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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(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 = 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.