Gas Pressure

Push down on the handle of a bicycle pump with your thumb blocking the end, and something strange happens: the harder you press, the harder the pump pushes back. You are squashing nothing but air — and yet the air fights you. Blow up a balloon and it strains outward in every direction at once, tight as a drum. A gas, it turns out, is always shoving on the walls that hold it.

That outward push, spread over the surface it presses on, is what we call pressure. Pressure is not just a force — it is a force sharing out over an area, the push felt on every square metre of the container:

p = \dfrac{F}{A} \qquad\text{(pressure} = \text{force} \div \text{area).}

Force is measured in newtons and area in square metres, so pressure comes out in newtons per square metre, which we name the pascal (Pa). A pascal is a tiny amount, so gas pressures are usually quoted in kilopascals (kPa): the air around you right now presses at about 100\ \text{kPa}, roughly the weight of a small car spread over every square metre.

Where the push comes from: collisions

A gas is mostly empty space with tiny particles zooming about freely, bouncing off one another and off the walls. Each time a single particle slams into a wall it bounces back, and — like a tiny ball thrown at a window — it gives the wall a minute push. One collision is far too small to feel. But a thimble of air holds billions upon billions of particles, and the walls are hammered by an unimaginable number of these collisions every second.

Add up all those countless tiny pushes and they blur into one smooth, steady, outward force — the pressure. This is the whole secret of gas pressure, and everything else on this page follows from it:

More collisions each second (the walls hit more often) → more pressure.
Harder collisions (each particle hits faster) → more pressure.

So anything that makes the particles strike the walls more often or harder drives the pressure up. There are two easy ways to do exactly that: squeeze the gas into less space, or heat it up. Let's watch both.

See it for yourself

Here is a box of gas particles with a pressure gauge on the right. Shrink the volume and the particles are packed into a smaller space, so they reach the walls far more often — the gauge climbs. Raise the temperature and the particles move faster, hitting the walls both harder and more often — the gauge climbs again. Both knobs push the pressure up, for the same underlying reason: more or fiercer collisions.

Notice the gauge never reads the same for two very different settings by accident — pressure depends on both how tightly the gas is packed and how fast its particles fly.

Heating a gas

Temperature is really a measure of how fast the particles are jiggling and flying about. Warm a gas and you speed its particles up. Two things then happen at the walls: each particle arrives carrying more energy, so it hits harder, and because it is moving faster it also comes back to the wall more often. Harder and more frequent collisions mean higher pressure.

If the gas is sealed in a rigid container (it cannot grow), all that extra collision goes into pressure — the pressure simply rises. That is why an aerosol can carries a stern warning never to throw it on a fire: heat it enough and the pressure inside climbs until the can bursts. If instead the gas is free to expand (a balloon, say), it swells outward until the push from inside balances the push of the air outside again — which is why a balloon left in a hot car puffs up tight, and a squashed ping-pong ball springs back into shape when dropped in hot water.

Squeezing a gas: Boyle's Law

Now keep the temperature fixed and just make the box smaller. The particles are the same and moving at the same speeds, but they now have a shorter distance to travel before meeting a wall — so they collide with the walls more often. Halve the volume and you roughly double how often the walls are struck, so you double the pressure. Squeeze the gas into a third of the space and the pressure roughly trebles.

This tidy trade-off — smaller volume, proportionally bigger pressure — is Boyle's Law. Pressure and volume rise and fall in exact opposite step, so their product stays fixed:

p\,V = \text{constant} \qquad\text{(at constant temperature).}

For a fixed amount of gas held at a constant temperature, the pressure and volume are inversely proportional — their product does not change:

p\,V = \text{constant}, so squeezing the gas (smaller V) raises the pressure, and letting it expand lowers it.
Comparing any two states of the same gas at that temperature: p_1 V_1 = p_2 V_2.

That second line, p_1 V_1 = p_2 V_2, is the working tool. Whenever a gas is squeezed or stretched at a steady temperature, its "before" pressure times volume equals its "after" pressure times volume.

Worked examples with p_1 V_1 = p_2 V_2

Example 1 — a bike pump. A pump holds 0.00060\ \text{m}^3 of air at 100\ \text{kPa}. You push the handle in until the air occupies only 0.00020\ \text{m}^3, quickly enough that the temperature barely changes. What is the new pressure?

Step 1 — write Boyle's Law. p_1 V_1 = p_2 V_2. Step 2 — rearrange for the unknown. p_2 = \dfrac{p_1 V_1}{V_2}. Step 3 — put the numbers in.

p_2 = \dfrac{100 \times 0.00060}{0.00020} = 300\ \text{kPa}.

Squashing the air to a third of its volume trebled its pressure — exactly the resistance you feel building under your thumb.

Example 2 — a bubble rising. A bubble of gas leaves a diver at the bottom of a lake where the pressure is 300\ \text{kPa}, with a volume of 2\ \text{cm}^3. It drifts up to just below the surface, where the pressure is only 100\ \text{kPa} (and take the water as all one temperature). How big is the bubble now?

Rearranging for the new volume, V_2 = \dfrac{p_1 V_1}{p_2}:

V_2 = \dfrac{300 \times 2}{100} = 6\ \text{cm}^3.

As the crushing pressure of the deep water eases off, the bubble swells to three times its size — which is why bubbles visibly grow as they rise.

Example 3 — a sealed syringe. You seal the nozzle of a syringe holding 40\ \text{cm}^3 of air at 100\ \text{kPa} and pull the plunger out until the air fills 50\ \text{cm}^3 (same temperature). The new pressure is

p_2 = \dfrac{p_1 V_1}{V_2} = \dfrac{100 \times 40}{50} = 80\ \text{kPa}.

Letting the gas expand lowers its pressure below the air outside — which is exactly why the plunger tries to spring back in.

Gas pressure comes from particles colliding with the walls — not from particles pushing on each other. Most of the time the particles are nowhere near each other, flying through empty space; it is the drumming on the container that we feel as pressure.
p_1 V_1 = p_2 V_2 only holds at constant temperature (and for a fixed amount of gas). If the gas is also heated or cooled while you squeeze it, Boyle's Law alone is not enough — the collisions change speed as well as frequency.
Heating a gas that is sealed raises its pressure, not its volume — the box can't grow, so the fiercer collisions push harder on fixed walls. It is a gas free to expand whose volume grows on heating.

Fill a drinks can with a little water and boil it so steam drives the air out, then quickly seal it and plunge it into cold water. In an instant the can crumples as if a giant had squeezed it — no one touched it. What happened?

Cooling the trapped gas slowed its particles right down, so their collisions on the inside walls became weaker and rarer and the inside pressure collapsed. But the ordinary air outside kept hammering away at full strength, roughly 100\ \text{kPa}. With nothing pushing back from within, the outside air simply crushed the can. The same physics puffs a sealed crisp packet up like a pillow on a plane: the cabin air thins at altitude, the pressure outside the packet drops, and the gas sealed inside — now facing weaker resistance — expands the bag until it is taut.