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.
Key equation
PV=constant
Key equation
V∝1P
Key equation
P1V1=P2V2
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.
1
Working
P₁V₁ = P₂V₂
2
Step 2
V₂ = P₁V₁/P₂
3
Step 3
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.
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Exam preparation
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.
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.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Boyle’s Law
Sticky Notes · Quick Revision
1.
Key Point 1
The amount of gas and temperature must remain constant.
2.
Key Point 2
Pressure and volume vary inversely: V ∝ 1P.
3.
Key Point 3
The product of pressure and volume remains constant: PV = constant.
