What Is Charles' Law?
Charles' law (also known as the law of volumes) describes the relationship between the volume of an ideal gas and its temperature at constant pressure. It states that the volume of a gas is directly proportional to its absolute temperature — when the pressure and the amount of gas remain unchanged.
Mathematically: V₁ / T₁ = V₂ / T₂, where T must be expressed in Kelvin (absolute temperature scale).
Charles' Law Formula
The Charles' law equation relates the four key variables of an isobaric (constant-pressure) process:
- V₁ — initial volume of the gas
- T₁ — initial absolute temperature (in Kelvin)
- V₂ — final volume of the gas
- T₂ — final absolute temperature (in Kelvin)
The formula can be rearranged to solve for any unknown:
- Find V₂:
V₂ = V₁ / T₁ × T₂ - Find V₁:
V₁ = V₂ / T₂ × T₁ - Find T₂:
T₂ = T₁ / V₁ × V₂ - Find T₁:
T₁ = T₂ / V₂ × V₁
Charles' Law Examples
Example 1: Heating a Gas
A gas occupies 2.0 L at 300 K. What volume does it occupy when heated to 450 K at constant pressure?
V₂ = V₁ / T₁ × T₂ = 2.0 / 300 × 450 = 3.0 L
Example 2: Cooling a Gas
A balloon has a volume of 5.0 ft³ at 77°F (298.15 K). It is placed outdoors where the temperature is 32°F (273.15 K). What is its new volume?
V₂ = 5.0 × 273.15 / 298.15 ≈ 4.58 ft³
Example 3: Finding the Temperature
A gas at 250 K has a volume of 1.5 L. At what temperature will it occupy 3.0 L?
T₂ = T₁ × V₂ / V₁ = 250 × 3.0 / 1.5 = 500 K
Real-Life Applications of Charles' Law
- Hot air balloons — heating air inside the balloon increases its volume, reducing density and providing lift.
- Bread rising — carbon dioxide gas expands when heated in the oven, making bread rise.
- Car tires in summer — tire pressure increases in hot weather because the gas inside expands.
- Thermometers — liquid-in-glass thermometers work on the principle that liquids expand with temperature.
- Engines — internal combustion engines rely on gas expansion when heated to do work.
Units Supported by This Calculator
This Charles' law calculator supports both metric and US customary units:
| Quantity | Metric | US / Imperial |
|---|---|---|
| Volume | L, mL, m³, cm³ | ft³, in³, gal |
| Temperature | K (Kelvin), °C (Celsius) | °F (Fahrenheit), °R (Rankine) |
Important: Temperatures entered in °C, °F, or °R are automatically converted to Kelvin for the calculation. The temperature must be above absolute zero.
Other Thermodynamic Gas Laws
- Boyle's Law — at constant temperature, pressure and volume are inversely proportional: p₁V₁ = p₂V₂
- Gay-Lussac's Law — at constant volume, pressure is proportional to absolute temperature: p₁/T₁ = p₂/T₂
- Combined Gas Law — combines Boyle's, Charles', and Gay-Lussac's laws: p₁V₁/T₁ = p₂V₂/T₂
- Ideal Gas Law — the most general form: pV = nRT
Frequently Asked Questions
Why must temperature be in Kelvin?
Charles' law requires absolute temperature because it is based on the proportional relationship between volume and kinetic energy. Celsius and Fahrenheit scales have arbitrary zero points, which would produce incorrect results. The Kelvin scale starts at absolute zero (−273.15°C), where molecular motion theoretically stops.
What is an isobaric process?
An isobaric process is one in which the pressure remains constant. Charles' law applies specifically to isobaric processes — when a gas is heated or cooled at constant pressure, its volume changes proportionally with temperature.
Does Charles' law apply to all gases?
Strictly speaking, Charles' law applies to ideal gases. Real gases closely follow Charles' law at low pressures and high temperatures, but deviate at high pressures or temperatures near the gas's condensation point.
Who discovered Charles' law?
The law is named after French scientist Jacques Alexandre César Charles (1746–1823), who formulated it around 1787 based on experiments with five different gases. It was later published by Joseph Louis Gay-Lussac in 1802, who gave credit to Charles.