OpenStax University Physics/V2

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Temperature and Heat[edit | edit source]

relates Celsius to Fahrenheit temperature scales. relates Kelvin to Celsius.

▭ Linear thermal expansion: relates a small change in length to the total length , where is the coefficient of linear expansion.
▭ For expansion in two and three dimensions: and , respectively.
▭ Heat transfer is where is the specific heat capacity. In a calorimeter,
▭ Latent heat due to a phase change is for melting/freezing and for evaporation/condensation.
▭ Heat conduction (power): where is heat conductivity and is thickness and is area.
▭  is the radiative energy transfer rate where is emissivity and is the Stefan–Boltzmann constant.

The Kinetic Theory of Gases[edit | edit source]

Ideal gas law: Pressure×Volume where is the number of moles and is an absolute temperature.

▭  is the number of particles. Gas constant = 8.3 J K−1/mol
▭ Avegadro's number: = 6.02×1023. Boltzmann's constant: = 1.38×10−23J/K.
▭ Van der Waals equation
▭ RMS speed where the overline denotes mean, is a particle's mass and is the molar mass.
▭ Mean free path where is the mean-free-time
▭ Internal energy of an ideal monatomic gas , where average kinetic energy of a particle.
▭  defines the molar heat capacity at constant volume.
▭  for ideal gas with degrees of freedom
▭ Maxwell–Boltzmann speed distribution
▭ Average speed ▭ Peak velocity

The First Law of Thermodynamics[edit | edit source]

(Pressure, volume, temperature) remain constant in an (isobaric, isochoric, isothermal) process. Heat is not transferred in an adiabatic process.

Heat engine icon.svg

▭ Equation of state ▭ Work done by a system
▭ Internal energy is a sum over all particles of kinetic and potential energies
▭ First law (Q is heat going in and W is work done by as shown in the figure)
▭  is the molar heat capacity at constant volume
▭  for an adiabatic process in an ideal gas, where the heat capacity ratio

The Second Law of Thermodynamics[edit | edit source]

work done in a heat engine cycle. ▭ Efficiency

▭ Coefficient of performance for a refrigerator , and heat pump
▭ Entropy change (reversible process at constant temperature)
▭  for any cyclic process is path independent.
▭  for any closed system. for any isothermal process.

Electric Charges and Fields[edit | edit source]

Coulomb's Law where the vacuum permittivity 8.85×10−12 F/m.

Elementary charge = e = 1.602×10−19C (electrons have charge q=−e and protons have charge q=+e.)

Dipole moment

▭ By superposition, where
▭ Electric field where is the field at due to charges at
▭ The field above an infinite wire and above an infinite plane
▭ An electric dipole in a uniform electric field experiences the torque

Gauss's Law[edit | edit source]

 closed .. open

Flux for a uniform electric field in general.

▭ Closed surface integral
▭ Gauss's Law . In simple cases:
▭ Electric field just outside the surface of a conductor

Electric Potential[edit | edit source]

Electric potential . Change in potential energy

▭  Electron (proton) mass = 9.11×10−31kg (1.67× 10−27kg). Electron volt: 1 eV = 1.602×10−19J
▭  Near an isolated point charge where =8.99×109 N·m/C2 is the Coulomb constant.
▭ Work done to assemble N particles
▭ Electric potential due to N charges. . For continuous charge . For a dipole, .
▭ Electric field as gradient of potential ▭ Del operatornote: Cartesian Cylindrical Spherical

Capacitance[edit | edit source]

defines capacitance. For a parallel plate capacitor, where A is area and d is gap length.

▭  and for a spherical and cylindrical capacitor, respectively
▭ For capacitors in series (parallel)
▭  ▭ Stored energy density
▭ A dielectric with will decrease the capacitor's electric field and stored energy , but increase the capacitance due to the induced electric field

Current and Resistance[edit | edit source]

Current (1A=1C/s) where (density, charge, drift velocity) of the carriers.

▭  , is the perpendicular area, and is current density. is electric field, where is resistivity.
▭ Resistivity varies with temperature as . Similarily, where is resistance (Ω)
▭ Ohm's law ▭  Power

Direct-Current Circuits[edit | edit source]

Terminal voltage where is the internal resistance and is the electromotive force.
▭ Resistors in series and parallel: ▭ 
▭ Kirchoff's rules. Loop: Junction:

▭  ▭  where is internal resistance of each voltage source.
▭ Charging an RC (resistor-capacitor) circuit: and where is RC time, and .
▭ Discharging an RC circuit: and

Magnetic Forces and Fields[edit | edit source]

▭  is the force due to a magnetic field on a moving charge.
▭ For a current element oriented along .

▭ The SI unit for magnetic field is the Tesla: 1T=104 Gauss.
▭ Gyroradius Period
▭ Torque on current loop where is the dipole moment. Stored energy
▭ Drift velocity in crossed electric and magnetic fields
▭ Hall voltage = where the electric field is
▭ Charge-to-mass ratio where the and fields are crossed and when the magnetic field is

Sources of Magnetic Fields[edit | edit source]

Magnetic field element (Biot-Savart Law).svg

▭ Permeability of free space T·m/A
▭ Force between parallel wires

▭ Biot–Savart law

▭ Ampère's Law:
▭ Magnetic field due to long straight wire ▭ At center of loop
▭ Inside a long thin solenoid where is the ratio of the number of turns to the solenoid's length.
▭ Inside a toroid

▭ The magnetic field inside a solenoid filled with paramagnetic material is where is the permeability

Electromagnetic Induction[edit | edit source]

Magnetic flux ▭ Electromotive force (Faraday's law)
▭ Motional emf ▭ rotating coil
▭ Motional emf around circuit

Inductance[edit | edit source]

The SI unit for inductance is the Henry: 1H=1V·s/A ▭ Mutual inductance: where is the flux through 1 due to the current in 2 and is the emf in 1. Likewise, it can be shownSEE TALK that, .

Toroid by Zureks labeled.svg

▭ Self-inductance ▭  Stored energy ▭ is the current in an LR circuit where is the LR decay time.
▭ The capacitor's charge on an LC circuit where is angular frequency
▭ LRC circuit where

Alternating-Current Circuits[edit | edit source]

AC voltage and current if
▭ RMS values and ▭ Impedance

▭ Resistor where
▭ Capacitor where ▭ Inductor where
▭ RLC series circuit where and
▭ Resonant angular frequency ▭ Quality factor
▭ Average power , where for a resistor.
▭ Transformer voltages and currents

Electromagnetic Waves[edit | edit source]

Displacement current where is the electric flux.

Maxwell's equations
See also
▭ Plane EM wave equation where is the speed of light
▭ The ratio of peak electric to magnetic field is and the Poynting vector represents the energy flux
▭ Average intensity
▭ Radiation pressure (perfect absorber) and (perfect reflector).