Combined Gas Law Calculator – Solve P₁V₁/T₁ = P₂V₂/T₂

The Combined Gas Law is a fundamental principle in physical chemistry and thermodynamics that unifies three classical gas relationships into a single equation. It states that the ratio of the product of pressure and volume to temperature remains constant for a fixed amount of an ideal gas: P₁V₁/T₁ = P₂V₂/T₂, where the subscripts 1 and 2 denote the initial and final states of the gas sample. This equation is derived by combining three historically independent gas laws. Boyle's Law, established by Robert Boyle in 1662, shows that at constant temperature, the pressure and volume of a gas are inversely proportional: P₁V₁ = P₂V₂. Charles's Law, developed by Jacques Charles around 1787, demonstrates that at constant pressure, gas volume is directly proportional to absolute temperature: V₁/T₁ = V₂/T₂. Gay-Lussac's Law, formulated by Joseph Louis Gay-Lussac in 1809, establishes that at constant volume, pressure is directly proportional to absolute temperature: P₁/T₁ = P₂/T₂. The Combined Gas Law encompasses all three as special cases. One critical requirement is that temperature must always be expressed in Kelvin. Using Celsius or Fahrenheit gives incorrect results because these scales have arbitrary zero points. To convert Celsius to Kelvin, add 273.15. The law also assumes the amount of gas (number of moles) remains constant throughout the process and that the gas behaves ideally — meaning gas molecules are treated as point particles with negligible volume and no intermolecular forces. The Combined Gas Law has widespread practical applications across science and engineering. In automotive engineering, it describes the compression of air-fuel mixtures inside cylinders during the compression stroke. In respiratory physiology, it explains how lung volumes change with pressure and temperature during breathing. Scuba divers rely on it to predict how air supply volumes change with depth and water temperature, since pressure increases approximately 1 atm for every 10 metres of water depth. Meteorologists apply the combined gas law to understand how atmospheric temperature and pressure changes affect weather systems. Engineers designing pressurised vessels, storage tanks, and gas pipelines use it to determine safe operating limits. The law is also fundamental to understanding the behaviour of gas in piston-cylinder systems in heat engines and refrigeration cycles. For very accurate results with real gases at high pressures or low temperatures, the van der Waals equation or more sophisticated equations of state such as Peng-Robinson may be more appropriate, as real gases deviate from ideal behaviour under extreme conditions. The Combined Gas Law remains an excellent first approximation for most practical engineering and educational calculations involving gases.