Energy Production (SL) — IB Physics SL SL Study Guide

For: IB Physics SL candidates sitting IB Physics SL.

Covers: Fossil fuel and renewable energy source basics, solar and wind power calculations, nuclear power generation mechanisms, and energy efficiency analysis with Sankey diagrams, aligned to the 2025 IB DP Physics SL syllabus.

You should already know: IGCSE Physics, basic algebra.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the IB Physics SL style for educational use. They are not reproductions of past IBO papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official IBO mark schemes for grading conventions.

1. What Is Energy Production (SL)?

Energy production is the study of how usable energy (mostly electrical energy for grid use) is extracted from natural sources, converted for human consumption, and the environmental, economic and technical tradeoffs of each generation method. It is Topic 8 in the IB Physics SL syllabus, accounting for ~10% of your final exam score, and almost always appears as a 6-10 mark structured question in Paper 2, plus 2-3 multiple choice questions in Paper 1. Examiners regularly test both conceptual comparisons of energy sources and quantitative calculations of power output and efficiency.

2. Fossil fuels and renewable sources

Fossil fuels are non-renewable energy sources formed from the compressed remains of dead organic matter over millions of years, including coal, crude oil and natural gas. Renewable energy sources are replenished naturally over human timescales, including solar, wind, hydro, geothermal and biofuel.

A key metric for comparing fuels is energy density, defined as the amount of energy released per unit mass (or per unit volume) when a fuel is fully combusted, with units $J/kg$ or $J/m^3$. Higher energy density fuels are cheaper to transport and store, as less volume/mass is needed to produce the same amount of energy.

Worked Example

Coal has an energy density of 32 MJ/kg. A 35% efficient coal-fired power plant produces 1 GWh of electricity per day. Calculate the mass of coal consumed daily.

1. Convert useful output to joules: $1\text{GWh}=1\times 10^9\text{W}\times 3600\text{s}=3.6\times 10^{12}\text{J}$
2. Calculate total input energy needed, accounting for efficiency: $E_{\text{input}}=\frac{E_{\text{useful}}}{\eta }=\frac{3.6\times 10^{12}}{0.35}\approx 1.03\times 10^{13}\text{J}$
3. Calculate mass of coal: $m=\frac{E_{\text{input}}}{E_d}=\frac{1.03\times 10^{13}}{32\times 10^6}\approx 320,000\text{kg}=320\text{tonnes}$

Key Tradeoffs (Exam-Focused)

• Fossil fuels: High energy density, low upfront cost, reliable base load power, but release greenhouse gases and air pollutants, and are finite.
• Renewables: Near-zero operational carbon emissions, infinite supply, but lower energy density, intermittent (dependent on weather/time of day), and higher upfront infrastructure cost. Examiners often ask you to select the best energy source for a specific context (e.g. remote island vs dense urban area) — always tie your answer directly to the context given, not just generic pros/cons.

3. Solar and wind power

Solar and wind are the most widely deployed variable renewable energy sources, with separate calculation frameworks tested regularly on exams.

Solar Power

There are two primary solar technologies:

1. Photovoltaic (PV) cells: Convert sunlight directly to electrical energy via the photoelectric effect, with typical efficiencies of 15-22%.
2. Solar thermal: Concentrate sunlight to heat water/working fluid, which drives a steam turbine to generate electricity, with typical efficiencies of 20-30%.

The solar constant ($S=1360{\text{W/m}}^2$) is the average power per unit area of sunlight incident on Earth’s upper atmosphere. Ground-level intensity is lower due to atmospheric absorption, albedo (reflection from clouds/ground) and the angle of incidence of sunlight. The formula for peak PV power output is: $$P=I\times A\times \eta$$ Where $I$ = ground-level solar intensity (${\text{W/m}}^2$), $A$ = total area of the PV array, $\eta$ = efficiency of the panels.

Wind Power

Wind turbines convert the kinetic energy of moving air to electrical energy. The formula for wind power output is derived from the kinetic energy of the air column passing through the turbine’s swept area:

1. Mass of air passing through the turbine per second: $\dot{m}=\rho Av$, where $\rho$ = air density ($1.2{\text{kg/m}}^3$, given in the data booklet), $A=\pi r^2$ = swept area of the turbine blades, $v$ = wind speed.
2. Kinetic energy per second (power) of the air: $P_{\text{total}}=\frac{1}{2}\dot{m}{v}^2=\frac{1}{2}\rho A{v}^3$
3. Useful power output, accounting for turbine efficiency: $$P=\frac{1}{2}\rho A\eta v^3$$ Critical note: Power output is proportional to the cube of wind speed, so a 2x increase in wind speed leads to an 8x increase in power output. This is the most commonly tested detail of wind power calculations.

Worked Example

A wind turbine has 30 m long blades, 40% efficiency, and operates in an area with average wind speed of 10 m/s. Calculate its peak power output.

1. Calculate swept area: $A=\pi r^2=\pi \times 30^2\approx 2827{\text{m}}^2$
2. Substitute into the wind power formula: $P=0.5\times 1.2\times 2827\times 0.4\times 10^3=678,480\text{W}\approx 680\text{kW}$

4. Nuclear power generation

Nuclear power generates heat via controlled nuclear fission of uranium-235, which is then used to produce steam and drive turbines identical to those used in fossil fuel power plants.

Core Fission Process

A U-235 nucleus absorbs a slow-moving neutron, splits into two smaller daughter nuclei, and releases 2-3 fast neutrons and ~200 MeV of energy per fission event. A controlled chain reaction is maintained when exactly one neutron from each fission event goes on to trigger another fission. Two core components control the chain reaction:

1. Moderator: Usually water or graphite, slows fast neutrons to speeds where they are more likely to be absorbed by U-235 nuclei.
2. Control rods: Made of boron or cadmium, absorb excess neutrons to reduce the reaction rate, or are inserted fully to shut down the reactor. Natural uranium is 0.7% U-235, which is too low to sustain a chain reaction, so it is enriched to 3-5% U-235 for use in power reactors.

Worked Example

A 40% efficient nuclear power plant produces 1 GW of electrical power. Each fission of U-235 releases 200 MeV of energy. Calculate the number of fission events occurring per second.

1. Calculate total thermal power needed from fission: $P_{\text{input}}=\frac{P_{\text{useful}}}{\eta }=\frac{1\times 10^9}{0.4}=2.5\times 10^9\text{W}$
2. Convert 200 MeV to joules: $200\text{MeV}=200\times 10^6\times 1.6\times 10^{-19}\text{J}=3.2\times 10^{-11}\text{J per fission}$
3. Number of fissions per second: $\frac{2.5\times 10^9}{3.2\times 10^{-11}}\approx 7.8\times 10^{19}$ fissions per second.

Key Tradeoffs

• Pros: Very high energy density (1 kg of U-235 produces as much energy as 2 million kg of coal), zero operational CO2 emissions, reliable base load power.
• Cons: High upfront construction cost, long-lived radioactive waste requires secure storage, small risk of catastrophic meltdown, risk of nuclear proliferation.

5. Energy efficiency and Sankey diagrams

Energy efficiency measures how much of the input energy to a system is converted to useful output, and is a core metric for evaluating all energy generation technologies.

Efficiency Formula

Efficiency is defined as: $$\eta =\frac{E_{\text{useful output}}}{E_{\text{total input}}}\times 100\%=\frac{P_{\text{useful output}}}{P_{\text{total input}}}\times 100\%$$ It can be written as a percentage (0-100%) or a unitless decimal (0-1).

Sankey Diagrams

Sankey diagrams are visual representations of energy flow through a system, with the following rules tested on exams:

1. The width of each arrow is proportional to the amount of energy/power it represents.
2. Total input energy is drawn on the left, with arrows branching to the right for useful output, and up/down for wasted energy (usually heat).
3. All arrows must be labeled with their value and units (J, kWh, W etc.). The sum of all output arrows (useful + wasted) must equal the total input energy, per the law of conservation of energy.

Worked Example

A Sankey diagram for an electric car shows 100 MJ of input electrical energy, 85 MJ of useful kinetic energy, 10 MJ of waste heat from the battery, and 5 MJ of waste heat from the motor. Calculate the efficiency of the car. $$\eta =\frac{85\text{MJ}}{100\text{MJ}}\times 100\%=85\%$$ Exam tip: If you are asked to draw a Sankey diagram, always choose a clear scale (e.g. 1 cm = 10 J) to ensure arrow widths are proportional, and label every arrow explicitly to avoid losing marks.

6. Common Pitfalls (and how to avoid them)

• Wrong move: Using the square of wind speed instead of the cube in wind power calculations. Why: Students confuse the kinetic energy formula $\frac{1}{2}m{v}^2$ with wind power, forgetting that the mass flow rate of air is also proportional to wind speed, leading to a $v^3$ dependence. Correct move: Write the 1-line derivation quickly before substituting values to confirm: $\dot{m}=\rho Av$, so $P=\frac{1}{2}\rho Av\times v^2=\frac{1}{2}\rho A{v}^3$.
• Wrong move: Forgetting to adjust for efficiency when calculating fuel mass or required input area. Why: Students jump straight to dividing output power by energy density or intensity without accounting for losses. Correct move: Always calculate total input energy first by dividing useful output by efficiency, then use that value for subsequent calculations.
• Wrong move: Stating that nuclear power produces CO2 during operation. Why: Students confuse lifecycle emissions (from mining, enrichment and construction) with operational emissions. Correct move: Explicitly distinguish: operational CO2 emissions are zero, lifecycle emissions are comparable to wind and solar, and far lower than fossil fuels.
• Wrong move: Mixing up the role of control rods and moderators in nuclear reactors. Why: Both components interact with neutrons, so students mix up their functions. Correct move: Moderators slow neutrons to make fission more likely, control rods absorb neutrons to slow or stop the chain reaction.
• **Wrong move: Drawing Sankey diagrams with non-proportional arrow widths. Why: Students rush to draw without setting a scale. Correct move: Choose a simple scale (e.g. 1 square = 10 W) before drawing, and measure each arrow width to match the energy value.

7. Practice Questions (IB Physics SL Style)

Question 1

A natural gas power plant has an efficiency of 42% and produces 500 MW of electrical power. The energy density of natural gas is 55 MJ/kg. (a) Define the term energy density of a fuel. [1] (b) Calculate the mass of natural gas consumed by the plant in one hour. [3] (c) State one advantage and one disadvantage of natural gas compared to coal for power generation. [2]

Solution

(a) Energy density is the amount of energy released per unit mass (or per unit volume) of a fuel when it is fully combusted. (b) Step 1: Useful energy output in 1 hour: $E_{\text{out}}=500\times 10^6\text{W}\times 3600\text{s}=1.8\times 10^{12}\text{J}$. Step 2: Total input energy: $E_{\text{in}}=\frac{1.8\times 10^{12}}{0.42}\approx 4.29\times 10^{12}\text{J}$. Step 3: Mass of gas: $m=\frac{4.29\times 10^{12}}{55\times 10^6}\approx 7.8\times 10^4\text{kg}$. (c) Advantage: Natural gas produces ~50% less CO2 per unit energy than coal, leading to lower greenhouse gas emissions. Disadvantage: Natural gas requires pressurized storage and transport, which is more expensive than transport of solid coal.

Question 2

A wind turbine has 40 m long blades and 38% efficiency. Air density is $1.2{\text{kg/m}}^3$. (a) Show that the maximum theoretical power output of the turbine at a wind speed of 12 m/s is approximately 5 MW. [3] (b) State two reasons why the actual average power output of the turbine will be lower than this maximum value. [2] (c) A 21% efficient solar farm is being considered as an alternative, with average ground-level solar intensity of $250{\text{W/m}}^2$. Calculate the area of solar panels needed to match the 5 MW peak output of the wind turbine. [2]

Solution

(a) Step 1: Swept area: $A=\pi r^2=\pi \times 40^2\approx 5027{\text{m}}^2$. Step 2: Maximum theoretical power assumes no efficiency losses: $P=0.5\times 1.2\times 5027\times 12^3=0.6\times 5027\times 1728\approx 5.2\times 10^6\text{W}=5.2\text{MW}$, which is approximately 5 MW. (b) Any two valid reasons: Wind speed is not always 12 m/s, turbine has mechanical/electrical losses, downtime for maintenance, wind direction is not always aligned with the turbine blades. (c) Rearrange PV power formula: $A=\frac{P}{I\eta }=\frac{5\times 10^6}{250\times 0.21}\approx 9.5\times 10^4{\text{m}}^2$.

Question 3

The Sankey diagram for a nuclear power plant shows 1000 MW of input thermal energy from fission, 330 MW of useful electrical output, 150 MW of waste heat lost to the atmosphere via cooling towers, and the remaining waste heat discharged to a nearby river. (a) Calculate the efficiency of the power plant. [2] (b) Calculate the amount of heat discharged to the river per hour. [2] (c) Explain the function of the moderator in a nuclear fission reactor. [2]

Solution

(a) $\eta =\frac{330\text{MW}}{1000\text{MW}}\times 100\%=33\%$. (b) Waste heat to river: $1000-330-150=520\text{MW}=520\times 10^6\text{J/s}$. Energy per hour: $520\times 10^6\times 3600=1.87\times 10^{12}\text{J}$. (c) The moderator slows down fast neutrons produced by fission events. Slow neutrons are far more likely to be absorbed by U-235 nuclei, sustaining the controlled chain reaction needed for steady power production.

8. Quick Reference Cheatsheet

9. What's Next

This topic connects directly to multiple other areas of the IB Physics SL syllabus: you will apply efficiency and energy transfer concepts to Topic 2 (Mechanics) when calculating work done by engines, to Topic 3 (Thermal Physics) when analyzing heat transfer in power generation systems, and to Topic 7 (Atomic, Nuclear and Particle Physics) when exploring fission and decay processes in nuclear fuel. Energy production questions often combine multiple topics, so mastering the formulas and tradeoffs here will help you answer cross-topic structured questions in Paper 2 that are worth 10+ marks.

If you struggle with any of the calculations, conceptual questions, or want more practice with past-paper style questions for this topic, you can ask Ollie for personalized help, extra worksheets, or step-by-step walkthroughs of official past paper questions at any time. Head to Ollie] to get instant support tailored to your learning gaps, or browse more IB Physics SL study guides on the homepage.