Boyle's Law
Boyle's law P₁V₁ = P₂V₂ describes how gas pressure and volume are inversely related at constant temperature.
Includes worked examples.
The Formula
At constant temperature, the pressure and volume of a gas are inversely proportional. When you compress a gas (decrease volume), its pressure increases, and vice versa.
Variables
| Symbol | Meaning |
|---|---|
| P₁ | Initial pressure |
| V₁ | Initial volume |
| P₂ | Final pressure |
| V₂ | Final volume |
Example 1
A gas occupies 4 L at 2 atm. What volume will it occupy at 8 atm (temperature constant)?
Identify the values: P₁ = 2 atm, V₁ = 4 L, P₂ = 8 atm
Rearrange: V₂ = P₁V₁ / P₂ = (2 × 4) / 8
V₂ = 1 L
Example 2
A syringe contains 60 mL of air at 101.3 kPa. The plunger is pushed in until the volume is 20 mL. What is the new pressure?
Identify the values: P₁ = 101.3 kPa, V₁ = 60 mL, V₂ = 20 mL
Rearrange: P₂ = P₁V₁ / V₂ = (101.3 × 60) / 20
P₂ = 303.9 kPa
When to Use It
Use Boyle's law when temperature is held constant and pressure or volume changes.
- Compressing or expanding gases in sealed containers
- Scuba diving depth-pressure calculations
- Syringe and piston problems
- Pressure and volume must be in consistent units (both in the same unit)
Key Notes
- Temperature must stay constant: Boyle's law only holds at constant temperature (isothermal process). If temperature changes, use the Combined Gas Law instead: P₁V₁/T₁ = P₂V₂/T₂.
- Units must be consistent: P₁ and P₂ must be in the same unit (both atm, both kPa, or both mmHg). The same applies to V₁ and V₂.
- Ideal gas assumption: Boyle's law is exact only for ideal gases. Real gases deviate at high pressures or low temperatures where intermolecular forces become significant.
- Practical applications: Used in designing syringes, bicycle pumps, and scuba equipment. A diver's lungs expand as they ascend because water pressure decreases, following Boyle's law.
- Relationship to the Ideal Gas Law: Boyle's law is a special case of PV = nRT where n, R, and T are all held constant, reducing to PV = constant.