The Kinetic Theory of Gases (Physics)

Recall cards on the kinetic theory of gases. The ideal gas law in molecular form (pV = N k_B T) and molar form (pV = nRT), the Boltzmann constant, Avogadro's number, the universal gas constant R = N_A k_B, moles and molar mass, and the empirical Boyle, Charles, and Amonton laws. Standard temperature and pressure, the 22.4 L molar volume, and the van der Waals equation for real gases. The molecular model: kinetic-theory assumptions, pressure from wall collisions (pV = (1/3) N m (v^2)avg), average translational kinetic energy K_avg = (3/2) k_B T, the rms speed v_rms = sqrt(3 k_B T / m) = sqrt(3 R T / M), monatomic internal energy (3/2) nRT, Dalton's law of partial pressures, and the mean free path and mean free time. Heat capacity and equipartition: C_V at constant volume, degrees of freedom, the equipartition theorem, C_V = (d/2) R for monatomic (3/2 R), diatomic (5/2 R), and polyatomic (3R) gases, the Dulong-Petit law for solids (3R), and temperature-activated degrees of freedom. The Maxwell-Boltzmann distribution of molecular speeds, the most probable, average, and rms speeds and their ordering (v_p < v_avg < v_rms), and how the distribution shifts with temperature and molecular mass.