Boyle's Law
Boyle's Law states that for a fixed amount of an ideal gas at constant temperature, the pressure of the gas is inversely proportional to its volume — when volume doubles, pressure halves, and vice versa. Mathematically, the product PV remains constant. This relationship arises because compressing a gas into a smaller volume increases the frequency of molecular collisions with the container walls, thereby raising pressure. It is applied in everyday contexts from tyre pumps and syringes to scuba diving depth calculations and the design of pneumatic systems.
Key Formula
P₁ × V₁ = P₂ × V₂ (constant n and T)
LaTeX: P_1 V_1 = P_2 V_2 \quad (\text{at constant } n, T)
| Symbol | Meaning | Unit |
|---|---|---|
| P₁ | Initial pressure of gas | Pa |
| V₁ | Initial volume of gas | m³ |
| P₂ | Final pressure of gas | Pa |
| V₂ | Final volume of gas | m³ |
Worked Example
Problem
A gas occupies 4.0 L at a pressure of 150 kPa. If the volume is compressed to 1.5 L at constant temperature, what is the new pressure?
Solution
Step 1: Write Boyle's Law: P₁V₁ = P₂V₂. Step 2: Solve for P₂: P₂ = P₁V₁ / V₂. Step 3: Substitute: P₂ = (150 × 4.0) / 1.5 = 600 / 1.5 = 400 kPa.
Answer
P₂ = 400 kPa
Boyle's Law Data — Gas at Constant Temperature
| Pressure (kPa) | Volume (L) | P × V (kPa·L) | Compression ratio |
|---|---|---|---|
| 50 | 8.0 | 400 | 1:1 (reference) |
| 100 | 4.0 | 400 | 2:1 |
| 200 | 2.0 | 400 | 4:1 |
| 400 | 1.0 | 400 | 8:1 |
| 800 | 0.5 | 400 | 16:1 |
Interactive Tools
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Related Terms
Ideal Gas Law
The Ideal Gas Law is an equation of state for a hypothetical ideal gas, combining the empirical gas laws of Boyle, Charles, and Gay-Lussac into a single relationship between the pressure, volume, amount, and absolute temperature of a gas. It assumes gas molecules have negligible volume and no intermolecular forces, making it an excellent approximation for real gases at low pressures and high temperatures. It is foundational to thermodynamics, chemistry, and engineering, used in everything from weather balloon calculations to industrial gas storage and the analysis of respiratory physiology.
Charles's Law
Charles's Law states that for a fixed amount of an ideal gas at constant pressure, the volume of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), volume doubles. This is an isobaric (constant pressure) process, and the ratio V/T remains constant. The law explains why a balloon expands when warmed, why hot air rises in atmospheric convection, and why gas-filled containers must be stored away from heat sources to prevent rupture.
Gay-Lussac's Law
Gay-Lussac's Law states that for a fixed amount of an ideal gas at constant volume, the pressure of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), pressure doubles. This isochoric (constant volume) relationship arises because higher temperatures cause gas molecules to collide with the container walls more frequently and with greater force. It explains why sealed aerosol cans or vehicle tyres can burst if overheated, and why pressure cookers build up pressure as the internal temperature rises above 100 °C.
Named after the Anglo-Irish chemist and physicist Robert Boyle (1627–1691), who published the law in 1662 in "New Experiments Physico-Mechanicall, Touching the Spring of the Air and Its Effects". Boyle used a J-shaped tube with trapped mercury to systematically measure pressure-volume relationships.