Fluid statics, kinematics and dynamics. Pressure and gravity waves. Non-ideal fluids, viscosity and turbulent motion.
Temperature measurements. Ideal and real gas. Kinetic theory. Calorimetry and transmission of heat. Thermodynamics: first and second principle. Entropy, enthalpy and thermodynamic potentials. Statistical physics:
H-theorem, Maxwell-Boltzmann distribution, classical statistical ensembles.
The notes of the lectures, written by Prof. E. Landi Degl’Innocenti, are available in the form of three booklets:
“Elementi di Meccanica dei Fluidi”,
“Elementi di Termodinamica”, and
“Elementi di Statistica".
Learning Objectives
Fundamental knowledge in fluidodynamics, thermodynamics and statistical mechanics. Basic competences of the physiscist relatively to classical physiscs. Skills in solving numerical problems of physics, in identifying the essential elements of a physical process, in working out physical models and verifying their validity, in guessing structural analogies among different phenomenological scenarios.
Prerequisites
Required courses: Matemathical Analysis I
Teaching Methods
56 hours of lecturing,
24 hours of exercises.
Further information
Students can consult the teachers on appointment.
Type of Assessment
Oral test.
Course program
FLUID MECHANICS
Difference beetween solid and fluid substances. Fluid Statics. Surface and volume forces. Concept of pressure. Pascal principle. The fundamental law of hydrostatic. Differences between liquids and gases. Compressibility coefficient. Variation of the pressure with height. Torricelli experiment. Unit of measurement for pressure. Archimede's principle. Center of buoyancy. Flotation and flotation stability. Surface and capillarity phenomena. Surface tension. Cohesion and adhesion forces. Tate and Jurin laws. Fluid kinematics. Lagrangian and Eulerian descriptions. Eulerian derivative. Advection term. Continuity equation. Leonardo's principle. Flux lines and flux tubes. Massic and volumetric flow rate. The fundamental law of hydrodynamics for ideal fluids. Bernoulli theorem for a liquid and for a compressibile fluid. Piezometric height and height of stop. Torricelli theorem. Applications of the Bernoulli theorem: Venturi tube and Pitot tube. Pressure waves. Concept of deformation. Sound velocity. Frequency and angular frequency, wavenumber, wavelenght, phase. Outline on gravity waves (surface waves). Dispersion relation for gravity waves. Dynamics of non-ideal fluids. Dynamic viscosity and kinematic viscosity. Newton formula. The fundamental law of non-ideal fluid hydrodynamics. Poiseuille law. Turbulent motion. Reynolds number. Drag force. Aeodynamic lift. Magnus effect.
THERMODYNAMICS
Historical introduction to the concept of temperature. Thermal expansion of physical bodies. Freezing and melting points. Thermometric substances. Scales of temperature. The principle zero of thermodynamics. Concept of thermal equilibrium. Gases laws (Boyle, Gay-Lussac, Dalton, and Avogadro laws, the perfect gas law). The perfect gas thermometer. Behavior of real gases. Concepts of critical temperature, critical pressure and critical volume. Liquid phase, vapor phase and saturated vapor phase. Van der Waals equation. Co-volume and the constant of internal pressure. Introduction to the kinetic theory of the gases. The clausius model. Mean quadratic velocity. Heat quantity. Calorimeters. Specific heat and latent heat. The Joule heat apparatus. Mechanical equivalent of the calorie. The transmission of heat. Conduction. Concept of thermal conductivity. Fourier postulate. The equation of heat diffusion. Convection. Newton Formula. Black body radiation. Planck law and Stefan law. Equivalence between heat and work. The first principle of thermodynamics. Concept of internal energy. Illustrations of the first principle. Work of a gas. Formula for the expansion of a perfect gas. Specific heats of gases. Constant-volume and constant-pressure specific heats and their relationship. Adiabatic transformations. Laws for the adiabatic of a perfect gas. The second principle of thermodynamics. Heat engines and their efficiency. The Carnot theorem. Carnot Cycle. Thermodynamic definition of temperature. The Clausius inequality. Definition of entropy. Illustrations of the concept of entropy. Consequences of the first and of the second principle: the internal energy equation and the TdS equation. Clayperon equation. The statistical meaning of entropy. Concept of thermodynamical probability. The Boltzmann equation. Enthalpy and thermodynamic potentials. Thermodynamic cycles (Rankine, Otto, and Diesel cycles). Refrigerating engines and heat pumps.
STATISTICAL MECHANICS
Virial theorem. Maxwellian distribution of velocities. Mean free path. Poisson distribution. Distribution of the distances among particles. Transport phenomena. Random-walk. Brownian motion. Desorder and its measurement. H-theorem. General laws of Statistical Thermodynamics. Gibbs ditribution. Fluctuations. Systems of identical particles: Boltzmann equation. Equipartition of energy. Entropy of the perfect gas. Statistics of open thermodynamical systems. Quantum Statistics.