 Isobaric ideal-gas internal-energy density

An ideal gas with constant heat capacity ratio $\gamma$ has $U=n{c}_{V,m}T$ up to a consistent thermal-energy reference, and $c_{V,m}=R/(\gamma -1)$. Combining this with $pV=nRT$ gives the displayed thermal internal-energy density. At fixed pressure it does not grow with temperature: the particle density falls as $1/T$. A fixed-volume space exchanging gas with the atmosphere therefore differs from a sealed fixed-particle system. Composition changes, activated internal modes or a pressure change require a modified comparison.