THEORETICAL QUESTIONS TP II 2006/07
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Derive the first equation of motion for a system of particles.
Derive the second equation of motion for a system of particles.
Derive relation for center of mass for a system of particles.
Derive equation of motion of a solid body rotating about a fixed axis.
From motion equation of a body rotating about a fixed axis derive equation of
motion of the physical pendulum and relation for its period. Draw a picture.
From motion equation of a body rotating about a fixed axis derive equation of
motion of the torsional pendulum and relation for its period.
Derive relation for kinetic energy of a solid body rotating about a fixed axis. Draw
a picture.
Derive relation for pressure of gas into the container wall introducing mean
quadratic speed of molecules.
From relation for pressure of gas into the container wall derive relation for mean
kinetic energy of one molecule.
From equipartition theorem derive relation for internal energy of gas.
From law of conservation of energy of a system of particles formulate the first law
of thermodynamics verbally as well as mathematically.
Derive relation for work of gas during change of its volume. Draw a picture.
From definition of molar heat capacity of gas at constant volume and pressure
derive Mayer’s relation.
Derive relations between molar heat capacities of gas at constant volume and
pressure and degrees of freedom of gas.
Describe mathematically isochoric process. Represent it on P-V diagram. Write
and explain the first law of thermodynamics for this process. Derive added heat,
work done by gas and change of internal energy during this process.
Describe mathematically isobaric process. Represent it on P-V diagram. Write and
explain the first law of thermodynamics for this process. Derive added heat, work
done by gas and change of internal energy during this process.
Describe mathematically isothermal process. Represent it on P-V diagram. Write
and explain the first law of thermodynamics for this process. Derive added heat,
work done by gas and change of internal energy during this process.
Describe mathematically adiabatic process. Represent it on P-V diagram. Write
and explain the first law of thermodynamics for this process. Derive added heat,
work done by gas and change of internal energy during this process.
From the first law of thermodynamics and the equation of state of ideal gas derive
Poisson’s equation.
Calculate work of gas for isochoric and adiabatic process.
Calculate work of gas for isobaric and isothermal process.
Calculate efficiency of Carnot cycle.
Derive mathematical formulation of the second law of thermodynamics.
From efficiency of Carnot cycle derive relation for change of entropy during
reversible and irreversible cycle processes. (Mathematical formulation of the
second law of thermodynamics).
Derive Gauss’ law for vacuum.
 Derive Coulomb’s law (intensity of electrostatic field in close vicinity of the
conductor surface).
 Derive properties of electrostatic field inside and outside of charged conductor.
 Derive intensity of electrostatic field in vicinity of infinite plane sheet.
 Derive intensity of electrostatic field in vicinity of two infinite parallel plane
sheets.
 Describe mechanism of dielectric polarization and derive quantities describing
electrostatic field in dielectric.
 Derive capacity of the plate capacitor.
 Derive relation for energy of electrostatic field.
 Derive Ohm’s law in differential form.
 Derive Ohm’s law in integral form.
 Derive relation for power of electric current.
 Derive relation between terminal and electromotive voltage.
 Derive Biot-Savart-Laplace law.
 Derive Ampere’s law of force.
 Derive relation for force of two linear straight parallel wires. Define the ampere.
 Derive relation for torque by which magnetic field affects on the current loop.
 Derive law of total current in vacuum.
 Describe interaction of magnetic field with matter. Define and derive quantities
describing magnetic field in matter.
 Derive Faraday’s law of electromagnetic induction.
 Describe mathematically phenomenon of self-inductance and mutual inductance.
 Derive relation for energy and energy density of magnetic field.
 Describe harmonic motion of the mass point along a line. Derive functions of
velocity and acceleration of this point and write their dependences.
 Write and solve motion equation of simple harmonic oscillations.
 Write and solve motion equation of damped harmonic oscillations.
 Derive relations for energy of the particle that is in simple harmonic motion.
 Write and solve motion equation of forced oscillations.
 Describe superposition of parallel harmonic oscillations.
 Describe superposition of perpendicular harmonic oscillations.
 Explain the principle of Fourier analysis.
 Describe and explain wave motion. Write and explain the function of planar
harmonic wave propagating in direction of x-axis.
 Derive the function describing standing wave. Draw and explain its course.
 Derive differential equation of longitudinal waves in solid state.
 Derive wave equation.