Topic 8.3.37 min read
Gay-Lussac’s Law
Gay-Lussac’s law, also called Amontons’s law, states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature.
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Beginner Level
Heating a gas in a rigid closed container makes its molecules collide with the walls more strongly and frequently, so pressure rises while volume stays fixed.
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Gay-Lussac’s Law
Overview
Gay-Lussac’s law, also called Amontons’s law, states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature.
Learning Outcomes
- The amount of gas and volume must remain constant.
- Pressure is directly proportional to absolute temperature: P ∝ T.
- The ratio PT remains constant.
- For two states, P₁T₁ = P₂T₂.
- Temperature must be expressed in kelvin.
- The P–T graph in kelvin is a straight line through the origin.
Intermediate Level
Statement and Conditions
For a fixed quantity of gas at constant volume, the applied pressure is directly proportional to the absolute temperature. The relation is also known as Amontons’s law.
- Fixed gas amount: n = constant
- Constant volume: V = constant
- Use absolute temperature T in kelvin
Equation
From PV = nRT, divide by V. Because n, R and V are constant, PT remains constant.
Graph and Molecular Explanation
The P–T graph in kelvin is a straight line through the origin. Heating raises the molecules’ average kinetic energy. In a rigid container they strike the same wall area more forcefully and frequently, which increases pressure.
| Kelvin temperature change | Pressure change at constant V |
|---|---|
| doubles | doubles |
| increases by 50% | increases by 50% |
| halves | halves |
Heating in a Rigid Container
A sealed rigid container holds gas at 100 kPa and 300 K. Find its pressure at 450 K.
P₁T₁ = P₂T₂
P₂ = P₁T₂/T₁
P₂ = (100 kPa)450 K300 K
Final answer: P₂ = 150 kPa
Common Mistakes
- Convert Celsius temperature to kelvin.
- Gay-Lussac’s law requires constant volume.
- Pressure and kelvin temperature are directly proportional.
- Use absolute pressure, not gauge pressure, in gas-law ratios.
Short-Question Preparation
Q. State Gay-Lussac’s law.
A. For a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature.
Q. What is another name for this law?
A. Amontons’s law.
Q. Write the law for two states.
A. P₁T₁ = P₂T₂.
Q. Why does pressure rise when a rigid gas container is heated?
A. Faster molecules transfer more momentum through stronger and more frequent wall collisions.
Sticky Notes
- The amount of gas and volume must remain constant.
- Pressure is directly proportional to absolute temperature: P ∝ T.
- The ratio PT remains constant.
- For two states, P₁T₁ = P₂T₂.
- Temperature must be expressed in kelvin.
- The P–T graph in kelvin is a straight line through the origin.
60-Second Revision
For fixed n and constant V: P ∝ T, PT = constant, and P₁T₁ = P₂T₂. Use kelvin and absolute pressure. The P–T graph is a straight line through the origin.
Summary
Gay-Lussac’s law, also called Amontons’s law, states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature.
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.
Exam Focus
Exam Focus
Important points
- The amount of gas and volume must remain constant.
- Pressure is directly proportional to absolute temperature: P ∝ T.
- The ratio PT remains constant.
- For two states, P₁T₁ = P₂T₂.
- Temperature must be expressed in kelvin.
- The P–T graph in kelvin is a straight line through the origin.
Important formulas
- P ∝ T
- PT = constant
- P₁T₁ = P₂T₂
- T(K) = θ(°C) + 273
Common exam traps
- Convert Celsius temperature to kelvin.
- Gay-Lussac’s law requires constant volume.
- Pressure and kelvin temperature are directly proportional.
- Use absolute pressure, not gauge pressure, in gas-law ratios.
Long question structure
Statement → fixed conditions → proportional form → two-state equation → graph → example.
Common Mistakes
Common Mistakes
- Mistake
Convert Celsius temperature to kelvin.
- Mistake
Gay-Lussac’s law requires constant volume.
- Mistake
Pressure and kelvin temperature are directly proportional.
- Mistake
Use absolute pressure, not gauge pressure, in gas-law ratios.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
The amount of gas and volume must remain constant.
Pressure is directly proportional to absolute temperature: P ∝ T.
The ratio PT remains constant.
For two states, P₁T₁ = P₂T₂.
Gay-Lussac’s law, also called Amontons’s law, states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature.
- Definition
- Gay-Lussac’s law, also called Amontons’s law, states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature.
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Exam Practice
Important Question
Q1. State Gay-Lussac’s law.
Important Question
Q2. What is another name for this law?
Important Question
Q3. Write the law for two states.
Important Question
Q4. Why does pressure rise when a rigid gas container is heated?