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General Chemistry I · Gases

Charles's Law

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On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Study tools
  7. Sources & references

In 30 seconds

Charles's law states that the volume of a fixed amount of gas at constant pressure is directly proportional to its absolute (kelvin) temperature: V₁/T₁ = V₂/T₂. Heating a gas makes it expand; cooling makes it contract. Extrapolating this trend to zero volume defines absolute zero (−273.15 °C).

Why this matters

Charles's law explains hot-air balloons (heated air expands and becomes less dense, so the balloon rises), why car tires and balloons change size with the weather, and why a sealed balloon shrinks in a freezer. It also underlies the concept of absolute zero used across all of thermodynamics.

The college version

Key Ideas

  • Direct relationship: as T (in K) increases, V increases (at constant n and P).
  • Kelvin required: gas-law temperatures are always absolute (K = °C + 273.15).
  • V/T is constant: V₁/T₁ = V₂/T₂.
  • Absolute zero: the temperature at which an ideal gas would have zero volume, −273.15 °C = 0 K.
  • Named for Jacques Charles (1787).

Equations and Variables

  • V₁/T₁ = V₂/T₂ — V = volume, T = absolute temperature (K).
  • Equivalent form: V₂ = V₁ × (T₂/T₁).
  • Temperature conversion: T(K) = T(°C) + 273.15.
  • Graphically: V vs T (K) is a straight line through the origin.

How It Works

  1. Fix the amount of gas (n) and the pressure (P).
  2. Raise the temperature. Particles move faster on average.
  3. To keep pressure constant, the faster particles must hit the walls with the same force — which happens only if they spread out into a larger volume (a free-moving piston rises).
  4. Volume therefore increases in proportion to the kelvin temperature.
  5. Lowering temperature shrinks the volume; extrapolating the straight line backward reaches V = 0 at T = 0 K (−273.15 °C).

Worked Example

A balloon contains 2.00 L of gas at 25.0 °C. What is its volume at 75.0 °C if the pressure is constant? Convert to kelvin: T₁ = 25.0 + 273.15 = 298.15 K; T₂ = 75.0 + 273.15 = 348.15 K. V₂ = V₁ × (T₂/T₁) = 2.00 L × (348.15 K / 298.15 K) = 2.34 L. The balloon expands from 2.00 L to 2.34 L.

Common Confusions

  • "Doubling the Celsius temperature doubles the volume" — false; the relationship is proportional to kelvin temperature, not Celsius. Going from 0 °C to 100 °C is only 273 K → 373 K.
  • "Charles's law lets me use °C if I'm careful" — no; using °C gives wrong (even negative-volume) results. Always use kelvin.
  • "A gas reaches zero volume at 0 °C" — no; zero volume is at −273.15 °C (0 K), and real gases liquefy first.
  • "Pressure changes too" — in a Charles's-law problem, pressure must be held constant.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Picture a balloon in a freezer: the air inside slows down, the particles nudge the walls more gently, and the balloon shrinks. Heat the same balloon and the air speeds up, shoving the walls outward so the balloon inflates. Hot gas wants more room, cold gas settles for less — and it's all proportional, so twice the temperature (in kelvin) means twice the volume. The analogy's limit: real gases eventually condense to liquid at very low temperature instead of shrinking all the way to zero — that's why absolute zero is an extrapolation, not something we actually reach.

Key takeaways

  • V₁/T₁ = V₂/T₂ (constant n and P).
  • Volume is directly proportional to kelvin temperature.
  • Always convert °C to K (add 273.15) before using any gas law.
  • Absolute zero = 0 K = −273.15 °C.
  • V vs T (K) is a straight line through the origin.
  • Charles's law: V₁/T₁ = V₂/T₂ (constant n and P).
  • Volume ∝ kelvin temperature.
  • Convert °C → K by adding 273.15.
  • Hotter gas expands; cooler gas contracts.
  • Extrapolating to V = 0 gives absolute zero.

Keep learning

Ready to build on this? Continue to the next lesson.

Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • State Charles's law in words and as an equation.
  • Explain why temperature must be in kelvin.
  • Solve for an unknown volume or temperature.
  • Connect Charles's law to the idea of absolute zero.

Sources & references

  1. OpenStax, "9.2 Relating Pressure, Volume, Amount, and Temperature," Chemistry 2e.
  2. Petrucci et al., "6.2 The Simple Gas Laws," Chemistry LibreTexts.
  3. NIST CODATA, "molar gas constant."

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

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