer?

• $t = 8 \times 60 = 480\,\text{s}$.
• $E = P \times t = 1500 \times 480 = 720{,}000\,\text{J} = 720\,\text{kJ}$.

Worked example 2. A motor lifts a 50 kg crate vertically 8 m in 20 s. Find its useful power output.

• Work done (= energy transferred): $W = Fs = mgh = 50 \times 9.8 \times 8 = 3920\,\text{J}$.
• Power: $P = W/t = 3920 / 20 = 196\,\text{W}$.

Worked example 3 (comparing). A 200 W lamp runs for 4 hours; a 2000 W heater runs for 30 minutes. Which transfers more total energy?

• Lamp: $E = 200 \times (4 \times 3600) = 200 \times 14{,}400 = 2{,}880{,}000\,\text{J}$.
• Heater: $E = 2000 \times (30 \times 60) = 2000 \times 1800 = 3{,}600{,}000\,\text{J}$.
• Heater transfers more total energy (3.6 MJ vs 2.9 MJ).

Unit shortcut — kilowatt-hours (kWh) are the units on UK electricity bills. 1 kWh = 1000 W × 3600 s = 3,600,000 J. Used by Ofgem and energy suppliers but not required for AQA exams.

Power ratings (UK retail prices in £; values typical for the British home):

Device	Power	Typical retail	UK note
LED bulb	6 – 10 W	£2 – £5	Replaced 60 W incandescent bulbs in most UK homes by 2023
Phone charger	5 – 30 W	£5 – £20	USB-C fast chargers 20–30 W
Laptop	50 – 100 W	£400 – £1500	Includes battery charging + screen
Fridge–freezer (running)	100 – 200 W	£300 – £900	Cycles on/off; average daily draw ~100 W
Microwave	800 – 1200 W	£80 – £200	Quoted as output power; input is higher
Toaster	800 – 1500 W	£25 – £100
Iron	1500 – 2400 W	£30 – £150
Kettle	2000 – 3000 W	£20 – £80	Most UK homes have a 3 kW kettle
Electric shower	7500 – 10500 W	£150 – £400	Requires a dedicated 30/40/45 A circuit
Hair dryer	1500 – 2200 W	£20 – £100

These values appear in AQA exam questions as 'compare' or 'estimate' prompts. For top grades 7–9, quote both numbers and the ratio: "The shower (10 kW) is about 1000 times more powerful than an LED bulb (10 W)."