Combined Gas Law Calculator (P, V, T)

Combined Gas Law Guide

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 +

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 vo

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

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 =