IB Physics HLThe Behaviour of GasesPaper 1 & 2Empirical Gas Laws~12 min read
Gas Laws
Squeeze a gas, heat it, or seal it in a rigid box — its pressure, volume and temperature all respond in tidy, predictable ways. The gas laws are just three simple rules linking those three quantities, each found by holding one of them still. Learn the three, then stitch them into one master equation, and you can predict what any fixed amount of gas will do.
📘 What you need to know
For a fixed amount of gas, the three quantities are pressure P, volume V and temperature T (always in kelvin)
Boyle’s law (constant T): P ∝ 1/V, so P1V1 = P2V2
Charles’s law (constant P): V ∝ T, so V1/T1 = V2/T2
Pressure law (constant V): P ∝ T, so P1/T1 = P2/T2
Combine all three: PV/T = constant, so P1V1/T1 = P2V2/T2
A P–V diagram shows these changes as paths, with curves of constant temperature called isotherms
One gas, three laws
Here’s the trick that makes this easy: each law comes from an experiment where you hold one quantity constant and watch how the other two behave. That’s it. Three “held constant” choices, three laws.
Law
Held constant
Relationship
Equation
Boyle’s law
Temperature
P ∝ 1/V
P1V1 = P2V2
Charles’s law
Pressure
V ∝ T
V1/T1 = V2/T2
Pressure law
Volume
P ∝ T
P1/T1 = P2/T2
Each law also has its own tell-tale graph shape — a curve for Boyle, a straight line through the origin for the other two:
The three gas laws at a glance. Boyle’s is a curve (inverse); Charles’s and the pressure law are straight lines through the origin (they pass through 0 only because T is in kelvin).
Boyle’s law: squeeze it (constant T)
Keep the temperature fixed and squash a gas into half the space, and its pressure doubles. Pressure and volume are inversely proportional.
Boyle’s law (constant T)P ∝ 1/V → P1V1 = P2V2
Why? Shrink the box and each molecule reaches the walls sooner, so it hits them more often — more collisions per second means more pressure.
WE 1
A gas occupies 0.50 m3 at a pressure of 1.0 × 105 Pa. At constant temperature it is compressed to 0.20 m3. Find the new pressure.
Step 1 — constant T, so use P₁V₁ = P₂V₂
P₂ = P₁V₁ ÷ V₂
Step 2 — substituteP₂ = (1.0×10⁵ × 0.50) ÷ 0.20P₂ = 2.5 × 10⁵ PaSqueezed to 2/5 of the volume, so the pressure rose by the factor 5/2. No need for kelvin here — temperature cancels.
Charles’s law: heat it (constant P)
Now hold the pressure fixed instead (imagine a piston free to slide). Warm the gas and it expands — volume is directly proportional to temperature.
Charles’s law (constant P)V ∝ T → V1/T1 = V2/T2
Heat the gas and its molecules move faster. To keep the pressure the same, they have to spread out — so the volume grows.
WE 2
A gas has a volume of 0.30 m3 at 27 °C. It is heated to 127 °C at constant pressure. Find the new volume.
Step 1 — convert to kelvinT₁ = 27 + 273 = 300 K ; T₂ = 127 + 273 = 400 KStep 2 — constant P, so V₁/T₁ = V₂/T₂
V₂ = V₁ × T₂/T₁
V₂ = 0.30 × 400/300V₂ = 0.40 m³Kelvin is essential — using °C here would give a badly wrong answer.
The pressure law: seal it (constant V)
Finally, seal the gas in a rigid box so the volume can’t change. Heat it now and the pressure climbs — pressure is proportional to temperature.
Pressure law (constant V)P ∝ T → P1/T1 = P2/T2
Same reason as before — hotter molecules move faster — but now they can’t spread out. So they simply hit the walls harder and more often, and the pressure rises.
WE 3
A sealed rigid canister holds gas at 1.5 × 105 Pa and 27 °C. It is heated to 127 °C. Find the new pressure.
Step 1 — convert to kelvinT₁ = 300 K ; T₂ = 400 KStep 2 — constant V, so P₁/T₁ = P₂/T₂
P₂ = P₁ × T₂/T₁
P₂ = (1.5×10⁵) × 400/300P₂ = 2.0 × 10⁵ PaThis is why sealed cans warn against heating — trapped gas pushes harder as it warms.
Putting them together: PV/T = constant
The three laws are really three faces of one bigger rule. Roll them into a single relationship for a fixed amount of gas:
The combined gas lawPV/T = constantP1V1/T1 = P2V2/T2
Hold any one quantity fixed and it cancels from both sides, handing you back Boyle, Charles or the pressure law. So you really only need to remember this one — the others fall out of it.
Which law should you reach for? Look at what the question keeps constant. Temperature fixed → Boyle. Pressure fixed → Charles. Volume fixed → pressure law. All three changing → the combined law. And whenever a temperature appears, your very first move is to turn °C into kelvin (add 273).
P–V diagrams
We can draw any change of state on a pressure–volume diagram. The special curves on it are isotherms — lines of constant temperature (each one is a Boyle’s-law curve). Curves further from the origin are hotter. A change of state is just a path from one point to another, and the direction of that path tells you which law is in play.
On a P–V diagram, each move matches a gas law: path A (horizontal, constant P) is Charles’s law, path B (along an isotherm, constant T) is Boyle’s law, and path C (vertical, constant V) is the pressure law. A general curve crossing between isotherms would change all three at once.
🛠️ Solving a gas-law problem
List what you’re given and label it P1, V1, T1 and P2, V2, T2.
Spot what’s held constant — that picks the law.
Convert every temperature to kelvin (add 273).
Substitute and rearrange for the unknown.
Check it’s sensible: squeezing raises pressure, heating expands or pressurises.
💡 Top tips
Always kelvin in any gas-law equation — add 273 to °C first.
Read what’s constant to choose the law (or use the combined law for everything).
Boyle’s is a curve; Charles and pressure law are straight lines through the origin.
Isotherms are Boyle curves — each is one fixed temperature; further out = hotter.
Sanity-check the direction: smaller volume → higher pressure, hotter → bigger V or higher P.
⚠ Common mistakes
Leaving temperature in °C — every gas law needs kelvin
Using the wrong law because you didn’t check what was held constant
Flipping Boyle’s law — it’s P1V1 = P2V2, not P1/V1 = P2/V2
Thinking Charles/pressure lines pass through 0 °C — they pass through 0 K
Changing the amount of gas — these laws assume a fixed mass of gas
Quick recap: Hold one quantity constant and you get a gas law — Boyle (P1V1 = P2V2), Charles (V1/T1 = V2/T2) and the pressure law (P1/T1 = P2/T2). Together they give PV/T = constant. Always work in kelvin, and read the P–V diagram by which quantity stays fixed.
You can now predict how a fixed amount of gas responds to any squeeze or heat. The last step is to bring in how much gas there is. Next up is the Ideal Gas Equation — PV = nRT — which folds the number of moles straight into the combined law and turns “= constant” into an exact number.
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