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.
Key equation
P∝ T
Key equation
PT=constant
Key equation
P1T1=P2T2
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.
1
Working
P₁T₁ = P₂T₂
2
Step 2
P₂ = P₁T₂/T₁
3
Step 3
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.
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Exam preparation
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.
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.
Quick revision
Revision Zone
Review the key facts, formulas and checks before you move on.
Gay-Lussac’s Law
Sticky Notes · Quick Revision
1.
Key Point 1
The amount of gas and volume must remain constant.
2.
Key Point 2
Pressure is directly proportional to absolute temperature: P ∝ T.
3.
Key Point 3
The ratio PT remains constant.
4.
Key Point 4
For two states, P₁T₁ = P₂T₂.
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8 concept questions
Easy → Medium → Hard
Explanation after each answer
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?
