Calculate pressure or volume using Boyle's Law: P₁V₁ = P₂V₂. Free online thermodynamics calculator for ideal gas law calculations with pressure and volume relationships at constant temperature.
Calculate pressure or volume using P₁V₁ = P₂V₂
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Boyle's Law is one of the fundamental gas laws in thermodynamics, describing how the volume of a gas changes with pressure when temperature remains constant. Named after Irish scientist Robert Boyle, this law states that for a given amount of gas at constant temperature, pressure and volume have an inverse relationship. Whether you're studying physics, chemistry, engineering, or working with gases, understanding Boyle's Law is essential. Our Boyle's Law Calculator makes it easy to calculate pressure or volume using the formula: P₁V₁ = P₂V₂.
Boyle's Law is part of the ideal gas law family and is crucial for understanding gas behavior. When you compress a gas (increase pressure), its volume decreases. When you expand a gas (decrease pressure), its volume increases. This inverse relationship is fundamental to understanding how gases behave in closed systems, making it perfect for calculations involving gas compression, expansion, and storage at constant temperature.
Our Boyle's Law Calculator is designed for simplicity and accuracy. Follow these steps to get your calculation:
The calculator uses Boyle's Law formula: P₁V₁ = P₂V₂
You can rearrange this formula to solve for any variable:
Important: Temperature must remain constant for Boyle's Law to apply. The law describes the inverse relationship between pressure and volume when temperature and amount of gas are held constant.
Boyle's Law is expressed mathematically as:
P₁V₁ = P₂V₂
Where: P = pressure, V = volume, subscripts 1 and 2 refer to initial and final states
Boyle's Law states that the pressure and volume of a given amount of gas have an inverse relationship when temperature and amount of gas remain constant. This means:
Boyle's Law is fundamental to understanding gas behavior in countless applications, from scuba diving and breathing to industrial gas storage and compression. It helps predict how gases will behave when compressed or expanded, which is essential for designing systems involving gases, calculating gas storage requirements, and understanding respiratory mechanics.
Boyle's Law calculations are used in countless real-world scenarios across various fields:
Our calculator supports various units for pressure and volume:
Tip: The calculator automatically handles all unit conversions. You can input values in any supported unit and get results in the same unit or convert between units as needed.
A gas occupies 2.0 L at 1.0 atm. What will be its volume at 2.0 atm if temperature remains constant?
P₁ = 1.0 atm, V₁ = 2.0 L, P₂ = 2.0 atm
V₂ = P₁V₁ / P₂ = (1.0 atm × 2.0 L) / 2.0 atm = 1.0 L
The gas compresses from 2.0 L to 1.0 L as pressure doubles
A gas occupies 500 mL at 2.0 atm. If it expands to 1000 mL at constant temperature, what is the final pressure?
P₁ = 2.0 atm, V₁ = 500 mL, V₂ = 1000 mL
P₂ = P₁V₁ / V₂ = (2.0 atm × 500 mL) / 1000 mL = 1.0 atm
The pressure halves as volume doubles
A scuba diver's lungs contain 6.0 L of air at the surface (1.0 atm). What volume will the air occupy at a depth where pressure is 3.0 atm?
P₁ = 1.0 atm, V₁ = 6.0 L, P₂ = 3.0 atm
V₂ = P₁V₁ / P₂ = (1.0 atm × 6.0 L) / 3.0 atm = 2.0 L
The air in the lungs compresses to 2.0 L at depth, which is why divers must breathe compressed air
Gas is stored at 10.0 atm in a 50.0 L container. What volume would it occupy at atmospheric pressure (1.0 atm)?
P₁ = 10.0 atm, V₁ = 50.0 L, P₂ = 1.0 atm
V₂ = P₁V₁ / P₂ = (10.0 atm × 50.0 L) / 1.0 atm = 500 L
The gas expands to 500 L when released to atmospheric pressure
Boyle's Law is one of several fundamental gas laws. Understanding how they relate helps in comprehensive gas calculations:
Boyle's Law is a special case of the Ideal Gas Law when temperature and amount of gas are constant. It's essential for understanding how gases behave when only pressure and volume change.
Understanding Boyle's Law has practical applications in daily life:
Boyle's Law states that the pressure and volume of a gas have an inverse relationship when temperature and amount of gas remain constant. It applies to ideal gases when temperature doesn't change during the pressure/volume change. The formula is P₁V₁ = P₂V₂, meaning as pressure increases, volume decreases proportionally, and vice versa.
Boyle's Law describes the relationship between pressure and volume specifically when temperature is constant. If temperature changes, you need to use the Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) or the Ideal Gas Law (PV = nRT) to account for all three variables: pressure, volume, and temperature.
If temperature changes, Boyle's Law alone cannot accurately describe the gas behavior. You would need to use the Combined Gas Law or Ideal Gas Law to account for the temperature change. Boyle's Law is only valid when temperature remains constant.
Boyle's Law is most accurate for ideal gases (gases that follow the ideal gas law perfectly) at constant temperature. Real gases deviate from ideal behavior, especially at high pressures or very low temperatures, but the law provides good approximations for many practical applications at moderate conditions.
Common conversions: 1 atm = 101,325 Pa = 14.7 psi = 760 Torr = 1.01325 bar. Our calculator automatically handles these conversions, so you can input pressures in any supported unit and get results in your preferred unit.
Pressure and volume are inversely proportional in Boyle's Law. This means if you double the pressure, the volume halves (assuming constant temperature). If you halve the pressure, the volume doubles. The product P × V remains constant, so P₁V₁ = P₂V₂.
According to Boyle's Law, as pressure approaches infinity, volume approaches zero, and vice versa. However, these are theoretical limits. Real gases cannot be compressed to zero volume, and infinite pressure is physically impossible. Both pressure and volume must be positive for practical calculations.
Boyle's Law is a special case of the Ideal Gas Law (PV = nRT). When temperature (T) and amount of gas (n) are constant, the Ideal Gas Law simplifies to PV = constant, which is Boyle's Law. Both laws describe gas behavior, with the Ideal Gas Law being more general and accounting for temperature and amount of gas.
Common examples include: scuba diving (air volume changes with depth/pressure), breathing (lung volume changes with pressure), syringes (pulling plunger reduces pressure), balloons (volume changes when squeezed), gas storage cylinders, bicycle pumps, and medical ventilators. All of these involve pressure and volume changes at constant temperature.
Understanding Boyle's Law and the inverse relationship between pressure and volume is fundamental to thermodynamics and gas physics. Our Boyle's Law Calculator simplifies these calculations, making it easy to solve problems involving gas compression and expansion at constant temperature.
Whether you're studying gas laws, designing systems involving gases, or understanding everyday phenomena like breathing and scuba diving, this calculator provides accurate results with support for multiple units and automatic conversions. Ready to explore more thermodynamics concepts? Check out our other calculators like the Charles's Law Calculator for volume-temperature relationships, or use our Ideal Gas Law Calculator for comprehensive gas law calculations that combine pressure, volume, temperature, and amount of gas.
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