Physics and Mathematics at high school level (bachillerato)

By the end of this subject, students will be able to have: 1. Knowledge and understanding of the physics principles underlying their branch of engineering; 2. The ability to apply their knowledge and understanding to identify, formulate and solve mechanics and thermodynamic problems using established methods; 3. The ability to design and conduct appropriate experiments, interpret the data and draw conclusions; 4. The ability to select and use appropriate tools and methods to solve mechanics and thermodynamics problems; 5. The ability to combine theory and practice to solve mechanics and thermodynamic problems; 6. Laboratory skills.

1. Kinematics of a particle -Vectors position, velocity and acceleration -Equation of trajectory -Intrinsic components of acceleration -Circular motion 2. Relative motion -Systems of reference -Transformations among systems of reference -Applications 3. Dynamics of a particle -Fundamental concepts: mass, linear moment and forces -Newton's laws -Examples of forces: weight, elastic force, friction... -Angular moment and moment of forces 4. Conservative and non-conservative forces. Work and energy. -Scalar and vector fields. Gradient and curl. -Conservative fields. Potential function. -Work. Power. Kinetic energy -Conservative forces and potential energy -Non-conservative forces. 5. Systems of particles -Internal and external forces. -Statics. General condition of equilibrium. -Motion of the center of masses. -Kinetic energy of a system of particles. -Conservation theorems for a system of particles. 6. Kinematics of the Rigid Body -Rotation and translation motion. -Motion of the rigid body in the plane. -Moment of inertia. -Theorem of Steiner. 7. Dynamics of the Rigid Body -Equations of motion of the rigid body -Rotation work and power. -Kinetic energy of rotation. 8. Introduction to Thermodynamics -Thermodynamics: concept and definitions. -Equilibrium States. Quasistatic processes and reversible processes. -Work. 9. Temperature. Ideal gases -Definition of temperature -Thermometry. Ideal gas scale -Thermal coefficients: expansion and isotherm compressibility 10. First principle -Experiment of Joule and statement of Helmholtz. -Internal energy; energy equation of state. -Heat. Heat capacities and specific heats. Heat and work sources. -Phase Changes -Application to ideal gases. -Diagrams PV and PT 11. Second principle -Statement of Kelvin-Planck. Thermal engines. -Statement of Clausius. Refrigerating machines. Irreversibility. -Cycle of Carnot. Theorem of Carnot. Consequences -Cycles with ideal gases. 12. Entropy -Theorem of Clausius. Entropy -Diagrams T-S. Entropy in ideal gases. -Entropy in irreversible processes. Entropy balance.

Lectures where the theoretical concepts are explained The lecturer provide a file with the following information (1 week in advance) - Main topics to be discussed during the session - Chapters/sections in each of the text books provided in the bibliography were the student can read about these topics Activities in groups (~ 40 students divide in 2-3 people groups) to solve problems The main skills to be developed in these activities are - To understand the statement of the problem (for instance drawing an scheme that summarizes the statement) - To identify the physical phenomenon involved in the statement and the physical laws related to it. - To develop a strategy to reach the objective (for instance breaking the problem in small sub-problems). - To be careful in the use of mathematics - To analyze the result (is the final number reasonable?, are the dimensions consistent?) Small works focused to the search of scientific information in different sources (mainly internet). (PO: a,d) Laboratoy sessions (~ 24 students divide in 2 people groups) The main skills to be developed in this activity are: - To understand that physics is an experimental science and they can reproduce the laws that have been theoretically explained in the lectures - To use scientific instruments and to be careful in its operation - To be careful in the acquisition of the experimental data - To learn the basis of the management of a scientific data set - To write a report with the main results of the experiment - To reason in a critical way these results: have we achieve the goals of the