Charles's Law
Charles's law V₁/T₁ = V₂/T₂ shows how gas volume changes with temperature at constant pressure.
Step-by-step examples included.
The Formula
At constant pressure, the volume of a gas is directly proportional to its absolute temperature. When you heat a gas, it expands. When you cool it, it contracts.
Variables
| Symbol | Meaning |
|---|---|
| V₁ | Initial volume |
| T₁ | Initial temperature (must be in kelvin, K) |
| V₂ | Final volume |
| T₂ | Final temperature (must be in kelvin, K) |
Example 1
A balloon has a volume of 2.5 L at 20°C. What is its volume at 80°C (pressure constant)?
Convert to kelvin: T₁ = 20 + 273.15 = 293.15 K, T₂ = 80 + 273.15 = 353.15 K
Rearrange: V₂ = V₁ × T₂ / T₁ = 2.5 × 353.15 / 293.15
V₂ ≈ 3.01 L
Example 2
A gas occupies 500 mL at 300 K. To what temperature must it be heated to expand to 750 mL?
Rearrange: T₂ = T₁ × V₂ / V₁ = 300 × 750 / 500
T₂ = 450 K (which is 176.85°C)
When to Use It
Use Charles's law when pressure is constant and temperature or volume changes.
- Predicting how a gas volume changes with heating or cooling
- Hot air balloon calculations
- Industrial gas storage and transport
- Always use kelvin for temperature — never Celsius or Fahrenheit
Key Notes
- Temperature must be in Kelvin: Always convert Celsius to Kelvin (K = °C + 273.15) before using Charles's law. Using Celsius temperatures will give completely wrong answers because 0°C is not "zero temperature."
- Pressure must be constant: Charles's law only applies at constant pressure (isobaric process). If both pressure and temperature change, use the Combined Gas Law: P₁V₁/T₁ = P₂V₂/T₂.
- Direct proportionality: V ∝ T means doubling the absolute temperature doubles the volume. Halving the temperature halves the volume — a linear relationship.
- Ideal gas assumption: Like all individual gas laws, Charles's law is exact only for ideal gases. Real gases deviate most significantly at low temperatures near their liquefaction point.
- Real-world example: A hot air balloon rises because heating the air inside increases its volume, lowering its density below that of the surrounding cooler air — a direct application of Charles's law.