Gas and atmospheric pressure

The Earth is wrapped in a thick layer of air called the atmosphere. Air is matter, and like all matter it has weight. The atmosphere presses down on every surface beneath it because of the weight of the entire column of air stacked above that surface — this is exactly the same reasoning used for liquid pressure, applied to a fluid that happens to be a gas rather than a liquid. A few facts fix the idea precisely.

• Atmospheric pressure is caused by the weight of the column of air above a surface. A taller or denser column presses harder, which is why pressure falls as you climb a mountain — there is less air left above you.
• Like liquid pressure, atmospheric pressure acts in all directions at once — sideways and upward as well as downward — not only straight down.
• At sea level, atmospheric pressure has a standard value that is worth memorising exactly:

where: $1\ \text{atm}$ is one standard atmosphere, $\text{Pa}$ (pascal) is the SI unit of pressure equal to one newton per square metre, and $76\ \text{cm of mercury}$ is the equivalent height of a mercury column that this pressure can support — the two are simply two ways of stating the same push. That number is enormous once you connect it back to $P = F/A$: since $P = F/A$, the force on any area is $F = P \times A$, so the atmosphere pushes on every square metre of surface at sea level with a force of about $1.013 \times 10^{5}\ \text{N}$ — roughly the weight of ten large cars resting on that one square metre. We are not crushed by this because the fluids and gases inside our bodies push outward with a matching internal pressure, so the net force on our skin is essentially zero. A diagram makes the balance easier to hold in mind than the number alone.

Many familiar devices work by deliberately creating a pressure difference: some action lowers the air pressure in a confined region, and the greater atmospheric pressure of the surrounding air then pushes a liquid or a surface from high pressure toward low pressure.

• Drinking straw: sucking removes air from inside the straw, lowering the pressure there; the atmosphere pushes on the open drink and forces liquid up into your mouth.
• Syringe: pulling the plunger back lowers the pressure inside the barrel; atmospheric pressure pushes liquid in through the needle to fill the empty space.
• Rubber sucker: pressing it onto a surface squeezes out the trapped air beneath it, creating low pressure there; the full atmospheric pressure on the outside then holds the sucker firmly against the surface.

Question: A rubber sucker with a flat circular base of area $A = 8.0 \times 10^{-4}\ \text{m}^2$ is pressed onto a smooth glass surface, squeezing out nearly all the air beneath it. Estimate the force with which the sucker is held against the glass by atmospheric pressure.

Step 1. Identify the pressure difference driving the effect. Once the trapped air is squeezed out, the pressure beneath the sucker is close to zero, while the full standard atmospheric pressure, $P = 1.013 \times 10^{5}\ \text{Pa}$, still acts on the outer face of the rubber.

Step 2. Apply $F = P \times A$ using the atmospheric pressure and the sucker's base area: $F = 1.013 \times 10^{5} \times 8.0 \times 10^{-4} = 81.0\ \text{N}$.

Step 3. Interpret the result. A force of about $81\ \text{N}$ is roughly the weight of an $8\ \text{kg}$ mass — more than enough to hold a light object firmly against a vertical or even an upside-down surface, which is exactly why suckers work in any orientation: atmospheric pressure pushes equally in all directions.

The sucker is held against the glass by a force of about 81 N, supplied entirely by the unbalanced atmospheric pressure on its outer face.

Competitive stretch

If the same sucker were used on a mountain where atmospheric pressure is only about $0.8 \times 10^{5}\ \text{Pa}$, the holding force drops to $F = 0.8 \times 10^{5} \times 8.0 \times 10^{-4} = 64\ \text{N}$ — noticeably weaker, since a shorter, thinner air column above presses down with less force.

• Thinking suction "pulls" liquid up a straw with some special force — it is actually the higher atmospheric pressure outside that pushes the liquid up; nothing pulls from inside.
• Forgetting that atmospheric pressure acts in all directions, not only downward — this is essential to explaining why suckers stick to vertical or upside-down surfaces.
• Believing we do not feel atmospheric pressure because it is weak — it is actually very large, about $1.013 \times 10^{5}\ \text{Pa}$; we do not feel it because internal body pressure balances it almost exactly.
• Using $F = P \times A$ with the wrong area or forgetting to convert $\text{cm}^2$ to $\text{m}^2$ before substituting, which gives an answer that is off by a factor of $10^4$.

Ask the tutor: Want to work through more $F = P \times A$ examples, or see how atmospheric pressure connects to the barometer you will meet in later classes? Ask the AI tutor to walk through it with you.