Charles' Law - Thermodynamics and Statistical Mechanics Step by Step

Charles' law says that at constant pressure, volume grows in step with absolute temperature, V / T = constant, so the gas expands as it warms. The temperature must be in kelvin, because the law is anchored to absolute zero. It holds for a fixed amount of ideal gas in equilibrium; real gases leak, depart from ideal behavior at extremes, and the volume and temperature readings carry calibration uncertainty.

At fixed pressure, volume is proportional to absolute kelvin temperature. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Use absolute kelvin

At fixed pressure, compare volume to absolute temperature. The first state is 6 cubic meters at 300 kelvin.

\frac{V_i}{T_i} = \frac{6\ \text{m}^{3}}{300\ \text{K}}

Raise kelvin temperature

The second state is 8 cubic meters at 400 kelvin.

\frac{V_f}{T_f} = \frac{8\ \text{m}^{3}}{400\ \text{K}}

The ratio stays constant

Both ratios equal one fiftieth cubic meter per kelvin.

\frac{V}{T} = \tfrac{1}{50}\ \text{m}^{3}/\text{K}

Volume follows absolute kelvin

The diagram draws the last two rows. At fixed pressure, doubling absolute kelvin doubles volume in this ideal-gas comparison.

\begin{array}{c|c|c}V&T&V/T\\3\ \text{m}^{3}&150\ \text{K}&\tfrac{1}{50}\ \text{m}^{3}/\text{K}\\6\ \text{m}^{3}&300\ \text{K}&\tfrac{1}{50}\ \text{m}^{3}/\text{K}\\8\ \text{m}^{3}&400\ \text{K}&\tfrac{1}{50}\ \text{m}^{3}/\text{K}\\\end{array}