Boyle's Law Calculator
Find the new pressure of a gas when its volume changes at constant temperature.
Boyle's law: at constant temperature, gas pressure and volume are inversely related.
How the Math Works
Boyle's Law states that for a fixed amount of gas at a constant temperature, the pressure and volume are inversely proportional. This means when volume increases, pressure decreases, and vice versa. The mathematical relationship is expressed as P₁V₁ = P₂V₂, where P represents pressure and V represents volume at two different states. To find the unknown variable, you rearrange the equation: P₂ = (P₁ × V₁) / V₂ or V₂ = (P₁ × V₁) / P₂. The calculator uses these relationships to compute how much pressure changes when you know the initial conditions and either the new volume or new pressure.
Practical Applications
To use this calculator effectively, you need to measure or obtain the initial pressure (P₁) and volume (V₁) of your gas system before making changes. Then determine either the final volume (V₂) you want to achieve or the final pressure (P₂) you need. Simply input these three known values into the calculator, and it will instantly compute the fourth unknown value. This is essential in laboratory experiments, industrial gas processing, scuba diving equipment maintenance, and any situation where you need to predict how changing the volume of a confined gas will affect its pressure.
Day-to-Day Use
Understanding Boyle's Law helps explain many everyday phenomena involving gases. When you use a bicycle pump, the pressure increases as you decrease the volume of air inside. Your lungs operate on similar principles—expanding your chest cavity decreases pressure, allowing air to flow in, while contracting it increases pressure to push air out. Even the operation of aerosol spray cans relies on this principle: the gas expands from a high-pressure, low-volume state to a low-pressure, high-volume state when you press the nozzle. This knowledge can help you troubleshoot issues with tires, spray cans, and other pressurized containers.
Worked example
100 kPa at 2 L compressed to 1 L → 200 kPa.
FAQ
What must stay constant?
Temperature and the amount of gas.