Gas Laws4 min read

Charles's Law

V₁/T₁ = V₂/T₂

What is the Charles's Law?

Charles's Law states that at constant pressure, a gas's volume is directly proportional to its absolute temperature. Heat a gas and it expands; cool it and it contracts. Temperature must always be measured in Kelvin — using Celsius directly would break the direct proportionality, since Celsius has an arbitrary zero point rather than an absolute one.

Jacques Charles discovered this relationship in 1787 — the same year he also made the first hydrogen balloon flight.

What Each Variable Means

V₁, T₁
Initial volume and temperatureThe gas's state before the change. Temperature must be in Kelvin.
V₂, T₂
Final volume and temperatureThe gas's state after the change, also in Kelvin.

Units

QuantitySymbolUnit
VolumeVliters (L), or any consistent volume unit
TemperatureTkelvin (K) — required

When to Use It

  • Predicting how a gas's volume changes with temperature, at constant pressure
  • Predicting the temperature needed to reach a target volume
  • As one of the three laws that combine into the ideal gas law
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Step-by-Step Example

Problem: A gas has volume 3 L at 300 K. What is its volume at 600 K (same pressure)?

1
Identify the known values

Both temperatures are already in Kelvin.

V₁=3 L, T₁=300 K, T₂=600 K
2
Apply Charles's Law

Set up the equal-ratios relationship.

V₁/T₁ = V₂/T₂ → 3/300 = V₂/600
3
Solve for V₂

Cross-multiply and simplify.

V₂ = 3 × (600/300) = 3 × 2
Answer: V₂ = 6 L

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Common Mistakes

  • Mistake: Using Celsius instead of Kelvin.

    Fix: Always convert first: K = °C + 273.15. Using Celsius directly breaks the direct proportionality this law depends on.

  • Mistake: Applying Charles's Law when pressure is also changing.

    Fix: Charles's Law assumes constant pressure — if pressure changes too, use the combined gas law or the full ideal gas law instead.

Practice Questions

  1. A gas at 2 L and 250 K is heated to 500 K. Find the new volume.

  2. A gas at 5 L and 400 K is cooled until its volume is 2 L. Find the new temperature.

Frequently Asked Questions

Why must temperature be in Kelvin?

Because Celsius and Fahrenheit have arbitrary zero points, not an absolute one — the direct proportionality V ∝ T only holds true measured from absolute zero, which is what the Kelvin scale starts from.

What happens to volume as temperature approaches absolute zero?

In theory, volume would approach zero too — in practice, real gases condense into liquids (and then solids) long before reaching absolute zero, so Charles's Law stops applying.