How this instrument works
Trap a fixed quantity of gas, hold its temperature steady, and pressure multiplied by volume refuses to change. Halve that space and molecules strike each wall twice as often, so pressure doubles; cut it to a third and pressure triples. Plotted on a pressure-volume diagram, constant product traces a hyperbola — an isotherm — and every point along one such curve holds identical molecule count at identical temperature. Nothing in this relation cares which gas you use: nitrogen, helium, carbon dioxide all track one curve at ordinary conditions, because molecules sit mostly empty distance apart, rebounding like indifferent billiard balls.
Robert Boyle published his result in 1662, tucked into an appendix defending earlier air-pump work against critics. His apparatus was a J-shaped glass tube sealed at its short end: pour mercury down that tall open leg and trapped air in the short one shrinks, with column height giving pressure, tube length giving volume. Robert Hooke, then his assistant, did much of that glasswork plus measuring. Boyle credited Richard Towneley and Henry Power for suggesting the idea to him. French texts call it Mariotte's law, after Edme Mariotte, who published independently in 1679, spelling out a condition Boyle had left implicit — temperature must not change.
That condition is where things usually break in practice. Compress air quickly and it heats; a bicycle pump barrel warms in your hand precisely because each stroke runs adiabatic rather than isothermal, so pressure climbs faster than this instrument predicts, following P·V^1.4 instead. Push hard enough and even ideal-gas reasoning fails on its own terms: past roughly 10 bar, molecular volume and mutual attraction begin to register, and van der Waals or a tabulated compressibility factor becomes the honest tool. Vapours near condensation disobey outright — squeeze steam or butane past saturation and part of it turns liquid while pressure simply stops rising.
- Enter Initial pressure as an absolute value rather than a gauge reading. That field accepts Pa, kPa, bar, atm or psi; one standard atmosphere is 101325 Pa.
- Set Initial volume to whatever gas space you begin with, in ml, litres, m³ or ft³. Only a ratio matters here, so any unit serves provided Final volume uses that same one.
- Set Final volume to the space your gas ends up occupying — smaller to compress it, larger to let it expand.
- Read Final pressure, flipping its unit menu to bar or psi once pascals grow unwieldy.
- Keep temperature honest: let everything settle back to room temperature before comparing this figure against a real gauge.
Worked example — two litres of air squeezed into one
A 2-litre gas syringe of room air, plunger drawn right out, nozzle capped. Initial pressure reads 101325 Pa, Initial volume reads 0.002 m³, and that plunger goes slowly down to a 1-litre mark, making Final volume 0.001 m³. So P₂ = 101325 × 0.002 ⁄ 0.001 = 202650 Pa — exactly two standard atmospheres, equivalently 2.0265 bar or 29.4 psi absolute.
Halving available space doubled pressure, which is Boyle's whole law in one line. Doing quiet work in that paragraph is one word: slowly. Ram that plunger down inside a second instead, compression turns adiabatic: air inside climbs past 110 °C, your gauge briefly shows nearer 267000 Pa, and only once heat bleeds away into glass plus bench does a reading settle where this arithmetic says it belongs. Scuba instructors teach identical physics as a rule about ascending — breath held at 10 m tries to double on its way up, and lungs tear well before they manage it.
Questions
Must I use absolute pressure, or will a gauge reading do?
Absolute, always. Gauge pressure counts upward from atmosphere, so a tyre showing 2 bar actually sits near 3 bar absolute. Feed gauge figures into P₁V₁ = P₂V₂ and every term is wrong by roughly one atmosphere, yet nothing looks broken — arithmetic still runs, an answer still appears, merely plausible instead of correct. Near sea level, add 101325 Pa to any gauge reading before entering it. Of all the ways this law goes wrong in practice, that slip accounts for most of them.
Do my pressure and volume units have to be SI?
No. Each side carries one pressure plus one volume, so consistent units cancel and any pairing works — psi with cubic inches, atmospheres with litres. What breaks things is mixing: Initial volume in litres against Final volume in cubic metres gives nonsense a thousand times off. Per-field unit menus handle conversion for you, which is safer than converting by hand.
What happens if temperature does not stay constant?
Boyle's law stops applying and you need the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, with both temperatures in kelvin. Anything fast deserves suspicion: compressing air warms it, letting air expand cools it, which is how diesel ignition and refrigeration both earn a living. Wait for thermal equilibrium and Boyle's law becomes accurate again. Fix volume instead and vary temperature and you have Gay-Lussac's law; fix pressure and you have Charles's law.
How does this differ from the ideal gas law?
Boyle's law is one slice through PV = nRT. Hold amount n and temperature T fixed, and everything on that right-hand side becomes a constant, leaving PV constant — which is precisely P₁V₁ = P₂V₂. Working with two states rather than one has a real advantage: n, T, R all cancel between before versus after, so you never need to know any of them. Wanting absolute pressure from a stated mass of gas at a stated temperature? Reach for the ideal gas law instead.
At what pressures do real gases start to disagree?
Air at room temperature stays within about 1% of ideal up to roughly 10 bar, then drifts. By 200 bar, nitrogen's compressibility factor sits a few per cent above unity, meaning it resists squeezing rather more than Boyle promises. Gases near their condensation point misbehave far earlier and far worse. A 200-bar scuba cylinder genuinely lives outside ideal territory, which is why fill tables come from measured data instead of PV arithmetic.
Why does a scuba cylinder hold so much more air than its size suggests?
Because pressure and volume trade against each other. Apply P₁V₁ = P₂V₂ to a 12-litre cylinder charged at 200 bar absolute and it releases about 12 × 200 ⁄ 1 = 2400 litres measured at surface pressure. That second number is what divers plan around, and it explains why cylinders carry two ratings, water capacity plus working pressure. Real-gas behaviour shaves a few per cent off at 200 bar, so 2300 litres is nearer truth.