IB Physics SLTopic B.3 — The Behaviour of GasesPaper 1 & 2Boyle’s · Charles’s · Gay-Lussac’s Laws~8 min read
Gas Laws
Hold one variable of a gas fixed and the other two lock into a simple relationship. Three separate experimental laws describe those relationships — and together, they combine into a single rule that governs how any ideal gas behaves.
📘 What you need to know
An ideal gas obeys PV ∝ T, or equivalently, PV ÷ T = constant.
Boyle’s law (constant temperature): P ∝ 1 ÷ V — pressure and volume are inversely proportional.
Charles’s law (constant pressure): V ∝ T — volume and thermodynamic temperature are directly proportional.
Gay-Lussac’s law, also called the pressure law (constant volume): P ∝ T — pressure and thermodynamic temperature are directly proportional.
All three laws assume the mass and number of molecules of the gas stay fixed throughout.
The Ideal Gas Relation
Each of the three empirical laws only holds one variable constant at a time. Combine all three together and you get a single relationship that links pressure, volume and temperature simultaneously:
Ideal gas relationPV ∝ T ⇔ PV ÷ T = constant
This is the relationship an ideal gas is defined to obey. It’s the foundation the full ideal gas equation is built on — but before adding in the amount of substance, it’s worth getting comfortable with each of the three individual laws it’s built from.
Boyle’s Law — Constant Temperature
Squeeze a gas into a smaller space at constant temperature and its pressure rises — compress it into half the volume and the pressure roughly doubles. With less room to move, the same number of molecules collide with the walls more frequently, so pressure and volume move in opposite directions.
Boyle’s lawP ∝ 1 ÷ V ⇒ P1V1 = P2V2
Charles’s Law — Constant Pressure
Heat a gas at constant pressure and it expands. Faster-moving molecules would otherwise hit the walls harder and more often, raising the pressure — so to keep pressure unchanged, the gas has to occupy more volume, spacing the collisions back out.
Charles’s lawV ∝ T ⇒ V1 ÷ T1 = V2 ÷ T2
Gay-Lussac’s Law — Constant Volume
Seal a gas into a rigid, fixed-volume container and heat it, and the pressure climbs steadily. The molecules move faster and collide with the walls both more often and with greater force, and since the volume can’t change to compensate, that extra collision activity shows up directly as higher pressure.
Gay-Lussac’s law (pressure law)P ∝ T ⇒ P1 ÷ T1 = P2 ÷ T2
Boyle’s law produces a curve (inverse proportion); Charles’s law and Gay-Lussac’s law both produce straight lines through the origin (direct proportion to thermodynamic temperature).
Reading a Pressure–Volume Diagram
Changes to a gas’s state — pressure, volume and temperature all shifting together — can be plotted on a pressure–volume (P–V) diagram. Curved lines called isotherms mark out every possible pressure–volume combination at one fixed temperature; isotherms further from the origin represent higher temperatures. The path a gas’s state traces across this diagram tells you exactly which variable was held constant during a process:
A horizontal line represents changing volume and temperature at constant pressure (an isobaric process).
A curved line running along a single isotherm represents changing pressure and volume at constant temperature (an isothermal process).
A vertical line represents changing pressure and temperature at constant volume (an isochoric process).
A curved line that crosses between isotherms represents a general process in which pressure, volume and temperature all change together.
Each path type on a P–V diagram corresponds to holding a different variable constant — horizontal for constant pressure, along an isotherm for constant temperature, vertical for constant volume.
Quick recap: Boyle’s (P∝1/V), Charles’s (V∝T) and Gay-Lussac’s (P∝T) laws each hold one variable fixed. Combined, they give PV∝T — the defining relationship of an ideal gas.
WE 1
A gas occupies 2.4 × 10⁻³ m³ at a pressure of 1.8 × 10⁵ Pa. It is compressed at constant temperature until its volume is 9.0 × 10⁻⁴ m³. Calculate the new pressure.
Step 1 — Identify the law
Temperature is constant, so this is Boyle’s law: P₁V₁ = P₂V₂
Step 2 — Rearrange and substituteP₂ = (P₁V₁) ÷ V₂ = [(1.8 × 10⁵)(2.4 × 10⁻³)] ÷ (9.0 × 10⁻⁴)P₂ = 4.8 × 10⁵ PaThe volume shrank to less than half its original size, so the pressure more than doubled — exactly what Boyle’s law predicts.
WE 2
A sealed, rigid canister contains gas at 1.2 × 10⁵ Pa and 290 K. It is heated at constant volume to 350 K. Calculate the new pressure.
Step 1 — Identify the law
Volume is fixed (rigid, sealed container), so this is Gay-Lussac’s law: P₁ ÷ T₁ = P₂ ÷ T₂
Step 2 — Rearrange and substituteP₂ = (P₁T₂) ÷ T₁ = [(1.2 × 10⁵)(350)] ÷ 290P₂ ≈ 1.45 × 10⁵ Pa (3 s.f.)Both temperatures must be in kelvin — this calculation would go wrong immediately if left in °C.
💡 Top tips
Always convert temperature to kelvin before substituting into any gas law — none of these relationships work correctly in °C.
Identify which variable is held constant first — that single decision tells you which of the three laws to use.
On a P–V diagram, check whether a curved path stays on one isotherm (constant T) or crosses between isotherms (T also changing) before describing the process.
⚠ Common mistakes
Substituting temperature in °C instead of kelvin — always convert with T(K) = θ(°C) + 273.
Applying the wrong law because the constant variable wasn’t identified first — check the question carefully for what’s fixed.
Assuming any curved line on a P–V diagram is automatically isothermal — only a curve that stays on a single isotherm represents constant temperature; a curve crossing isotherms means temperature is changing too.
Up next: The Ideal Gas Equation — where we bring in the amount of substance and turn PV ∝ T into a full equation you can actually calculate with.
Want this to actually stick before the exam?
Book a free session and we’ll work through Boyle’s, Charles’s and Gay-Lussac’s law problems until they’re second nature.
