What Is the Combined Gas Law?

The combined gas law brings together Boyle's, Charles's, and Gay-Lussac's laws into a single relationship for a fixed amount of gas: P₁V₁/T₁ = P₂V₂/T₂. It describes how a gas responds when its pressure, volume, and temperature change at the same time — the usual situation in real life, where no single variable stays put.

How This Calculator Works

Enter the initial pressure, volume, and temperature plus the final pressure and temperature, and the calculator solves for the final volume: V₂ = V₁ × (P₁/P₂) × (T₂/T₁). Both temperatures are converted to Kelvin first, since the law only holds in absolute temperature. The results panel shows the pressure factor and temperature factor separately, so you can see which change dominated.

With the defaults — 2.0 L of gas at 1.0 atm and 25°C, heated to 50°C while pressure rises to 1.5 atm — the final volume is 1.445 L. The pressure increase squeezes the gas (factor 0.667), while the temperature rise expands it (factor 1.084); together they produce the net 27.8% contraction.

The Three Component Laws

Boyle's law (constant temperature): P₁V₁ = P₂V₂ — volume falls as pressure rises. Charles's law (constant pressure): V₁/T₁ = V₂/T₂ — volume rises with absolute temperature. Gay-Lussac's law (constant volume): P₁/T₁ = P₂/T₂ — pressure rises with temperature. The combined law is their product, valid whenever the amount of gas stays fixed.

Real-World Applications

Weather balloons expand as they rise into lower-pressure, colder air. Scuba divers account for the volume changes their equipment experiences with depth and temperature. Tire pressure climbs on hot days and after long drives. In each case, the combined gas law predicts the new state — and knowing the numbers in advance makes the behavior expected rather than surprising.