Combined Gas Law Calculator (P, V, T)

Combined Gas Law Guide

What do I need to know about The Combined Gas Law?

The combined gas law unifies Boyle's law (P × V = constant), Charles' law (V / T = constant), and Gay-Lussac's law (P / T = constant) into one equation: P₁V₁ / T₁ = P₂V₂ / T₂. Where: P = pressure (any unit, but same on both sides). V = volume (any unit, but same on both sides). T = absolute temperature — MUST be in Kelvin. The amount of gas (moles) stays the same; the law only describes pressure, volume, and temperature changes of a fixed sample. Critical: temperature MUST be in Kelvin (K = °C + 273.15) — using Celsius directly in the gas law equations gives wrong, sometimes negative or nonsensical, results, since the relationship between pressure, volume and temperature only holds on an absolute temperature scale where zero represents the theoretical point of no molecular motion.

What's the key thing to understand about Special Cases?

Boyle's law (constant temperature): T₁ = T₂, so P₁V₁ = P₂V₂. Pressure rises as volume decreases. Examples: squeezing a balloon (more pressure, less volume). Compressing air in a syringe with finger over nozzle. SCUBA tank pressure as breath compressed deeper. Charles' law (constant pressure): P₁ = P₂, so V₁/T₁ = V₂/T₂. Volume rises with temperature. Examples: hot air balloon (warm air rises). Tyres expanding on hot day. Bread rising in oven (CO₂ from yeast expands). Gay-Lussac's law (constant volume): V₁ = V₂, so P₁/T₁ = P₂/T₂. Pressure rises with temperature. Examples: a sealed can heated on a fire (risk of explosion as internal pressure builds), a car tyre's pressure reading being higher after a motorway drive once the tyres have warmed up.

What do I need to know about The Ideal Gas Law?

Full ideal gas law: PV = nRT. Where: n = moles of gas. R = universal gas constant = 8.314 J/(mol·K). For SI units (Pa, m³, K, mol). R = 0.0821 L·atm/(mol·K) for litres and atmospheres. Used when: you need to find moles, mass, or density of gas. Or you want to find a single state (not a change). PV = nRT shows: at standard temperature and pressure (STP: 273.15K, 1atm): 1 mole of any gas occupies 22.4 L. Density of gas: ρ = PM / RT (where M is molar mass). Limits of ideal gas behaviour: works well at typical laboratory conditions (moderate pressure, temperature well above the gas's boiling point) but breaks down at very high pressure or very low temperature, where intermolecular forces and the finite volume of gas molecules themselves become significant — this is where a real-gas correction like the van der Waals equation is needed instead.

What should I know about Worked Examples?

Tyre pressure on cold day: tyre at 32 PSI when 20°C inflated (warm). Same tyre at -10°C: P₂ = P₁ × T₂/T₁ = 32 × 263/293 = 28.7 PSI. Lost ~3 PSI just from temperature drop. Why winter requires re-checking tyre pressure. Hot air balloon: 1m³ of air at 20°C (293K). Heat to 100°C (373K). New volume at same pressure: V₂ = V₁ × T₂/T₁ = 1 × 373/293 = 1.27 m³. 27% expansion creates lift. Compressed gas safety: gas at 200 bar in cylinder (typical SCUBA). Leak to atmosphere (1 bar). Volume increase: V₂ = V₁ × P₁/P₂ = V₁ × 200 (a 200-fold expansion). This is why holding your breath while ascending during a SCUBA dive is dangerous — the air in the lungs expands as ambient pressure drops, and can over-expand the lungs if the diver doesn't exhale continuously on the way up.