Charles's Law Calculator

Solve for volume or temperature at constant pressure using V₁/T₁ = V₂/T₂. Leave one field blank to solve for it.

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Result:

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What is Charles's Law?

Charles's Law, discovered by French scientist Jacques Charles in 1787, states that the volume of a gas is directly proportional to its absolute temperature when the pressure remains constant. In simple terms: heat a gas and it expands; cool it and it shrinks.

V₁ / T₁ = V₂ / T₂

Charles's Law Formula — All Rearranged Forms

V₂ = V₁T₂ / T₁
T₂ = V₂T₁ / V₁
V₁ = V₂T₁ / T₂
T₁ = V₁T₂ / V₂

How to Solve Charles's Law

  1. Identify which variable is unknown (V₁, T₁, V₂, or T₂).
  2. Convert all temperatures to Kelvin: K = °C + 273.15.
  3. Make sure volumes are in the same unit.
  4. Plug values into the appropriate rearranged formula.
  5. Calculate and convert the result back to desired units if needed.

Step-by-Step Examples

Example 1: Find V₂ (gas is heated)

Given: V₁ = 4.0 L, T₁ = 300 K, T₂ = 450 K. Find V₂.

1. Formula: V₂ = V₁T₂ / T₁
2. Substitute: V₂ = (4.0)(450) / 300
3. Calculate: V₂ = 1800 / 300 = 6.0 L

Example 2: Find T₂ (volume increases)

Given: V₁ = 2.5 L, T₁ = 250 K, V₂ = 5.0 L. Find T₂.

1. Formula: T₂ = V₂T₁ / V₁
2. Substitute: T₂ = (5.0)(250) / 2.5
3. Calculate: T₂ = 1250 / 2.5 = 500 K

Example 3: Find V₁ with °C to K conversion

Given: T₁ = 25°C, V₂ = 3.0 L, T₂ = 100°C. Find V₁.

1. Convert temperatures: T₁ = 25 + 273.15 = 298.15 K, T₂ = 100 + 273.15 = 373.15 K
2. Formula: V₁ = V₂T₁ / T₂
3. Substitute: V₁ = (3.0)(298.15) / 373.15
4. Calculate: V₁ = 894.45 / 373.15 = 2.397 L

Charles's Law vs Boyle's Law

Charles's Law relates volume and temperature at constant pressure. Boyle's Law relates pressure and volume at constant temperature. Charles's Law shows a direct relationship (V increases with T), while Boyle's Law shows an inverse relationship (V decreases as P increases).

Real-World Applications

  • Hot air balloons: Heating the air inside expands its volume, making the balloon rise.
  • Freezing a balloon: A balloon shrinks in cold temperatures because the gas volume decreases.
  • Tire pressure: Tires slightly expand in summer heat and contract in winter cold.

Frequently Asked Questions

  • Charles's Law states that the volume of a gas is directly proportional to its temperature (in Kelvin) when pressure is held constant. As temperature increases, volume increases proportionally, and vice versa. It was discovered by Jacques Charles in 1787.

  • The formula is V₁/T₁ = V₂/T₂, where V is volume and T is temperature in Kelvin. This can be rearranged to V₂ = V₁T₂/T₁ or T₂ = V₂T₁/V₁.

  • Rearrange the formula: V₂ = V₁ × T₂ / T₁. Make sure both temperatures are in Kelvin before calculating. If given in °C, add 273.15 to convert.

  • Gas laws require an absolute temperature scale. Kelvin starts at absolute zero (0 K = -273.15°C), where molecular motion theoretically stops. Using Celsius or Fahrenheit would give incorrect ratios because they have arbitrary zero points.

  • According to Charles's Law, volume and temperature have a direct linear relationship at constant pressure. If you double the temperature (in Kelvin), the volume doubles. If you halve the temperature, the volume halves.