What you'll learn
The principle of energy conservation is fundamental to understanding all physical processes. This revision guide covers how energy transfers between different stores, why total energy remains constant in closed systems, and how to calculate efficiency in energy transfers. You'll develop the skills to analyse energy pathways and solve quantitative problems that regularly appear in Edexcel GCSE Physics exams.
Key terms and definitions
Energy store — a system or object that contains energy, such as kinetic, gravitational potential, elastic potential, chemical, thermal, magnetic, electrostatic, or nuclear stores
Energy transfer — the process by which energy moves from one store to another through four main pathways: mechanical work, electrical work, heating, or radiation
Conservation of energy — the principle that energy cannot be created or destroyed, only transferred from one store to another; the total energy in a closed system remains constant
Closed system — a system where no energy transfers take place to or from the surroundings; all energy transfers occur only within the system itself
Dissipation — the spreading out of energy to the surroundings, usually by heating, making it less useful for doing work
Efficiency — the ratio of useful energy output to total energy input, expressed as a percentage or decimal; a measure of how effectively energy is transferred
Wasted energy — energy that is not usefully transferred or stored, typically dissipated to the surroundings as thermal energy
Sankey diagram — a visual representation showing energy transfers, where arrow widths are proportional to the amount of energy in each pathway
Core concepts
The principle of conservation of energy
Energy cannot be created or destroyed in any process. In a closed system, the total amount of energy before any process equals the total amount after. This fundamental principle applies universally, from simple mechanical systems to complex electrical circuits.
When analysing energy transfers:
- Identify the initial energy stores and their values
- Determine the final energy stores after the transfer
- Account for all energy transfers, including wasted energy
- Verify that total initial energy = total final energy
For example, when a ball falls, gravitational potential energy decreases while kinetic energy increases. If air resistance is negligible (creating an approximate closed system), the decrease in gravitational potential energy equals the increase in kinetic energy.
In real-world situations, systems are rarely perfectly closed. Energy dissipates to surroundings through heating caused by friction, air resistance, or electrical resistance. However, even when energy spreads out to surroundings, the total energy remains constant.
Energy stores
Energy exists in different stores within systems. For GCSE Physics, you must understand these eight energy stores:
Kinetic energy stores hold energy in moving objects. The amount depends on mass and velocity. A car travelling at 30 m/s has more kinetic energy than the same car at 15 m/s.
Gravitational potential energy stores hold energy in objects raised above ground level. The amount depends on mass, height, and gravitational field strength. A book on a high shelf has more gravitational potential energy than one on a low shelf.
Elastic potential energy stores hold energy in stretched or compressed objects. Springs, elastic bands, and bungee cords store energy when deformed. The amount depends on the spring constant and extension or compression.
Chemical energy stores hold energy in the bonds between atoms and molecules. Food, batteries, and fuels contain chemical energy released during reactions.
Thermal energy stores hold energy in the vibration and movement of particles. Hotter objects have more energy in their thermal stores than cooler ones.
Magnetic energy stores hold energy when magnetic poles interact. Energy is stored when attracting poles are separated or when repelling poles are pushed together.
Electrostatic energy stores hold energy when electric charges interact. Energy is stored when opposite charges are separated or when like charges are pushed together.
Nuclear energy stores hold energy in the nucleus of atoms, released during nuclear reactions like fission or fusion.
Energy transfer pathways
Energy transfers between stores through four main pathways:
Mechanical work occurs when a force moves an object through a distance. When you lift a bag, you do mechanical work, transferring energy from your chemical energy store to the bag's gravitational potential energy store. The work done equals force × distance moved in the direction of the force.
Electrical work occurs when charge flows through a potential difference. In a circuit, electrical work transfers energy from the power supply to components like motors, lamps, or heaters.
Heating transfers energy from a hotter object to a cooler one due to a temperature difference. This occurs through conduction, convection, or radiation. Heating always transfers energy from higher to lower temperature regions.
Radiation transfers energy by electromagnetic waves (light, infrared, microwaves, etc.) that can travel through a vacuum. The Sun transfers energy to Earth through radiation across empty space.
Calculating energy transfers
Several equations allow you to calculate energy in different stores and transfers:
Kinetic energy: KE = ½ × m × v²
Where:
- KE = kinetic energy (J)
- m = mass (kg)
- v = velocity (m/s)
Gravitational potential energy: GPE = m × g × h
Where:
- GPE = gravitational potential energy (J)
- m = mass (kg)
- g = gravitational field strength (N/kg) — approximately 9.8 N/kg on Earth
- h = height (m)
Elastic potential energy: EPE = ½ × k × e²
Where:
- EPE = elastic potential energy (J)
- k = spring constant (N/m)
- e = extension (m)
Work done: W = F × d
Where:
- W = work done (J)
- F = force (N)
- d = distance moved in direction of force (m)
Power: P = E ÷ t or P = W ÷ t
Where:
- P = power (W)
- E = energy transferred (J)
- W = work done (J)
- t = time (s)
Efficiency calculations
No energy transfer is 100% efficient. Some energy always dissipates to the surroundings, usually as thermal energy. Efficiency measures what proportion of input energy is usefully transferred.
Efficiency equation:
Efficiency = (useful energy output ÷ total energy input) × 100%
Or:
Efficiency = (useful power output ÷ total power input) × 100%
Efficiency can be expressed as a percentage (0-100%) or as a decimal (0-1).
For example, a light bulb might transfer 100 J of electrical energy. If 20 J transfers to light (useful) and 80 J to thermal energy (wasted), the efficiency is:
Efficiency = (20 ÷ 100) × 100% = 20%
Higher efficiency means less energy is wasted. Improving efficiency reduces energy consumption and costs. Methods include:
- Lubrication to reduce friction
- Thermal insulation to reduce heating losses
- Streamlining to reduce air resistance
- Using more efficient components
Sankey diagrams
Sankey diagrams visually represent energy transfers. The width of each arrow is proportional to the amount of energy it represents. They clearly show:
- Total energy input (single arrow on the left)
- Useful energy output (arrow continuing to the right)
- Wasted energy (arrows branching off, typically downward)
Key features:
- Arrow widths drawn to scale
- Energy values labelled on or near arrows
- Useful and wasted outputs clearly distinguished
- Total input width equals total output widths
In exam questions, you may need to draw Sankey diagrams from given data or interpret existing ones to calculate efficiency or identify energy transfers.
Energy dissipation and waste
Whenever energy transfers occur, some energy dissipates to the surroundings. This energy is not destroyed—it spreads out into the environment, usually as thermal energy, making it less useful.
Common causes of energy dissipation:
- Friction between moving surfaces converts kinetic energy to thermal energy
- Air resistance converts kinetic energy to thermal energy in the air
- Electrical resistance in wires and components converts electrical energy to thermal energy
- Sound spreads energy to surroundings through vibrations
Once energy dissipates and spreads out, it becomes increasingly difficult to use for further energy transfers. This is why no real process is 100% efficient—some energy always becomes less useful.
However, "wasted" energy in one context might be useful in another. The thermal energy from a car engine is normally wasted, but in winter it can heat the car's interior—making it useful.
Worked examples
Example 1: Calculating efficiency from energy values
Question: An electric motor transfers 500 J of electrical energy. It lifts a load, doing 350 J of useful work. The remaining energy is wasted as thermal energy and sound. Calculate the efficiency of the motor. (3 marks)
Solution:
Step 1: Identify the values
- Total energy input = 500 J
- Useful energy output = 350 J
Step 2: Apply the efficiency equation Efficiency = (useful energy output ÷ total energy input) × 100%
Step 3: Substitute and calculate Efficiency = (350 ÷ 500) × 100% Efficiency = 0.7 × 100% Efficiency = 70%
Mark scheme:
- Correct equation stated or implied (1 mark)
- Correct substitution (1 mark)
- Correct answer with unit (1 mark)
Example 2: Energy conservation in a falling object
Question: A stone of mass 0.5 kg is dropped from a height of 20 m. Assuming air resistance is negligible, calculate: (a) The gravitational potential energy lost by the stone (2 marks) (b) The speed of the stone just before it hits the ground (3 marks) (Use g = 10 N/kg)
Solution:
(a) Calculating GPE lost:
Step 1: Write the equation GPE = m × g × h
Step 2: Substitute values GPE = 0.5 × 10 × 20
Step 3: Calculate GPE = 100 J
(b) Calculating final speed:
Step 1: Apply conservation of energy GPE lost = KE gained 100 J = KE
Step 2: Use kinetic energy equation KE = ½ × m × v² 100 = ½ × 0.5 × v² 100 = 0.25 × v²
Step 3: Rearrange and solve v² = 100 ÷ 0.25 v² = 400 v = 20 m/s
Mark scheme:
- (a) Correct equation (1 mark), correct answer with unit (1 mark)
- (b) Recognition that GPE = KE (1 mark), correct rearrangement (1 mark), correct answer with unit (1 mark)
Example 3: Drawing and interpreting a Sankey diagram
Question: A television transfers 200 J of electrical energy every second. 50 J is transferred as light and sound (useful), and 150 J is wasted as thermal energy. (a) Draw a Sankey diagram to represent this energy transfer (2 marks) (b) Calculate the efficiency of the television (2 marks)
Solution:
(a) Sankey diagram: [In exam, you would draw arrows where the input arrow is 200 units wide, useful output is 50 units wide continuing right, and wasted output is 150 units wide branching downward]
Key points for marks:
- Input arrow labelled 200 J
- Useful output (50 J) and wasted output (150 J) arrows drawn proportionally
- Arrows correctly labelled
(b) Calculating efficiency:
Efficiency = (50 ÷ 200) × 100% Efficiency = 25%
Mark scheme:
- (a) Correct proportions (1 mark), correct labels (1 mark)
- (b) Correct calculation (1 mark), correct answer with unit (1 mark)
Common mistakes and how to avoid them
• Confusing energy and power — Energy is measured in joules (J), while power is the rate of energy transfer measured in watts (W). Always check which quantity the question asks for and use the appropriate equation.
• Forgetting to account for all energy transfers — When applying conservation of energy, students often forget to include wasted energy. Remember: total input = useful output + wasted output. All energy must be accounted for.
• Incorrect rearrangement of equations — When calculating velocity from kinetic energy, students often forget to square root. From KE = ½mv², rearranging gives v² = 2KE ÷ m, then v = √(2KE ÷ m). Always perform operations in the correct order.
• Using inconsistent units — Energy calculations require mass in kg, distance in m, and time in s. Convert all values to standard SI units before calculating. A common error is using cm instead of m or g instead of kg.
• Stating efficiency as a decimal when percentage is required — Always check whether the answer should be a percentage or decimal. If you calculate 0.65, convert to 65% if the question asks for percentage efficiency.
• Assuming 100% efficiency in real situations — No real energy transfer is perfectly efficient. Even if not explicitly stated, exams expect you to recognise that some energy dissipates to surroundings unless told to ignore resistance or friction.
Exam technique for "Conservation of energy"
• Identify command words carefully — "State" requires a brief answer without explanation (1 mark). "Explain" requires reasoning or a mechanism (2-3 marks). "Calculate" requires working shown with the final answer. "Show that" means demonstrate step-by-step that a given answer is correct.
• Show all working in calculations — Even if your final answer is incorrect, you can earn method marks for correct equations, substitutions, or rearrangements. Write the equation, substitute values with units, then calculate. This structured approach maximises marks.
• Use correct significant figures — Match your answer's precision to the data given. If values are given to 2 significant figures, give your answer to 2 or 3 significant figures. Avoid over-precise answers like 66.666666%—write 66.7% or 67%.
• Draw Sankey diagrams to scale — When asked to draw diagrams, use a ruler and ensure arrow widths are proportional. If 200 J is 10 cm wide, then 50 J should be 2.5 cm wide. Label all values clearly. This attention to detail earns full marks.
Quick revision summary
Energy cannot be created or destroyed, only transferred between stores through mechanical work, electrical work, heating, or radiation. In closed systems, total energy remains constant. Efficiency measures useful energy output as a proportion of total input—no real transfer is 100% efficient due to dissipation. Use equations for kinetic, gravitational potential, and elastic potential energy to solve problems. Sankey diagrams visually represent energy transfers with arrow widths proportional to energy amounts. Always account for all energy including wasted thermal energy when applying conservation principles.