Topic 8.3.27 min read
Charles’s Law
Charles’s law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.
Choose Your Level
Beginner Level
When a gas is heated while pressure stays constant, it expands. When it cools, it contracts. Temperature must be measured in kelvin.
Recommended for Class 11
Charles’s Law
Overview
Charles’s law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.
Learning Outcomes
- The amount of gas and pressure must remain constant.
- Volume is directly proportional to absolute temperature: V ∝ T.
- The ratio VT remains constant.
- For two states, V₁T₁ = V₂T₂.
- Temperature must be expressed in kelvin.
- The extrapolated V–°C graph reaches zero volume near −273 °C, the idealized absolute-zero intercept.
Intermediate Level
Statement and Conditions
For a fixed quantity of gas at constant pressure, volume is directly proportional to its absolute temperature.
- Fixed gas amount: n = constant
- Constant pressure: P = constant
- Use absolute temperature T in kelvin
Equation
From PV = nRT, divide by P. Because n, R and P are constant, VT remains constant.
Graph and Absolute Zero
A V–T graph in kelvin is a straight line through the origin. If experimental values are extended backward on a Celsius scale, the line approaches zero volume at about −273 °C. Real gases condense before zero volume is reached, so the intercept is an extrapolation.
| Kelvin temperature change | Volume change at constant P |
|---|---|
| doubles | doubles |
| increases by 20% | increases by 20% |
| halves | halves |
Heating at Constant Pressure
A gas occupies 2.40 L at 300 K. Find its volume at 360 K if pressure remains constant.
V₁T₁ = V₂T₂
V₂ = V₁T₂/T₁
V₂ = (2.40 L)360 K300 K
Final answer: V₂ = 2.88 L
Common Mistakes
- Convert Celsius temperature to kelvin before using ratios.
- Charles’s law requires constant pressure.
- Volume and kelvin temperature are directly proportional.
- The −273 °C intercept is an extrapolation for an ideal gas.
Short-Question Preparation
Q. State Charles’s law.
A. For a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.
Q. Write Charles’s law for two states.
A. V₁T₁ = V₂T₂.
Q. Why must temperature be in kelvin?
A. Direct proportionality is measured from absolute zero, so Celsius ratios are invalid.
Q. What does the V–T graph show?
A. It is linear in kelvin and extrapolates to zero volume near −273 °C on the Celsius scale.
Sticky Notes
- The amount of gas and pressure must remain constant.
- Volume is directly proportional to absolute temperature: V ∝ T.
- The ratio VT remains constant.
- For two states, V₁T₁ = V₂T₂.
- Temperature must be expressed in kelvin.
- The extrapolated V–°C graph reaches zero volume near −273 °C, the idealized absolute-zero intercept.
60-Second Revision
For fixed n and constant P: V ∝ T, VT = constant, and V₁T₁ = V₂T₂. Use kelvin. The V–T graph is linear and points toward the absolute-zero intercept.
Summary
Charles’s law states that for a fixed amount of gas at constant pressure, volume 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 pressure must remain constant.
- Volume is directly proportional to absolute temperature: V ∝ T.
- The ratio VT remains constant.
- For two states, V₁T₁ = V₂T₂.
- Temperature must be expressed in kelvin.
- The extrapolated V–°C graph reaches zero volume near −273 °C, the idealized absolute-zero intercept.
Important formulas
- V ∝ T
- VT = constant
- V₁T₁ = V₂T₂
- T(K) = θ(°C) + 273
Common exam traps
- Convert Celsius temperature to kelvin before using ratios.
- Charles’s law requires constant pressure.
- Volume and kelvin temperature are directly proportional.
- The −273 °C intercept is an extrapolation for an ideal gas.
Long question structure
Statement → fixed conditions → proportional form → two-state equation → graph → example.
Common Mistakes
Common Mistakes
- Mistake
Convert Celsius temperature to kelvin before using ratios.
- Mistake
Charles’s law requires constant pressure.
- Mistake
Volume and kelvin temperature are directly proportional.
- Mistake
The −273 °C intercept is an extrapolation for an ideal gas.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
The amount of gas and pressure must remain constant.
Volume is directly proportional to absolute temperature: V ∝ T.
The ratio VT remains constant.
For two states, V₁T₁ = V₂T₂.
Charles’s law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.
- Definition
- Charles’s law states that for a fixed amount of gas at constant pressure, volume is directly proportional to absolute temperature.
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Exam Practice
Important Question
Q1. State Charles’s law.
Important Question
Q2. Write Charles’s law for two states.
Important Question
Q3. Why must temperature be in kelvin?
Important Question
Q4. What does the V–T graph show?