500561 - THERMODYNAMICS

Relevant physical systems: gaseous, liquid, and solid phases of matter. Macroscopic variables describing systems at equilibrium and quasi-static processes. Ideal gases: Boyle–Mariotte’s law, Volta–Gay Lussac’s law, and Avogadro’s law; derivation of the characteristic equation of state. Isothermal curves and the concept of thermal equilibrium. The zeroth law of thermodynamics. Thermometric scales. Limits of validity of the ideal gas law and introduction to the phenomenological Van der Waals model. Thermal expansion in liquids and solids. Achievement of thermal equilibrium; definition of heat and specific heat at constant volume for monoatomic and diatomic ideal gases. Extension to solids: specific heat expressed per unit mass and the definition of the calorie. Dependence of heat exchange on the type of transformation: specific heat at constant volume versus constant pressure, Mayer’s relation, and the recognition of heat as an inexact differential. Temperature dependence of specific heat: the case of solids (classical Dulong–Petit law compared with the Debye model). Heat transfer in water at the phase-transition temperatures between solid–liquid and liquid–vapor states: latent heats of fusion/solidification and evaporation/condensation. Heat propagation by conduction, convection, and radiation. Thermal conductivity and its relation to electrical conductivity in metals: the Wiedemann–Franz law. Joule’s experiments on adiabatic heating of fluids through conversion of mechanical potential energy; formalization of infinitesimal work for a gas in a movable-wall container as an inexact differential. Internal energy as a state function and the first law of thermodynamics for general transformations. Work and heat in the free expansion of an ideal gas. Internal energy of an ideal gas as a state function dependent solely on temperature. Isochoric transformations: variation of internal energy in terms of specific heat at constant volume. Isobaric transformations: formal derivation of Mayer’s relation. Derivation of the characteristic equation relating thermodynamic variables in adiabatic processes. Reversible transformations defined as quasi-static processes free of friction and dissipation. Reversible thermodynamic cycles as cyclic processes composed exclusively of reversible transformations; interpretation of such cycles as the fundamental operating principle of heat engines. The Carnot cycle as the prototype of a reversible cyclic process: heat exchange between the system and two thermal reservoirs only. Calculation of Carnot efficiency as the fraction of absorbed heat converted into work, expressed solely in terms of the reservoir temperatures; numerical evaluation and implications for the unavoidable exchange of heat with the cold reservoir. Kelvin–Planck statement of the second law of thermodynamics. Clausius theorem for reversible cycles. Representation of a general reversible process as a succession of infinitesimal isothermal and adiabatic steps. Consequences of Clausius’ theorem: path independence of the Clausius integral and the consequent definition of entropy as a new state function. Analysis of entropy variation in the system and environment during a reversible process: conservation of total entropy in the thermodynamic universe (system plus environment) considered as an isolated system. Entropy variation of the thermodynamic universe: implications for reversibility and irreversibility of processes. Statement of the second law of thermodynamics based on entropy variation of the universe.