28628 - General Physics T-B

Learning outcomes

The student acquires and consolidates the basic concepts of general physics using the language of mathematical analysis, integral calculus, and vector calculus. He/she acquires the scientific-technical methodology necessary to quantitatively address problems in physics, with particular attention to electromagnetism.

Course contents

Thermodynamics

 Thermodynamic systems and their transformations. System, environment, and thermodynamic universe. Open, closed, and isolated systems. Thermodynamic coordinates (variables). Thermodynamic equilibrium state. Equation of state. State changes: thermodynamic transformations. Quasi-static transformations. Reversible and irreversible transformations. Diathermic and adiabatic substances. Engineering convention on the signs of heat and work exchanges. The Zeroth Law of Thermodynamics. Empirical temperature measurement. Thermometers. Thermometric characteristic. Thermal expansion in solids and liquids. Linear thermal expansion coefficient. Volumetric thermal expansion coefficient. Thermometric function. Calibration and graduation of thermometers. Mercury thermometer. Temperature scales: Celsius scale. Pressure in fluids. Units of pressure measurement. Issues related to the unique measurement of temperature. Constant volume gas thermometer. Limit temperature: absolute zero. Triple point of water. Kelvin temperature scale. Fahrenheit scale. Perfect gas laws: Boyle's law, Charles's or Gay-Lussac's isobaric law, Gay-Lussac's isochoric law, Avogadro's law. Molar volume. Perfect gas state equation. Isothermal compressibility modulus and cubic expansion coefficient. Thermodynamic transformations and state changes. Adiabatic work. Internal energy. Thermodynamic work. Energy exchanges between system and environment. The first law of thermodynamics. Amount of heat and conservation of energy in a generalized sense. Measurement of heat. Units of heat measurement. Mechanical equivalent of a calorie. Thermal and refrigeration machines. Thermal capacity. Exact differential of a function of two variables. Molar, specific, and latent heats. Molar specific heat of metals: Dulong and Petit's law. Heat sources (reservoirs). Thermodynamic work in reversible thermodynamic transformations of a perfect gas. Representation in the Clapeyron plane. Internal energy of rarefied real gases: Joule's experiment. Internal energy of a perfect gas: dependence of internal energy only on temperature. Determination of internal energy variations in reversible transformations. Molar specific heats for monoatomic and diatomic gases. Mayer's relation. Adiabatic transformations, Poisson's equations. Polytropic transformations. Reversibility and irreversibility of real thermodynamic transformations. The second law of thermodynamics. Kelvin-Planck and Clausius statements. Cyclic thermal machines with heat exchanges between two heat sources. Efficiency of a thermal cycle. Carnot's theorem. Carnot cycle. Absolute thermodynamic temperature scale. Brief notes on refrigeration cycles. Clausius theorem. Clausius inequality and entropy state function. Determination of entropy variation in various transformations: heat exchange between two heat sources, heat exchange between a body and a heat source, phase transitions. Isoentropic transformations. Entropy variation of perfect gases. T-S diagrams. Entropy growth law. Mathematical formulation of the second law of thermodynamics. Entropy and the arrow of time. Entropy and unusable energy. Brief notes on the kinetic theory of gases. Entropy and thermodynamic probability. Boltzmann's law. Entropy and disorder. Entropy and information. Third law of thermodynamics. Brief notes on thermodynamic potentials. Enthalpy. Hess's law. Gibbs potential. Helmholtz potential. General properties of pVT systems. Maxwell's relations. Born's square. Dependence of internal energy on volume and temperature in a generic pVT system. Open pVT systems. Chemical potential. Brief notes on real gases. Lennard-Jones potential. Real gas state equations. Van der Waals equation. Virial expansion. Phase transitions. Phase diagram. Vapor pressure. Relative humidity. Brief notes on second-order phase transitions. Heat transfer: heat conduction: Fourier's law. Brief notes on heat transfer by convection. Heat radiation. Stefan-Boltzmann law. Clapeyron equation.

 

Electromagnetism: Electrostatics - Coulomb's law, electric field and potential of a point charge. Linear, surface, and volumetric distributions of electric charges. Electric field generated by a straight wire charged with uniform linear charge density. Electric field generated by a disk charged with uniform surface charge density. Electric field generated by an infinite plane sheet charged with uniform surface charge density. Electric field of a double layer. Force acting on electric charges in the presence of electric fields. Electrostatic energy. Potential and field of an electric dipole at a great distance from the dipole. Torque and electric potential energy of a dipole in an external electric field. Gauss's theorem for the electric field and its applications. Derivation of the electric field using Gauss's theorem: field produced by an infinite straight wire, by an infinite plane sheet, by a solid sphere charged with uniform volumetric charge density, and by a spherical shell charged with uniform surface charge density. Divergence and curl of the electrostatic field. Divergence theorem and Stokes' theorem. Poisson's and Laplace's equations. Conductors and dielectrics. Conductors in electrostatic equilibrium. Electrical capacity. Capacitors. Dielectrics. Electric current. Electromotive field. E.m.f., Electrical resistance. Ohm's law. Joule's law. Direct current circuits. Electrical networks. Kirchhoff's laws. Transients of charge and discharge of a capacitor. Magnetism: magnetic forces and their properties. Gauss's law for the magnetic field. Biot-Savart law. First Laplace equation, or "generalized Biot-Savart equation". Applications of the first Laplace formula: determination of the magnetic field produced by a loop carrying direct current at points on the loop axis. Magnetic field of the solenoid. Determination of the magnetic field produced by an infinite plane sheet carrying direct current. Magnetic field produced by a charge in uniform rectilinear motion for speeds lower than the speed of light. Conservation law of electric charge: continuity equation. Magnetic dipole moment. Lorentz force. Force exerted by a magnetic field on a circuit carrying direct current: second Laplace formula. Forces between currents. Definition of Ampere in the International System. Forces between charges in rectilinear motion. Ampère's law. Faraday-Lenz law. Mutual induction and self-induction. Inductance of a circuit. Magnetic field energy density. Brief notes on magnetism in matter. Electromagnetism: Displacement current. Ampère-Maxwell law. Maxwell's equations. Maxwell's equations in vacuum. Electromagnetic waves.

Waves and oscillations

 Introduction to wave phenomena. Definition of perturbation and wave. Definition of phase velocity, wave number, pulsation, initial phase, wave phase, and wavefront. D'Alembert wave equation. Wave intensity. Definition of decibel. Longitudinal waves. Acoustic waves. Speed of sound propagation. Transverse waves. Polarization of transverse waves. Transverse wave on a tense string. Speed of propagation of a wave on a tense string. Reflection and refraction: reflection and transmission coefficients. Impedance of a material medium. Plane waves, cylindrical waves, and spherical waves. Harmonic waves. Brief notes on Fourier's theorem. Wave superposition. Beats, phase and group velocity. Standing waves. Standing waves on a tense string: quantization conditions of frequencies. Three-dimensional harmonic plane waves. Brief notes on interference, diffraction, and evanescent waves. Electromagnetic waves: properties of electromagnetic waves in vacuum. Energy aspects of the electromagnetic field: energy theorem and Poynting vector. Radiation pressure. Brief notes on electromagnetic wave sources. Electromagnetic wave spectrum. Brief notes on light reflection and refraction. Brief notes on the vector potential.

Readings/Bibliography

S. Focardi, I. Massa, A. Uguzzoni - Fisica Generale - Termodinamica e Fluidi - Casa Editrice Ambrosiana

▪ S. Focardi, I. Massa, A. Uguzzoni, M. Villa - Fisica Generale - Elettromagnetismo - Casa Editrice Ambrosiana

▪ S. Focardi, I. Massa, A. Uguzzoni, M. Villa - Fisica Generale - Onde e Ottica - Casa Editrice Ambrosiana

▪ A. Bertin, M. Poli, A. Vitale, Fondamenti di termodinamica, Esculapio Editore (Progetto Leonardo),

Bologna.

▪ A. Bertin, N. Semprini Cesari, A. Vitale, A. Zoccoli, Lezioni di elettromagnetismo, Esculapio Editore

(Progetto Leonardo), Bologna.

▪ P. Mazzoldi, M. Nigro, C. Voci - Fisica - Meccanica e Termodinamica - EdiSES Università

▪ P. Mazzoldi, M. Nigro, C. Voci - Fisica - Elettromagnetismo e Onde - EdiSES Università

Teaching methods

The lecturer makes use of electonic devices and blackboard during llectures. Exercises are solved during lectures and dedicated sessions. 

Assessment methods

A written examination gives access to a VIVA.

Office hours

See the website of Iacopo Vivarelli