PHYS 409 (3-0-3) Statistical Physics
Definition of terms: macroscopic system, atomic/microscopic states, ordered and random motion, equilibrium, fluctuation and noise. Numerical values of typical macroscopic quantities: particle density, mean energy, mean pressure, RMS fluctuation in density of atmosphere, noise in a resistor. Basic probability theory: definition of probability, ensemble, mean value, standard deviation, combination of probabilities of independent events, derivation of the binomial distribution and its application to spin -1/2 system, the Gaussian distribution, and application to the random walk problem and density fluctuation in a gas, treatment of continuous distributions. Statistical description of a macroscopic system: specification of quantum microstates of the system, density of states, definition of a statistical ensemble, the fundamental postulate of statistical mechanics, statistical interpretation of irreversibility, definition and examples of thermal and non-thermal interactions between macroscopic system, accessible states, the condition for maximum number of accessible states for two interacting systems, definition of temperature, definition of heat reservoir, the Boltzmann distribution and application of to spin-1/2 system and ideal gas to obtain the equation of state for an ideal gas. Macroscopic measurements: The measurement of temperature and the definition of the Kelvin scale, the triple point of water, the He gas thermometer, computation of work W = p dV. Joule’s equipment: Mechanical equivalent of heat, computation of entropy changes S = S = (c"T"/T)dT, definition of intensive and extensive parameters, absolute entropy of N spin-1/2 particles. Statistical mechanics in the classical approximation: Maxwell-Boltzmann velocity distribution of particles in a gas, the equipartition theorem and its application to derivation of specific heats of molecular gases and solids, range of validity of classical approximation.
Prerequisite: PHYS 303