Charles Kelvin Three-State Scan - Thermodynamics and Statistical Mechanics Step by Step

A Charles-Kelvin three-state scan holds pressure fixed and walks volume through three states, checking that V / T stays constant with temperature in kelvin across the rows. The arithmetic is exact only for the stated volumes, kelvin temperatures, and fixed pressure in the ideal gas model. Real experiments add temperature-scale error, pressure/volume calibration, thermal-equilibrium limits, gas nonideality, and measurement uncertainty.

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}