How this instrument works
Jacques Charles worked this out around 1787 and never bothered publishing it; he was busy flying hydrogen balloons over Paris. Joseph Louis Gay-Lussac ran cleaner experiments and printed them in 1802, generously naming Charles in his paper. What both men found: with pressure held steady and no gas escaping, volume tracks absolute temperature in strict proportion. Warm one fixed portion of air from 300 K to 600 K beneath a freely sliding piston and it occupies exactly twice as much space.
That proportionality is why kelvin exists. Plot volume against Celsius temperature for any dilute gas and your data falls on straight lines; extend each line downward and every gas points at one shared intercept near −273.15 °C, where extrapolated volume would vanish. Gay-Lussac's coefficient of expansion placed that intercept near −266 °C; Regnault's patient remeasurement through the 1840s pushed it toward −273. William Thomson argued in 1848 that such an intercept was no quirk of air but a floor under temperature itself.
Two assumptions carry all of it. Pressure must stay fixed — sealed rigid vessels obey quite different arithmetic, with pressure rather than volume climbing — and molecules must be far enough apart to ignore one another. Real gases drift off those straight lines as they near condensation: steam at its boiling point, carbon dioxide above two or three atmospheres, ammonia at almost any pressure worth using. Near 1 atm and well above its boiling point, though, dilute gases track this formula to within small fractions of one percent.
- Enter Initial volume in whatever unit suits your vessel — millilitres, litres, cubic metres or cubic feet.
- Convert both temperatures to kelvin first (K = °C + 273.15), then put your starting figure into Initial absolute temperature (K).
- Type your target into Final absolute temperature (K). Anything at or below zero is rejected, since a ratio taken against absolute zero means nothing.
- Read Final volume, and switch its unit menu if litres suit you better than cubic metres.
Worked example — a litre of air, ice point to 273 °C
One litre of dry air sits in a syringe at 273.15 K, with a freely sliding piston keeping pressure at one atmosphere. Slide that syringe into an oven at 546.30 K — 273.15 °C, hot enough to scorch paper, well short of glowing. Substituting: V₂ = 0.001 × 546.30 ⁄ 273.15 = 0.001 × 2 = 0.002 m³. Your litre has become two litres, and that piston has travelled far enough to double its barrel length.
Doubling absolute temperature doubles volume — Charles's whole discovery in one measurement, which is why 546.30 K makes such a clean test case. Run those same numbers in Celsius and you get nonsense: 0 °C rising to 273.15 °C reads as an infinite ratio. That single confusion produces more wrong answers here than every other slip combined.
Questions
Why must temperature be in kelvin?
Because this is a ratio, and ratios need scales whose zero truly means zero. Celsius and Fahrenheit put their zeros at arbitrary places — melting ice, freezing brine — so 20 °C is not physically twice 10 °C. Convert first: K = °C + 273.15, or K = (°F + 459.67) × 5 ⁄ 9. Warming a balloon from 10 °C to 20 °C expands it by 3.5%, not 100%.
What if pressure is not constant?
Then this sheet no longer applies; move up to P₁V₁ ⁄ T₁ = P₂V₂ ⁄ T₂, or to PV = nRT outright. Charles's relation is simply one constant-pressure slice through that larger surface. Heating gas inside rigid steel cylinders moves pressure instead of volume, which is Gay-Lussac's law, P₁ ⁄ T₁ = P₂ ⁄ T₂ — same shape, different quantity in motion.
How much does air expand per degree?
Roughly 1/273 of its ice-point volume for each kelvin, near 0.37% per degree at room temperature. Hot-air balloons live on exactly this: heating one 2,800 m³ envelope from 20 °C to 100 °C expands its air by 27%, and because that envelope's mouth stays open, roughly one fifth spills out. Whatever remains is 21% less dense than surrounding air, and such density deficit is your lift.
When does a real gas stop obeying it?
Near condensation, and at high density. Approach any boiling point and intermolecular attraction draws molecules closer than ideal lines predict, so measured volume falls short of what this sheet returns; squeeze hard enough instead and finite molecular size pushes volume back above it. Steam at 100 °C and one atmosphere already sits about 1.5% low. Dry air, nitrogen, helium and argon at ordinary pressures stay inside about 0.1%.
Does how much gas I have matter?
Only that it stays put. Volume scales with molecule count, so leaking seals, chemical reactions, or gas dissolving into liquid all wreck this accounting. Charles's law compares one sample against itself at two temperatures — same molecules, same pressure, nothing added or lost between readings.
Was Charles actually first?
Not quite. Guillaume Amontons had shown around 1699 that trapped air pushes harder as it warms, and John Dalton published expansion measurements in 1801, a year ahead of Gay-Lussac. Charles's unpublished 1787 notes gave him priority; Gay-Lussac chose to credit him anyway, which is how a Frenchman better known for ballooning ended up on every chemistry syllabus.