How the Units That Quantify Both the Gas Constant R and the Boltzmann Constant k_B Link the Temperature Dependence of Gas Volume with the Temperature Dependence of Entropy

This study uses the PΔV term in the ideal gas equation PΔV = nRΔT to show how the 1-degree temperature increase that expands the occupied volume of a gas by ΔV against constant pressure P also causes the system to increase its entropy by ΔS. As the volume available to a gas sample increases, the locations for disordered molecular relocation also increase. The causal agent linking a volume increase ΔV and an entropy increase ΔS is absolute temperature T measured in kelvin units. Since a volume increase is empirically observable while an increase in randomized molecular disorder is not, a per-kelvin increase in gas volume provides a method for estimating entropy increase. Both volume and entropy are extensive variables dependent upon the number of molecules in the system. Both are deemed to be at their absolute minima at the absolute zero of temperature. This study provides an insight into how a per-kelvin temperature increase causes both a linear increase in gas volume and a linear increase in gas entropy. When people talk about randomized disorder without specifying absolute temperature and molecule-count for the system, they are discussing a concept other than thermodynamic entropy.