The first law states $delta_U$ = q + w (IUPAC: work done ON system is positive). At constant volume (bomb calorimeter): w = 0, so $delta_U$ = qv. At constant pressure (open containers): $delta_H$ = qp. For ideal gas expansion: w = -$P_{ext}$ * $delta_V$ (irreversible) or w = -nRT ln$\frac{V2}{V1}$ (reversible isothermal). Reversible work is the maximum work extractable. For adiabatic processes: q = 0, so $delta_U$ = w = nCv*$delta_T$. Key relationships: Cp - Cv = R (per mole, ideal gas). gamma = $\frac{Cp}{Cv}$. For monoatomic ideal gas: Cv = 3R/2, Cp = 5R/2. For diatomic: Cv = 5R/2, Cp = 7R/2.