Squeeze Play: Boyle's Law

Why it matters

Block a bicycle pump's nozzle with your thumb and push the handle — the further you push, the harder the trapped air fights back. You are squeezing a fixed mass of gas into less and less space, and its pressure is climbing exactly as fast as its volume falls.

Predict first

You seal a syringe's nozzle, trapping 60 mL of air at 1 atm, then push the plunger until only 30 mL is left (temperature constant). What is the pressure now?

The same molecules now have half the space, so twice as many strike each bit of wall every second — the pressure doubles. Boyle's law: P₁V₁ = P₂V₂, and indeed 1 × 60 = 2 × 30. The product stays constant.

• 2 atm — halving the volume doubles the pressure — correct
• Still 1 atm — pressure cannot change in a sealed syringe
• 0.5 atm — a smaller volume means a smaller pressure

What you do

Trap the gas and push: slide the piston to each dashed target volume and record the point. Watch the P × V readout as you squeeze — it refuses to change. That constant product IS Boyle's Law.

Check yourself

Which of these is Boyle's law for a fixed mass of dry gas?

Boyle's law: the volume of a given mass of a dry gas is inversely proportional to its pressure at constant temperature. Equivalently, P × V is constant, giving the equation P₁V₁ = P₂V₂.

A gas occupies 800 cm³ at 760 mm Hg. At what pressure will it occupy 380 cm³, the temperature remaining constant?

By Boyle's law, P₁V₁ = P₂V₂: 760 × 800 = P₂ × 380, so P₂ = 760 × 800 ÷ 380 = 1600 mm Hg. Squashing the gas to less than half its volume needs more than double the pressure.

At constant temperature, the graph of V against P for a fixed mass of gas is…

Because V ∝ 1/P, plotting V against P gives a hyperbolic curve in the first quadrant — an isotherm. V against 1/P gives a straight line through the origin, and PV against P gives a line parallel to the P-axis.

• At constant temperature, volume is inversely proportional to pressure — correct
• At constant pressure, volume is directly proportional to temperature
• At constant temperature, volume is directly proportional to pressure
• 1600 mm Hg — correct
• 380 mm Hg
• 760 mm Hg
• a smooth falling curve (hyperbola) — called an isotherm — correct
• a straight line passing through the origin
• a straight line parallel to the pressure axis