Charles's Law

Charles's Law states that volume and temperature are directly proportional at constant pressure. Heat a gas and it expands; cool it and it contracts.

Charles's Law

V₁ / T₁ = V₂ / T₂

Initial volume / initial temperature = Final volume / final temperature

⚠️ CRITICAL: Temperature MUST Be in Kelvin!

ALWAYS convert °C or °F to Kelvin before using Charles's Law. Using Celsius will give completely wrong answers!

K = °C + 273.15

Example: 25°C = 298.15 K (often rounded to 298 K)

The Direct Relationship

V ∝ T (at constant P and n)

  • Double the temperature (K) → volume doubles
  • Halve the temperature (K) → volume halves
  • Heat a gas → it expands
  • Cool a gas → it contracts

Variable Definitions

V₁ = Initial Volume

Common Units: L, mL, cm³, m³

Volume before the temperature change

T₁ = Initial Temperature

Units: K (Kelvin) - MUST USE KELVIN!

Temperature before the change

❌ Do NOT use °C or °F directly!

V₂ = Final Volume

Units: Same as V₁

Volume after the temperature change

T₂ = Final Temperature

Units: K (Kelvin) - MUST USE KELVIN!

Temperature after the change

⚠️ Constant Conditions

Pressure (P) must remain constant
Amount of gas (n) must remain constant
No gas can enter or leave the system

Rearranged Forms

Find V₂:

V₂ = V₁T₂ / T₁

Most common use!

Find T₂:

T₂ = V₂T₁ / V₁

Find V₁:

V₁ = V₂T₁ / T₂

Find T₁:

T₁ = V₁T₂ / V₂

Step-by-Step Example

Problem: A balloon has volume 2.50 L at 20°C. If heated to 80°C at constant pressure, what is its new volume?

Given:

  • V₁ = 2.50 L
  • T₁ = 20°C = 293 K
  • T₂ = 80°C = 353 K
  • Find: V₂

Step 1: Convert to Kelvin

T₁ = 20 + 273 = 293 K
T₂ = 80 + 273 = 353 K

Step 2: Write Charles's Law

V₁/T₁ = V₂/T₂

Step 3: Rearrange to solve for V₂

V₂ = V₁T₂ / T₁

Step 4: Substitute values

V₂ = (2.50 L)(353 K) / (293 K)

Step 5: Calculate

V₂ = 882.5 L·K / 293 K = 3.01 L

Answer: V₂ = 3.01 L

✅ Makes sense: Temperature increased by 20%, volume increased by 20%

Real-World Applications

🎈 Hot Air Balloons

Heat the air inside → volume tries to expand → since balloon is open, air escapes → lower density → balloon rises!

❄️ Balloon in Winter

Take balloon from warm house to cold outdoors → temperature drops → volume decreases → balloon deflates

🏀 Basketball Pressure

Cold ball feels flat (V decreased), warm ball feels firm (V increased) - though pressure also changes

🔥 Fire Piston

Compress air rapidly → temperature skyrockets (adiabatic) → demonstrates inverse of Charles's Law

Common Mistakes

❌ Using Celsius instead of Kelvin

THE #1 MISTAKE! Temperature MUST be in Kelvin. Using °C gives completely wrong answers. Always convert: K = °C + 273.

❌ Pressure not constant

Charles's Law ONLY works when pressure is constant. If P changes, use the Combined Gas Law instead.

❌ Unit mismatches

V₁ and V₂ must be in the same units. T₁ and T₂ must BOTH be in Kelvin. Convert before calculating!

❌ Not checking your answer

If temperature increases, volume MUST increase. If temperature decreases, volume MUST decrease. Verify your answer makes physical sense!

Related Calculators

Frequently Asked Questions

What is Charles's Law?

V₁/T₁ = V₂/T₂ at constant pressure. Volume and temperature are directly proportional - when one goes up, the other goes up.

Why must temperature be in Kelvin?

Charles's Law requires an absolute temperature scale. 0 K is absolute zero - no molecular motion. Using °C would incorrectly suggest gas has zero volume at 0°C!

Why does this happen?

Higher temperature = faster molecular motion = molecules hit walls harder and more often. At constant pressure, container must expand to accommodate the increased kinetic energy.

What happens at absolute zero (0 K)?

Theoretically, volume would be zero. In reality, gases liquefy or solidify before reaching 0 K, so the law breaks down at very low temperatures.

How is this different from Boyle's Law?

Boyle's Law: P and V (T constant) - inverse relationship. Charles's Law: V and T (P constant) - direct relationship. Different variables!