Charles's Law

Relates the volume and absolute temperature of a fixed amount of gas at constant pressure: heating expands the gas.

\frac{V_1}{T_1} = \frac{V_2}{T_2}

V1/T1 = V2/T2

What it means

Charles's law says that at fixed pressure, a gas's volume is directly proportional to its absolute temperature: heat the gas and it expands in exact proportion. The molecules move faster when heated, hitting the walls harder, so the gas must occupy more space to keep the pressure constant. Crucially, the temperature must be in kelvin — the law is only a true proportionality on the absolute scale, where doubling the temperature really doubles the average kinetic energy. When to use it: for a gas sample heated or cooled while pressure and amount stay fixed — hot-air balloons, tire pressure in winter, expanding pistons.

Variables

Symbol	Name	Unit	Meaning
$V1$	Initial volume	L (or m^3)	Volume of the gas before the temperature change.
$T1$	Initial temperature	K	Absolute temperature before the change — must be in kelvin.
$V2$	Final volume	L (or m^3)	Volume of the gas after the temperature change.
$T2$	Final temperature	K	Absolute temperature after the change — must be in kelvin.

Assumptions

The amount of gas (n) does not change.
The pressure stays constant (e.g. a freely moving piston against the atmosphere).
Temperature MUST be in kelvin; using Celsius makes the ratio meaningless.
The gas behaves ideally.

Worked example

Problem

A 3.00 L gas sample at 300 K is heated to 450 K at constant pressure. What is its new volume?

Given:

V1 = 3.00 L at T1 = 300 K
Heated to T2 = 450 K, n and P constant

Write Charles's law: V1/T1 = V2/T2.
Solve for V2: V2 = V1 × (T2/T1).
Substitute: V2 = 3.00 L × (450 K / 300 K).
Calculate: 450 / 300 = 1.50; 3.00 × 1.50 = 4.50 L.

V2 = 4.50 L

Raising the absolute temperature by a factor of 1.5 expands the volume by the same factor — the direct proportionality Charles observed.