What you'll learn
This Higher tier extension builds on the particle model to explain how gases behave under changing conditions of pressure, volume and temperature. You'll apply mathematical relationships between these variables and use the particle model to explain observations — skills tested regularly in 6-mark extended response questions and calculation tasks on Edexcel GCSE Physics papers.
Key terms and definitions
Pressure — the force per unit area exerted by gas particles colliding with container walls, measured in pascals (Pa) or N/m²
Absolute zero — the lowest possible temperature (0 Kelvin or -273°C) at which particles have minimum kinetic energy and pressure of an ideal gas would theoretically reach zero
Kelvin scale — the absolute temperature scale starting at absolute zero, where temperature in Kelvin = temperature in °C + 273
Boyle's Law — for a fixed mass of gas at constant temperature, pressure × volume = constant (p₁V₁ = p₂V₂)
Pressure Law — for a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature (p₁/T₁ = p₂/T₂)
Charles's Law — for a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature (V₁/T₁ = V₂/T₂)
Work done on a gas — when a gas is compressed, work is done on the gas, increasing its internal energy and typically raising its temperature
Atmospheric pressure — the pressure exerted by the weight of air in the atmosphere, approximately 100,000 Pa or 1 × 10⁵ Pa at sea level
Core concepts
The particle model explanation of gas pressure
Gas particles move randomly at high speeds in all directions. Pressure results from particles colliding with container walls. Each collision exerts a tiny force; billions of collisions per second create a steady measurable pressure.
Three factors affect gas pressure according to the particle model:
- Temperature increase: Particles gain kinetic energy, move faster, collide more frequently and with greater force → pressure increases
- Volume decrease: Particles travel shorter distances between collisions with walls, colliding more frequently → pressure increases
- More particles added: More collisions per second with walls → pressure increases
This model explains everyday observations. A bicycle pump becomes warm when compressing air because work done on the gas increases particle kinetic energy. Aerosol cans carry warnings not to heat them because higher temperatures increase internal pressure, potentially causing explosion.
Boyle's Law — pressure and volume relationship
For a fixed mass of gas at constant temperature, the product of pressure and volume remains constant. Mathematically:
p₁V₁ = p₂V₂
Where:
- p₁ = initial pressure (Pa)
- V₁ = initial volume (m³)
- p₂ = final pressure (Pa)
- V₂ = final volume (m³)
The particle model explains this inverse relationship. When volume decreases (compression), particles have less space to move. They collide with walls more frequently, causing higher pressure. When volume increases (expansion), collision frequency decreases, lowering pressure.
Typical exam contexts:
- Syringes with blocked outlets
- Gas trapped in cylinders
- Diving and pressure changes with depth
- Weather balloons rising through the atmosphere
Graph representation: plotting pressure (y-axis) against volume (x-axis) produces a curve called a rectangular hyperbola. Plotting pressure against 1/volume gives a straight line through the origin, confirming the inverse proportionality.
The Kelvin scale and absolute zero
The Kelvin scale provides an absolute temperature measurement essential for gas law calculations. Unlike Celsius, which arbitrarily sets water's freezing point at 0°C, Kelvin starts at the theoretically lowest possible temperature.
Conversion formula: T(K) = T(°C) + 273
At absolute zero (0 K or -273°C), particles possess minimum kinetic energy. They cannot lose more energy. For an ideal gas, particle motion and therefore pressure would theoretically reach zero.
Real gases liquify before reaching absolute zero, but the concept remains fundamental. Scientists have achieved temperatures within billionths of a degree above absolute zero in laboratory conditions.
Exam requirement: Always convert Celsius temperatures to Kelvin before using pressure or volume-temperature equations. Forgetting this conversion loses marks even if your method is otherwise correct.
Pressure Law — pressure and temperature relationship
For a fixed mass of gas at constant volume, pressure is directly proportional to absolute temperature:
p₁/T₁ = p₂/T₂
Where:
- p₁ = initial pressure (Pa)
- T₁ = initial absolute temperature (K)
- p₂ = final pressure (Pa)
- T₂ = final absolute temperature (K)
The particle model explanation: heating increases particle kinetic energy. Faster-moving particles collide with walls more frequently and with greater force. Both factors increase pressure. The volume cannot change, so pressure must rise.
Typical exam contexts:
- Car tyres heated by friction
- Gas cylinders in fires
- Pressure cookers
- Aerosol can safety warnings
Graph representation: plotting pressure (y-axis) against temperature in Kelvin (x-axis) produces a straight line through the origin, demonstrating direct proportionality. If temperature were plotted in Celsius, the line would intercept the temperature axis at -273°C (absolute zero).
Charles's Law — volume and temperature relationship
For a fixed mass of gas at constant pressure, volume is directly proportional to absolute temperature:
V₁/T₁ = V₂/T₂
Where:
- V₁ = initial volume (m³)
- T₁ = initial absolute temperature (K)
- V₂ = final volume (m³)
- T₂ = final absolute temperature (K)
Particle explanation: heating increases particle speed. To maintain constant pressure with faster-moving particles, the container must expand. Greater volume means particles travel further between wall collisions, keeping collision frequency (and therefore pressure) constant despite increased particle speed.
Typical exam contexts:
- Hot air balloons
- Bimetallic strip thermometers with gas sensors
- Weather balloon expansion rising through atmosphere
Work done and internal energy changes
When a gas is compressed, work is done on the gas. This energy transfer increases the internal energy (kinetic energy) of particles, typically raising temperature.
W = p × ΔV
Where:
- W = work done (J)
- p = pressure (Pa)
- ΔV = change in volume (m³)
This explains why bicycle pumps warm during use and why diesel engines can ignite fuel through compression alone (compression ignition). Conversely, when gases expand, they do work on surroundings and cool — the principle behind refrigerators and aerosol spray coolness.
Combined gas equation
When neither pressure nor volume remains constant, combine the laws:
(p₁V₁)/T₁ = (p₂V₂)/T₂
This equation handles scenarios where two or three variables change simultaneously. Always ensure temperature is in Kelvin and units are consistent throughout.
Worked examples
Example 1: Boyle's Law calculation
Question: A syringe contains 50 cm³ of air at atmospheric pressure (100,000 Pa). The plunger is pushed in, reducing the volume to 20 cm³ while temperature remains constant. Calculate the new pressure. [3 marks]
Solution:
Given information:
- p₁ = 100,000 Pa
- V₁ = 50 cm³
- V₂ = 20 cm³
- Temperature constant → use Boyle's Law
p₁V₁ = p₂V₂ [1 mark for correct equation]
100,000 × 50 = p₂ × 20
5,000,000 = p₂ × 20
p₂ = 5,000,000 ÷ 20 [1 mark for rearrangement]
p₂ = 250,000 Pa (or 2.5 × 10⁵ Pa) [1 mark for answer with unit]
Example 2: Pressure Law calculation
Question: A gas cylinder contains gas at 20°C with a pressure of 2.0 × 10⁶ Pa. The cylinder is left in sunlight and heats to 50°C. The volume remains constant. Calculate the new pressure. [4 marks]
Solution:
Convert temperatures to Kelvin: [1 mark]
- T₁ = 20 + 273 = 293 K
- T₂ = 50 + 273 = 323 K
Given: p₁ = 2.0 × 10⁶ Pa
Use p₁/T₁ = p₂/T₂ [1 mark for correct equation]
(2.0 × 10⁶)/293 = p₂/323
p₂ = (2.0 × 10⁶ × 323)/293 [1 mark for rearrangement]
p₂ = 2.21 × 10⁶ Pa (accept 2.2 × 10⁶ Pa) [1 mark for answer]
Example 3: Extended response — particle model explanation
Question: Explain in terms of particles why the pressure inside a sealed container of gas increases when the temperature is raised. [4 marks]
Mark scheme answer:
When temperature increases, gas particles gain kinetic energy [1 mark] and move faster [1 mark]. The particles collide with the container walls more frequently [1 mark] and with greater force / momentum change per collision [1 mark]. Both effects increase the pressure exerted on the walls.
Common mistakes and how to avoid them
Mistake: Forgetting to convert Celsius to Kelvin in gas law calculations. Correction: Always add 273 to Celsius values before substituting into p₁/T₁ = p₂/T₂ or V₁/T₁ = V₂/T₂ equations. Write the conversion step explicitly in your working.
Mistake: Using volume in cm³ when pressure is in Pa, creating unit inconsistency. Correction: Either convert cm³ to m³ (divide by 1,000,000) or keep both volumes in cm³ since the ratio remains valid. For work done calculations (W = p × ΔV), you must convert to m³.
Mistake: Stating "particles get bigger" or "particles expand" when temperature increases. Correction: Individual particles do not change size. They move faster and occupy more space collectively, but each molecule remains the same size.
Mistake: Rearranging gas law equations incorrectly, particularly with fractions. Correction: Cross-multiply carefully. For p₁/T₁ = p₂/T₂, cross-multiplying gives p₁T₂ = p₂T₁, then p₂ = (p₁T₂)/T₁. Show each algebraic step.
Mistake: Confusing which variable remains constant in each law. Correction: Boyle's Law requires constant temperature; Pressure Law requires constant volume; Charles's Law requires constant pressure. Read the question carefully for clues like "sealed rigid container" (constant volume) or "movable piston" (potentially constant pressure).
Mistake: Writing "the particles have more energy" without specifying kinetic energy. Correction: Be precise — write "particles have more kinetic energy" or "particles move with greater average speed." Potential energy between gas particles is negligible in ideal gases.
Exam technique for Gas laws and particle model (Higher tier extension)
Calculation questions typically award 3-4 marks: 1 mark for identifying the correct equation, 1-2 marks for substitution and rearrangement, 1 mark for the final answer with units. Always show working clearly, even if using a calculator. Partial credit is available for correct method even if the final answer contains arithmetic errors.
"Explain" questions using particle model typically award 3-4 marks. Structure answers with: (1) state what happens to particles (energy increase/decrease), (2) describe motion changes (speed/kinetic energy), (3) describe collision changes (frequency/force), (4) link to macroscopic effect (pressure/volume change). Use connecting words like "therefore" and "because" to show cause-and-effect relationships.
Graph questions may ask you to sketch pressure-volume or pressure-temperature relationships, or to identify which law a graph represents. Remember straight lines indicate direct proportionality (Pressure Law, Charles's Law) while curves indicate inverse relationships (Boyle's Law). Always check axis labels for temperature scale — Kelvin graphs pass through the origin.
Command words matter: "State" requires a brief answer without explanation (1 mark). "Explain" requires reasoning with particle behaviour (3-4 marks). "Calculate" requires numerical working and units. "Describe" needs observable changes without particle-level explanation.
Quick revision summary
Gas pressure results from particle collisions with container walls. Three gas laws govern behaviour at GCSE: Boyle's Law (p₁V₁ = p₂V₂ at constant temperature), Pressure Law (p₁/T₁ = p₂/T₂ at constant volume), and Charles's Law (V₁/T₁ = V₂/T₂ at constant pressure). Always convert Celsius to Kelvin by adding 273. Temperature increases give particles more kinetic energy, increasing collision frequency and force. Work done compressing gases increases internal energy. Particle model explanations must link particle motion changes to macroscopic pressure or volume effects for full marks.