IB Physics SLTopic B.3 — The Behaviour of GasesPaper 1 & 2Gas Pressure · Force per Unit Area~6 min read
Gas Pressure
Before any gas law makes sense, you need a solid grip on what pressure actually is. It isn’t force — it’s force spread out, and that one distinction explains everything from why a pin sinks into a surface to why a gas pushes evenly on every wall of its container.
📘 What you need to know
Pressure is defined as the force applied per unit area: P = F ÷ A.
Pressure is measured in pascals (Pa), where 1 Pa = 1 N m⁻².
The equation only applies when the force acts perpendicular (at 90°) to the surface.
Gas pressure comes from huge numbers of molecules colliding with the walls of their container — each tiny collision contributes a small force, and together they add up to a steady, uniform pressure.
For a fixed force, a smaller area produces a larger pressure, and a larger area produces a smaller pressure.
Defining Pressure
Pressure describes how concentrated a force is. Push the same force through a small area and the effect is intense; spread that same force across a wide area and the effect barely registers. That relationship is captured in one compact equation:
PressureP = F ÷ A
where P is pressure (Pa), F is force (N), and A is the cross-sectional area the force acts on (m²). This relationship only holds when the force is directed straight into the surface — at right angles to it. A force applied at an angle needs to be resolved into its perpendicular component first.
Where Gas Pressure Actually Comes From
A gas isn’t pushing on its container the way a solid object rests on a table. Instead, gas pressure is the combined effect of an enormous number of individual molecules constantly colliding with the container walls. Each collision delivers a brief, tiny force perpendicular to the wall — and because there are so many molecules moving in every direction at once, those countless small impacts blend into a steady, uniform pressure across the entire surface.
Each molecule that collides with the wall exerts a tiny force perpendicular to it. Summed over an enormous number of collisions per second, this produces a uniform gas pressure.
You can feel a version of this force yourself: puff out your cheeks and you’ll notice the strain of air pushing outward — that’s the same perpendicular push gas molecules exert on any surface they’re confined by.
Same Force, Different Area
Because pressure is a ratio, the same force can produce wildly different pressures depending on how much area it’s spread across.
The finger applies the same force whether it pushes on a flat surface or a pin — but concentrating that force onto the pin’s tiny tip area makes the pressure at the tip huge, which is why it’s the tip that sinks into the surface.
Quick recap: P = F ÷ A applies whenever a force acts perpendicular to a surface. Gas pressure is this same idea applied to countless molecular collisions with a container’s walls, all averaging out to one steady value.
WE 1
A hydraulic car jack has a piston of cross-sectional area 3.20 × 10⁻² m². The pump creates a pressure of 4.85 × 10⁵ Pa in the fluid beneath the piston. Calculate the force applied to the piston.
Step 1 — Write the equationP = F ÷ A → F = PAStep 2 — Substitute the valuesF = (4.85 × 10⁵) × (3.20 × 10⁻²)F = 15 520 NF ≈ 15.5 kN (3 s.f.)Always double-check that the area you use is the cross-sectional area the force is actually acting on.
WE 2
A hiker weighing 750 N stands still on one boot. The sole of the boot has a contact area of 1.5 × 10⁻² m². Calculate the pressure the hiker exerts on the ground.
Step 1 — Write the equationP = F ÷ AStep 2 — Substitute the valuesP = 750 ÷ (1.5 × 10⁻²)P = 50 000 Pa = 50.0 kPaThe same 750 N spread over a narrower heel, rather than the whole sole, would produce a noticeably higher pressure.
💡 Top tips
Always pin down exactly which area a force is acting on before substituting into P = F ÷ A — questions often give you more than one area to choose from.
Convert any area given in cm² into m² (divide by 10⁴) before using the pressure equation, since pascals are defined as N m⁻².
Remember pressure is a ratio, not a fixed property of the force alone — the same force can give very different pressures depending on the area involved.
⚠ Common mistakes
Using the wrong area — for example, the total surface area of a container rather than the specific cross-section the force acts through.
Applying P = F ÷ A to a force that isn’t perpendicular to the surface, without resolving it first.
Forgetting to convert units — mixing cm² and m², or N and kN, is one of the most common ways marks are lost in pressure calculations.
Up next: Amount of Substance — where we start counting exactly how many gas particles are actually colliding with those walls, using the mole and the Avogadro constant.
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Book a free session and we’ll work through pressure and gas law problems until they’re second nature.
