Charles's Law
Charles's Law states that for a fixed amount of an ideal gas at constant pressure, the volume of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), volume doubles. This is an isobaric (constant pressure) process, and the ratio V/T remains constant. The law explains why a balloon expands when warmed, why hot air rises in atmospheric convection, and why gas-filled containers must be stored away from heat sources to prevent rupture.
Key Formula
V₁/T₁ = V₂/T₂ (constant n and P)
LaTeX: \frac{V_1}{T_1} = \frac{V_2}{T_2} \quad (\text{at constant } n, P)
| Symbol | Meaning | Unit |
|---|---|---|
| V₁ | Initial volume of gas | m³ or L |
| T₁ | Initial absolute temperature | K |
| V₂ | Final volume of gas | m³ or L |
| T₂ | Final absolute temperature | K |
Worked Example
Problem
A gas occupies 3.0 L at 27 °C and constant pressure. What volume will it occupy if heated to 127 °C at the same pressure?
Solution
Step 1: Convert temperatures to Kelvin: T₁ = 27 + 273.15 = 300.15 K ≈ 300 K; T₂ = 127 + 273.15 = 400.15 K ≈ 400 K. Step 2: Apply Charles's Law: V₂ = V₁ × T₂ / T₁. V₂ = 3.0 × 400 / 300 = 3.0 × 1.333 = 4.0 L.
Answer
V₂ = 4.0 L
Charles's Law Data — Gas at Constant Pressure
| Temperature (°C) | Temperature (K) | Volume (L) | V/T (L K⁻¹) |
|---|---|---|---|
| 0 | 273 | 2.73 | 0.010 |
| 27 | 300 | 3.00 | 0.010 |
| 127 | 400 | 4.00 | 0.010 |
| 227 | 500 | 5.00 | 0.010 |
| 327 | 600 | 6.00 | 0.010 |
Interactive Tools
PhET Gas Properties
Heat gas at constant pressure and observe volume changes consistent with Charles's Law.
Open ToolDesmos Charles's Law Graph
Plot V vs T (Kelvin) to visualise the linear direct proportionality.
Open ToolKhan Academy: Charles's Law
Explanation and worked examples of Charles's Law, with emphasis on Kelvin temperature.
Open Tool
Wikimedia Commons, CC BY-SA
Related Terms
Ideal Gas Law
The Ideal Gas Law is an equation of state for a hypothetical ideal gas, combining the empirical gas laws of Boyle, Charles, and Gay-Lussac into a single relationship between the pressure, volume, amount, and absolute temperature of a gas. It assumes gas molecules have negligible volume and no intermolecular forces, making it an excellent approximation for real gases at low pressures and high temperatures. It is foundational to thermodynamics, chemistry, and engineering, used in everything from weather balloon calculations to industrial gas storage and the analysis of respiratory physiology.
Boyle's Law
Boyle's Law states that for a fixed amount of an ideal gas at constant temperature, the pressure of the gas is inversely proportional to its volume — when volume doubles, pressure halves, and vice versa. Mathematically, the product PV remains constant. This relationship arises because compressing a gas into a smaller volume increases the frequency of molecular collisions with the container walls, thereby raising pressure. It is applied in everyday contexts from tyre pumps and syringes to scuba diving depth calculations and the design of pneumatic systems.
Gay-Lussac's Law
Gay-Lussac's Law states that for a fixed amount of an ideal gas at constant volume, the pressure of the gas is directly proportional to its absolute (Kelvin) temperature — when temperature doubles (in Kelvin), pressure doubles. This isochoric (constant volume) relationship arises because higher temperatures cause gas molecules to collide with the container walls more frequently and with greater force. It explains why sealed aerosol cans or vehicle tyres can burst if overheated, and why pressure cookers build up pressure as the internal temperature rises above 100 °C.
Named after the French physicist and inventor Jacques Alexandre César Charles (1746–1823), who discovered the law around 1787 through experiments with hydrogen balloons, though he did not publish his findings. John Dalton and Joseph Louis Gay-Lussac independently confirmed and published the relationship in 1802, with Gay-Lussac crediting Charles.