Gases, pressure–volume and the kelvin scale
Keep the conditions clear, convert temperatures confidently, and use an inverse relationship to predict gas pressure.
Core: particle explanations and kelvin conversions. Supplement / Extended: pV = constant, calculations and graphs. This is Cambridge IGCSE, separate from Egyptian Baccalaureate / Thanaweya Amma and not Year 3.
A fair comparison starts with fixed conditions
Imagine the same gas trapped behind a movable piston. No particles enter or leave, and no gas changes state. A fixed mass means the same sample, not the same volume. Before predicting pressure, ask: is the volume fixed, or is the temperature fixed?
Worked example
A rigid sealed vessel keeps the gas volume approximately fixed. A movable piston allows volume to change. Neither statement alone guarantees constant temperature. Heating sealed containers is a thought experiment here, not a home activity.
Think first: Why is “I pushed the piston” not a complete description?
Fast compression may warm the gas, and a leak changes the amount of gas. You need the conditions before choosing an equation.
A reliable calculation method
- State what stays fixed. Choose Boyle’s law only for fixed mass and constant temperature.
- List p₁, V₁, p₂ and V₂. Match pressure units and volume units; use absolute pressures.
- Rearrange before substituting: p₂ = p₁V₁/V₂ or V₂ = p₁V₁/p₂.
- Calculate, include the unit, and check the inverse direction of change.
Worked pressure example: three mark points
A fixed sample at 90 kPa occupies 200 cm³ and expands to 300 cm³ at constant temperature. Choose p₁V₁ = p₂V₂ [1]. Rearrange and substitute p₂ = 90 × 200/300 [1]. Answer 60 kPa [1]. The volume increased by a factor of 1.5, so pressure fell by that factor. Both products equal 18000 kPa cm³.
Worked mixed-unit volume example
A gas at 100 kPa and 0.060 dm³ changes to 150 kPa at constant temperature. Convert 0.060 dm³ to 60 cm³. Then V₂ = 100 × 60/150 = 40 cm³. Alternatively keep dm³ consistently and obtain 0.040 dm³. The products have units; matching them does not make pV dimensionless.
Temperature-scale practice
Convert a temperature reading
Core. Use the syllabus offset 273. The 0 K case is a scale reference, not an achievable gas experiment.
Convert -273 °C to K.
Pressure–volume laboratory
Predict pressure before revealing the graphs
Supplement / Extended. A fixed mass of gas starts at 100 kPa absolute pressure and 60 cm³. Temperature stays at 300 K. This idealised model assumes no leaks or change of state; it is not a real pressure apparatus.
Enter up to two decimal places where needed. Think: should pressure be higher or lower than 100 kPa?
Changing the volume clears the prediction and hides the answer. The Kelvin conversion activity is separate; changing its example does not change this gas temperature.
Practise, then explain
Four multiple-choice questions, five numerical responses and five written tasks. Temperature conversions and qualitative particle explanations are Core; pressure–volume calculations and graph analysis are Supplement / Extended. Numerical answers are checked automatically; written answers use a self-assessment guide. The suggested marks are for this original practice, not an official Cambridge mark scheme.
Practice stays only while this page is open. Refreshing or leaving clears these responses. Copy useful written work into your notes before leaving.
Convert 37 °C to kelvin using the syllabus approximation.
Optional hint
Move the zero point of the scale; use the same-sized temperature steps.
Source clarifications and safe boundaries
The original PDF is unchanged. We use its syllabus approximation T = θ + 273; the precise Celsius–kelvin offset is 273.15, but 273 is the required relation here. For ordinary gas states in this course, temperatures are not below 0 K. A temperature interval does not need the 273 offset.
The source’s “same speed” at constant temperature refers to average speed: individual particle speeds vary. Slow compression alone does not guarantee constant temperature. Boyle’s law uses absolute pressure, not an uncorrected pressure-gauge reading. Consistent units cancel in ratios; the product pV still has units.
Figure 22.1 informs the two graph views. Model curves and practice data are idealised, not experimental measurements. Never force a blocked pump or warm a sealed household container. Use supplied data or approved apparatus under a teacher’s supervision. Qualitative warming is Core; a numerical pressure–temperature law is not required by these objectives.
Source alignment: supplied Physics-0625 Volume A, PDF pp.155–160 / printed pp.147–152, Figure 22.1; official Cambridge 2026–2028 syllabus, section 2.1.3. Original teaching, activities and questions. Existing source-download access is unchanged.