Topic 8.3.17 min read
Boyle’s Law
Boyle’s law states that for a fixed amount of gas at constant temperature, volume is inversely proportional to pressure, so the product PV remains constant.
Choose Your Level
Beginner Level
If a gas is squeezed while its temperature stays unchanged, its pressure rises and its volume falls. If the pressure is reduced, the gas expands.
Scientists connected to this topic
Known for: Boyle’s law: at constant temperature, P ∝ 1/V for a fixed amount of gas.
Wikimedia Commons — portrait of Robert Boyle (public domain).
Recommended for Class 11
Boyle’s Law
Overview
Boyle’s law states that for a fixed amount of gas at constant temperature, volume is inversely proportional to pressure, so the product PV remains constant.
Learning Outcomes
- The amount of gas and temperature must remain constant.
- Pressure and volume vary inversely: V ∝ 1P.
- The product of pressure and volume remains constant: PV = constant.
- For two states of the same gas, P₁V₁ = P₂V₂.
- A P–V graph is a downward rectangular hyperbola.
Intermediate Level
Statement and Conditions
For an ideal-gas system containing a fixed quantity of gas at constant absolute temperature, the volume is inversely proportional to the applied pressure.
- Fixed gas amount: n = constant
- Constant temperature: T = constant
- Only P and V change
Equation
From PV = nRT, the right-hand side is constant because n, R and T are fixed.
Graph and Physical Meaning
The pressure–volume graph curves downward. Moving along one isotherm, a decrease in volume produces an increase in pressure so that every point has the same value of PV.
| Pressure change | Volume change | Product PV |
|---|---|---|
| doubles | halves | unchanged |
| triples | becomes one-third | unchanged |
| halves | doubles | unchanged |
Compression at Constant Temperature
A gas occupies 0.50 m³ at 100 kPa. Find its volume when pressure becomes 250 kPa at constant temperature.
P₁V₁ = P₂V₂
V₂ = P₁V₁/P₂
V₂ = (100 kPa)0.50 m³250 kPa
Final answer: V₂ = 0.20 m³
Common Mistakes
- Boyle’s law requires constant temperature.
- Pressure and volume are inversely, not directly, proportional.
- Use compatible pressure and volume units on both sides.
- Do not add pressures or volumes; use products.
Short-Question Preparation
Q. State Boyle’s law.
A. For a fixed amount of gas at constant temperature, volume is inversely proportional to pressure.
Q. Write Boyle’s law for two states.
A. P₁V₁ = P₂V₂.
Q. What is the shape of a P–V graph?
A. A downward rectangular hyperbola called an isotherm.
Q. Why is PV constant?
A. In PV = nRT, n, R and T are constant.
Sticky Notes
- The amount of gas and temperature must remain constant.
- Pressure and volume vary inversely: V ∝ 1P.
- The product of pressure and volume remains constant: PV = constant.
- For two states of the same gas, P₁V₁ = P₂V₂.
- A P–V graph is a downward rectangular hyperbola.
60-Second Revision
For fixed n and constant T: V ∝ 1P, PV = constant, and P₁V₁ = P₂V₂. The P–V curve is a downward hyperbola; increasing pressure reduces volume.
Summary
Boyle’s law states that for a fixed amount of gas at constant temperature, volume is inversely proportional to pressure, so the product PV remains constant.
Ask-the-Tutor Modes
- Explain the law simply.
- Show how the equation follows from PV = nRT.
- Solve a numerical step by step.
- Explain the graph.
- Test me with an MCQ.
Scientists connected to this topic
Known for: Boyle’s law: at constant temperature, P ∝ 1/V for a fixed amount of gas.
Wikimedia Commons — portrait of Robert Boyle (public domain).
Exam Focus
Exam Focus
Important points
- The amount of gas and temperature must remain constant.
- Pressure and volume vary inversely: V ∝ 1P.
- The product of pressure and volume remains constant: PV = constant.
- For two states of the same gas, P₁V₁ = P₂V₂.
- A P–V graph is a downward rectangular hyperbola.
Important formulas
- PV = constant
- V ∝ 1P
- P₁V₁ = P₂V₂
Common exam traps
- Boyle’s law requires constant temperature.
- Pressure and volume are inversely, not directly, proportional.
- Use compatible pressure and volume units on both sides.
- Do not add pressures or volumes; use products.
Long question structure
Statement → fixed conditions → proportional form → two-state equation → graph → example.
Common Mistakes
Common Mistakes
- Mistake
Boyle’s law requires constant temperature.
- Mistake
Pressure and volume are inversely, not directly, proportional.
- Mistake
Use compatible pressure and volume units on both sides.
- Mistake
Do not add pressures or volumes; use products.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
The amount of gas and temperature must remain constant.
Pressure and volume vary inversely: V ∝ 1P.
The product of pressure and volume remains constant: PV = constant.
For two states of the same gas, P₁V₁ = P₂V₂.
Boyle’s law states that for a fixed amount of gas at constant temperature, volume is inversely proportional to pressure, so the product PV remains constant.
- Definition
- Boyle’s law states that for a fixed amount of gas at constant temperature, volume is inversely proportional to pressure, so the product PV remains constant.
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Exam Practice
Important Question
Q1. State Boyle’s law.
Important Question
Q2. Write Boyle’s law for two states.
Important Question
Q3. What is the shape of a P–V graph?
Important Question
Q4. Why is PV constant?