Engine cycles (A-level only) — AQA A-Level Physics

Engine cycles are a core topic in AQA A-Level Physics that connects thermodynamics, energy transfer, and the limits of efficiency. You will study how a working substance, often an ideal gas, is taken through a series of processes such as isothermal, adiabatic, isobaric, and isochoric changes, and how these are represented on pressure-volume (p-V) diagrams. The area enclosed by the cycle represents the net work done per cycle, and the first law of thermodynamics is applied to each stage to track changes in internal energy, heat, and work.

This topic matters because it explains the fundamental principles behind real engines, refrigerators, and heat pumps, and introduces the Carnot cycle as the theoretical maximum efficiency any heat engine can achieve between two reservoirs. Understanding engine cycles also reinforces key ideas from earlier topics like the ideal gas law, internal energy, and the first law, and it prepares you for synoptic questions that link thermodynamics to practical applications and environmental considerations.

• →A cyclic process returns the system to its initial state, so the net change in internal energy over one complete cycle is zero (delta U = 0).
• →On a p-V diagram, the work done by the gas in a process is the area under the curve; for a complete cycle, the net work done is the area enclosed by the loop.
• →The direction of the cycle indicates its function: clockwise cycles are heat engines (net work done by the gas), anticlockwise cycles are refrigerators or heat pumps (net work done on the gas).
• →The Carnot cycle consists of two reversible isothermal processes and two reversible adiabatic processes, and its efficiency depends only on the absolute temperatures of the hot and cold reservoirs: efficiency = 1 - (T_C / T_H).
• →The first law of thermodynamics, delta U = Q + W (where W is work done on the gas), applies to each stage of a cycle and is essential for calculating unknown quantities.

• Identifies the four strokes in order as induction, compression, power (expansion) and exhaust, linking each to piston motion between top dead centre and bottom dead centre.
• Describes the petrol cycle: fuel–air mixture drawn in, compressed, ignited by a spark, hot gas expands doing work, burnt gas expelled.
• Describes the diesel cycle: air alone drawn in and compressed to a high pressure and temperature, fuel injected and self-ignited, expansion then exhaust.
• Reads an indicator diagram: the enclosed loop area represents net work done per cycle and the loop direction shows whether work is done by or on the gas.
• Compares the cycles, noting the diesel's higher compression ratio, higher peak pressure and ignition by compression heating rather than a spark.
• Relates the near-vertical sections of the diagram to rapid combustion at approximately constant volume and the sloping sections to compression and expansion.
• Explains that real diagrams have rounded corners and lower peak pressures than theoretical ones because combustion takes time and heat is lost.
• Calculates indicated power as the p−V loop area multiplied by cycles per second and by the number of cylinders.
• Calculates input power as calorific value of the fuel multiplied by the fuel flow rate, converting units such as kW and MJ kg⁻¹ consistently.
• Uses P = Tω with ω = 2πf to find brake power from measured torque and rotational frequency.
• Obtains friction power by subtracting brake power from indicated power.
• Distinguishes thermal efficiency (indicated power ÷ input power), mechanical efficiency (brake power ÷ indicated power) and overall efficiency (brake power ÷ input power).

• 💡Sketch both diagrams side by side and label the strokes, axes and enclosed area before writing prose.
• 💡Use comparative language such as higher compression ratio and greater peak pressure when contrasting diesel with petrol.
• 💡Link each diagram feature to the physical event in the cylinder so explanations stay causal rather than descriptive.
• 💡Write the defining equation before substituting numbers, and state units with every answer.
• 💡Show the conversion of fuel flow rate to kg s⁻¹ and calorific value to J kg⁻¹ explicitly.
• 💡Check that brake power is less than indicated power and that all efficiencies lie between 0 and 1.
• 💡Always label the axes of p-V diagrams with quantity and unit (e.g., p / Pa, V / m^3) and indicate the direction of the cycle with arrows. This helps you and the examiner track the processes.
• 💡When using the first law, write down your sign convention explicitly before substituting values. AQA expects you to use delta U = Q + W with W as work done on the system, so be consistent.
• 💡For efficiency calculations, convert temperatures to kelvin and show the formula clearly. Remember that efficiency is a ratio and has no units; express it as a decimal or percentage as requested.

• Treating the four strokes as simultaneous rather than sequential; correct by tracking one cylinder through two crankshaft revolutions.
• Believing the spark plug ignites fuel throughout the power stroke; correct by stating ignition occurs at one point near top dead centre.
• Assuming the diesel cycle compresses a fuel–air mixture; correct by stating only air is compressed and fuel is injected near the end of compression.
• Confusing the loop area with peak pressure; correct by explaining that area gives net work per cycle while peak pressure is a single point on the curve.
• Using the wrong area or forgetting the number of cylinders when finding indicated power; correct by multiplying loop area by cycles per second and cylinder count.
• Mixing units such as kW, MJ kg⁻¹ and g s⁻¹; correct by converting all quantities to SI before substituting.
• Using ω in rev s⁻¹ instead of rad s⁻¹; correct by applying ω = 2πf.
• Treating overall efficiency as the sum of thermal and mechanical efficiencies; correct by treating it as their product.
• Students often think that because a cycle returns to its starting point, no heat is exchanged. In fact, heat is absorbed and released in different parts of the cycle, and the net heat absorbed equals the net work done.
• Many believe that the area under a p-V curve always represents work done by the gas. It only does so for expansion; for compression, the area represents work done on the gas, and the sign must be considered.
• Some students assume that all heat engines can achieve 100% efficiency. The Carnot efficiency sets a theoretical upper limit, and real engines are less efficient due to friction and other irreversibilities.

1. 1Week 1: Start by revising the first law of thermodynamics and the ideal gas law. Then learn to identify and sketch the four basic processes on p-V diagrams, noting the shape of each curve and the work done.
2. 2Week 1: Practice applying the first law to each process type, calculating changes in internal energy, heat, and work. Use past paper questions to test your understanding of sign conventions.
3. 3Week 2: Study the Carnot cycle in detail, including its four stages and why it is the most efficient cycle. Derive and use the efficiency formula.
4. 4Week 2: Work through exam-style questions on engine cycles, focusing on calculating net work done, efficiency, and interpreting p-V diagrams. Review mark schemes to understand common pitfalls.
5. 5Ongoing: Create a summary sheet with key formulas, sign conventions, and cycle directions. Use active recall to test yourself on definitions and processes.

• 📋Calculation of efficiency or work done from a p-V diagram or given data. Advice: Identify the hot and cold temperatures, use the Carnot formula if applicable, and show all steps clearly.
• 📋Explanation of the first law applied to a specific process in a cycle. Advice: State the sign convention, identify whether Q, W, or delta U is zero, and explain the physical meaning.
• 📋Sketching and interpreting p-V diagrams for a given cycle. Advice: Label axes, draw curves correctly (isotherms as smooth curves, adiabats steeper), and indicate direction with arrows.
• 📋Comparison of real and ideal cycles, or discussion of efficiency limits. Advice: Refer to the Carnot cycle as the ideal, mention irreversible processes, and use correct terminology.