Charles Kelvin Three-State Scan - Heat & Thermodynamics Step by Step

Three exact kelvin-volume rows show why this relation uses absolute 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

Cool gas has smaller volume

At fixed pressure, volume 3 cubic metres at 150 kelvin gives the shared ratio.

V/T=3\ \text{m}^{3}/150\ \text{K}=\tfrac{1}{50}\ \text{m}^{3}/\text{K}

Middle kelvin doubles the volume

Temperature 300 kelvin pairs with volume 6 cubic metres. The ratio is unchanged.

V/T=6\ \text{m}^{3}/300\ \text{K}=\tfrac{1}{50}\ \text{m}^{3}/\text{K}

Warm gas keeps the same ratio

The third row uses 400 kelvin and 8 cubic metres. Three rows make the direct kelvin-volume pattern scannable.

\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}