Automatically solve for missing final pressure, volume, or temperature. Visualize the change of gas state on a P‑V diagram.
The Combined Gas Law merges Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law into a single relation: (P₁ × V₁) / T₁ = (P₂ × V₂) / T₂. It describes how pressure, volume, and temperature of a fixed amount of ideal gas change from one state to another. This law assumes the number of gas molecules remains constant and that the gas behaves ideally (no intermolecular forces).
P₁V₁/T₁ = P₂V₂/T₂ = constant
If temperature is constant → Boyle's Law (P₁V₁ = P₂V₂).
If pressure is constant → Charles's Law (V₁/T₁ = V₂/T₂).
If volume is constant → Gay-Lussac's Law (P₁/T₁ = P₂/T₂).
The individual gas laws were discovered between the 17th and 19th centuries. Robert Boyle (1662) described the inverse pressure-volume relationship. Jacques Charles (1787) and Joseph Louis Gay-Lussac (1802) quantified the relationship between temperature and volume or pressure. The combined gas law was later formalized as part of the ideal gas law (PV = nRT). Scientists like Émile Clapeyron and August Krönig helped develop the kinetic molecular theory, providing a microscopic explanation.[1] Today, the combined gas law remains a cornerstone in chemistry and engineering for predicting gas behavior under changing conditions.
To solve for an unknown, rearrange the equation algebraically:
Enter all known values (including three out of four final-state variables) and leave the target field blank. Our calculator instantly applies the correct formula, verifies consistency, and displays the precise missing value.
A diver’s tank contains 12 liters of air at 200 bar pressure and 295 K. At depth, the ambient pressure increases to 150 bar and water temperature drops to 280 K. Using the combined gas law: V₂ = (200 × 12 × 280) / (150 × 295) ≈ 15.2 liters. This explains why divers consume air faster at depth — the effective volume of air in the lungs changes with pressure. Our calculator provides instant insight for dive planning.
During the compression stroke, a gas-air mixture is compressed from initial state (P₁=1.0 atm, V₁=500 cm³, T₁=300 K) to final state (P₂=8.0 atm, V₂=80 cm³). The final temperature T₂ = (8.0 × 80 × 300) / (1.0 × 500) = 384 K (111°C). This rapid temperature rise is essential for efficient ignition. Engineers use the combined gas law to model thermodynamic cycles.
“After teaching gas laws for 12 years, I find students struggle most with unit conversion. This calculator lets them experiment – they can see instantly how forgetting Kelvin breaks the result. The P‑V diagram helps visual learners grasp the inverse relationship. I recommend it for introductory chemistry and physics courses.” — Dr. A. Chen, High School Chemistry Teacher & Curriculum Designer.
Always use absolute temperature (Kelvin). Pressure and volume can be any consistent units (e.g., both in atm and liters, or kPa and m³) because the law relies on ratios. For accurate results, convert Celsius to Kelvin by adding 273.15. Do not use gauge pressure without converting to absolute pressure if required by the scenario. This tool handles decimal inputs with high precision.
| Assumption | Validity / Limitation |
|---|---|
| Ideal gas behavior | Good at moderate P (≈1 atm) and moderate T (>200 K). Deviates at high pressure or near condensation. |
| Closed system (constant moles) | The combined gas law requires n constant; our calculator does not account for leaks or chemical reactions. |
| Absolute temperature (Kelvin) | Mandatory – the tool enforces T > 0 and will warn if you use Celsius directly. |
| Homogeneous gas mixture | Works for any ideal gas; for real gases, use compressibility factors. |