$word_{count}$: 220

The first law states $delta_U$ = q + w (IUPAC convention: work done ON the system is positive). Internal energy (U) is a state function; q and w are path functions. For ideal gases, U depends only on temperature. At constant volume: w = 0, so $delta_U$ = qv (measured in bomb calorimeter). At constant pressure: $delta_H$ = qp (measured in coffee-cup calorimeter). For expansion work: w = -$P_{ext}$ * $delta_V$ (irreversible against constant pressure), w = -nRT ln$\frac{V2}{V1}$ (reversible isothermal), w = 0 (free expansion, $P_{ext}$ = 0), w = 0 (isochoric, $delta_V$ = 0). For adiabatic processes: q = 0, so $delta_U$ = w = nCv*$delta_T$. Key heat capacity relations: Cp - Cv = R (per mole, ideal gas), gamma = $\frac{Cp}{Cv}$. Monoatomic: Cv = 3R/2, Cp = 5R/2, gamma = 5/3. Diatomic: Cv = 5R/2, Cp = 7R/2, gamma = 7/5. Reversible work gives the maximum magnitude of work extractable from expansion (or minimum work needed for compression). In a cyclic process, $delta_U$ = 0 and q = -w. The first law is essentially conservation of energy applied to thermodynamic systems.