Margins Study Assistant

Chapter 1

Temperature and Heat

Summary

The three phases of water (ice, liquid water, and water vapor) can coexist at a single pressure and temperature known as the triple point The zeroth law of thermodynamics states that when two systems, A and B, are in thermal equilibrium with each other, and B is in thermal equilibrium with a third system C , then A is also in thermal equilibrium with C The three main temperature scales are Celsius, Fahrenheit, and Kelvin. Temperature is operationally defined as the quantity measured by a thermometer.

Key terms

temperature: functionally defined as a quantity measured by a thermometer, which, at least for most of the systems discussed in this chapter, reflects the mechanical energy of particles in…
heat: energy transferred solely due to a temperature difference
thermal equilibrium: condition in which heat no longer flows between two objects that are in contact; the two objects have the same temperature
zeroth law of thermodynamics: law that states that if two objects are in thermal equilibrium, and a third object is in thermal equilibrium with one of those objects, it is also in thermal equilibrium with the…
triple point: pressure and temperature at which a substance exists in equilibrium as a solid, liquid, and gas
radiation: energy transferred by electromagnetic waves directly as a result of a temperature difference
vapor: gas at a temperature below the critical temperature
three main temperature scales: Celsius, Fahrenheit, and Kelvin

Chapter 2

The Kinetic Theory of Gases

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Summary

The ideal gas law can also be written and solved in terms of the number of moles of gas: p V = n R T , where n is the number of moles and R is the universal gas constant, R = 8.31 J/mol · K The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas The number of molecules in a mole is called Avogadro’s number N A , N A = 6.02 × 10 23 mol -1 The van der Waals equation of state for gases is valid closer to the boiling point than the ideal gas law

Key terms

kinetic theory of gases: theory that derives the macroscopic properties of gases from the motion of the molecules they consist of
mole: quantity of a substance whose mass (in grams) is equal to its molecular mass
ideal gas law: physical law that relates the pressure and volume of a gas, far from liquefaction, to the number of gas molecules or number of moles of gas and the temperature of the gas
supercritical: condition of a fluid being at such a high temperature and pressure that the liquid phase cannot exist
universal gas constant: R , the constant that appears in the ideal gas law expressed in terms of moles, given by R = N A k B
Avogadro’s number: N A , the number of molecules in one mole of a substance; N A = 6.02 × 10 23 particles/mole
critical temperature: T c at which the isotherm has a point with zero slope

Chapter 3

The First Law of Thermodynamics

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Summary

A thermodynamic system, its boundary, and its surroundings must be defined with all the roles of the components fully explained before we can analyze a situation Thermal equilibrium is reached with two objects if a third object is in thermal equilibrium with the other two separately A general equation of state for a closed system has the form f ( p , V , T ) = 0 , with an ideal gas as an illustrative example The internal energy of a thermodynamic system is a function of state and thus is unique for every equilibrium state of the system

Key terms

first law of thermodynamics: the change in internal energy for any transition between two equilibrium states is Δ E int = Q - W
closed system: system that is mechanically and thermally isolated from its environment
internal energy: average of the total mechanical energy of all the molecules or entities in the system
equilibrium: thermal balance established between two objects or parts within a system
equation of state: describes properties of matter under given physical conditions
boundary: imagined walls that separate the system and its surroundings
third object: in thermal equilibrium with the other two separately
surroundings: environment that interacts with an open system

Chapter 4

The Second Law of Thermodynamics

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Summary

The focus of a refrigerator is on removing heat from the cold reservoir with a coefficient of performance K R The focus of a heat pump is on dumping heat to the hot reservoir with a coefficient of performance K P An irreversible process is one in which the system and its environment cannot return together to exactly the states that they were in A refrigerator or a heat pump is a heat engine run in reverse

Key terms

reversible process: process in which both the system and the external environment theoretically can be returned to their original states
irreversible process: process in which neither the system nor its environment can be restored to their original states at the same time
focus of a refrigerator: on removing heat from the cold reservoir with a coefficient of performance K R
focus of a heat pump: on dumping heat to the hot reservoir with a coefficient of performance K P
coefficient of performance: measure of effectiveness of a refrigerator or heat pump
refrigerator: device that removes heat from a cold reservoir
heat pump: device that delivers heat to a hot reservoir
irreversibility: phenomenon associated with a natural process

Chapter 5

Electric Charges and Fields

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Summary

The electric charge of one electron is equal in magnitude and opposite in sign to the charge of one proton The SI unit for charge is the coulomb (C), with protons and electrons having charges of opposite sign but equal magnitude; the magnitude of this basic charge is e ≡ 1.602 × 10 -19 C An ion is an atom or molecule that has nonzero total charge due to having unequal numbers of electrons and protons The vast majority of positive charge in nature is carried by protons, whereas the vast majority of negative charge is carried by electrons.

Key terms

electric charge: physical property of an object that causes it to be attracted toward or repelled from another charged object; each charged object generates and is influenced by a force called an…
SI unit for charge: the coulomb (C), with protons and electrons having charges of opposite sign but equal magnitude; the magnitude of this basic charge is e ≡ 1.602 × 10 -19 C
proton: particle in the nucleus of an atom and carrying a positive charge equal in magnitude to the amount of negative charge carried by an electron
electron: particle surrounding the nucleus of an atom and carrying the smallest unit of negative charge
electric charge of one electron: equal in magnitude and opposite in sign to the charge of one proton
ion: atom or molecule with more or fewer electrons than protons
coulomb: SI unit of electric charge
electrostatic force: amount and direction of attraction or repulsion between two charged bodies; the assumption is that the source charges have no acceleration

Chapter 6

Gauss's Law

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Summary

The electric flux through a surface is proportional to the number of field lines crossing that surface. The electric flux is obtained by evaluating the surface integral Φ = ∮ S E → · n ^ d A = ∮ S E → · d A → , Φ = ∮ S E → · n ^ d A = ∮ S E → · d A → , where the notation used here is for a closed surface S Gauss’s law relates the electric flux through a closed surface to the net charge within that surface, Φ = ∮ S E → · n ^ d A = q enc ε 0 , Φ = ∮ S E → · n ^ d A = q enc ε 0 , where q enc is the total charge inside the… For spherical symmetry, the Gaussian surface is also a sphere, and Gauss’s law simplifies to 4 π r 2 E = q enc ε 0

Key terms

electric flux: dot product of the electric field and the area through which it is passing
spherical symmetry: system only varies with the distance from the origin, not in direction
magnitude: proportional to the portion of the field perpendicular to the area
electric flux through a surface: proportional to the number of field lines crossing that surface
flux: quantity of something passing through a given area
Gaussian surface: any enclosed (usually imaginary) surface
electric field: then determined with Gauss’s law
free electrons: also called conduction electrons, these are the electrons in a conductor that are not bound to any particular atom, and hence are free to move around

Chapter 7

Electric Potential

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Summary

The superposition principle holds for electric potential energy; the potential energy of a system of multiple charges is the sum of the potential energies of the individual pairs We can define an electric potential energy, which between point charges is U ( r ) = k e q Q r , with the zero reference taken to be at infinity Therefore, the electric field and electric force are conservative Electric potential is potential energy per unit charge

Key terms

electric potential: potential energy per unit charge
voltage: change in potential energy of a charge moved from one point to another, divided by the charge; units of potential difference are joules per coulomb, known as volt
electron-volt: energy given to a fundamental charge accelerated through a potential difference of one volt
electric potential energy: potential energy stored in a system of charged objects due to the charges
system of multiple charges: the sum of the potential energies of the individual pairs
ink jet printer: small ink droplets sprayed with an electric charge are controlled by electrostatic plates to create images on paper
grounding: process of attaching a conductor to the earth to ensure that there is no potential difference between it and Earth

Chapter 8

Capacitance

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Summary

When several capacitors are connected in a series combination, the reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances When several capacitors are connected in a parallel combination, the equivalent capacitance is the sum of the individual capacitances The capacitance of a capacitor is a parameter that tells us how much charge can be stored in the capacitor per unit potential difference between its plates. When a network of capacitors contains a combination of series and parallel connections, we identify the series and parallel networks, and compute their equivalent capacitances step by step until the entire network…

Key terms

capacitance: amount of charge stored per unit volt
parallel combination: components in a circuit arranged with one side of each component connected to one side of the circuit and the other sides of the components connected to the other side of the…
capacitance of a capacitor: a parameter that tells us how much charge can be stored in the capacitor per unit potential difference between its plates
series combination: components in a circuit arranged in a row one after the other in a circuit
capacitor: device that stores electrical charge and electrical energy
reciprocal of the equivalent capacitance: the sum of the reciprocals of the individual capacitances
equivalent capacitance: the sum of the individual capacitances
unit of capacitance: the farad, where 1 F = 1 C / 1 V

Chapter 9

Current and Resistance

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Summary

The average electrical current I ave is the rate at which charge flows, given by I ave = Δ Q Δ t , where Δ Q is the amount of charge passing through an area in time Δ t The direction of conventional current is taken as the direction in which positive charge moves. The instantaneous electrical current, or simply the current I , is the rate at which charge flows. In a simple direct-current (DC) circuit, this will be from the positive terminal of the battery to the negative terminal

Key terms

resistance: electric property that impedes current; for ohmic materials, it is the ratio of voltage to current, R = V / I
average electrical current I ave: the rate at which charge flows, given by I ave = Δ Q Δ t , where Δ Q is the amount of charge passing through an area in time Δ t
conventional current: current that flows through a circuit from the positive terminal of a battery through the circuit to the negative terminal of the battery
circuit: complete path that an electrical current travels along
direction of conventional current: taken as the direction in which positive charge moves
SI unit for current: the ampere, or simply the amp (A), where 1 A = 1 C/s
electrical current: rate at which charge flows, I = d Q d t
drift velocity: velocity of a charge as it moves nearly randomly through a conductor, experiencing multiple collisions, averaged over a length of a conductor, whose magnitude is the length of…

Chapter 10

Direct-Current Circuits

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Summary

All voltage sources have two fundamental parts: a source of electrical energy that has a characteristic electromotive force (emf), and an internal resistance r . The emf is the work done per charge to keep the potential difference of a source constant. The emf is equal to the potential difference across the terminals when no current is flowing. The voltage output of a device is called its terminal voltage V terminal and is given by V terminal = ε - I r , where I is the electric current and is positive when flowing away from the positive terminal of the…

Key terms

voltage output of a device: called its terminal voltage V terminal and is given by V terminal = ε - I r , where I is the electric current and is positive when flowing away from the positive terminal
terminal voltage: potential difference measured across the terminals of a source when there is no load attached
equivalent resistance: resistance of a combination of resistors; it can be thought of as the resistance of a single resistor that can replace a combination of resistors in a series and/or parallel…
series: the sum of the individual resistances: R s = R 1 + R 2 + R 3 + ⋯ = ∑ i = 1 N R i R s = R 1 + R 2 + R 3 + ⋯ = ∑ i = 1 N R i
potential drop: loss of electric potential energy as a current travels across a resistor, wire, or other component
potential difference: difference in electric potential between two points in an electric circuit, measured in volts
electromotive force (emf): energy produced per unit charge, drawn from a source that produces an electrical current
emf: the work done per charge to keep the potential difference of a source constant

Chapter 11

Magnetic Forces and Fields

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Summary

Magnets have two types of magnetic poles, called the north magnetic pole and the south magnetic pole. North magnetic poles are those that are attracted toward Earth’s geographic North Pole Charges moving across a magnetic field experience a force determined by F → = q v → × B → . The force is perpendicular to the plane formed by v → and B →

Key terms

magnetic force: force applied to a charged particle moving through a magnetic field
force: perpendicular to the plane formed by v → and B →
north magnetic pole: currently where a compass points to north, near the geographic North Pole; this is the effective south pole of a bar magnet but has flipped between the effective north and south…
south magnetic pole: currently where a compass points to the south, near the geographic South Pole; this is the effective north pole of a bar magnet but has flipped just like the north magnetic pole
helical motion: superposition of circular motion with a straight-line motion that is followed by a charged particle moving in a region of magnetic field at an angle to the field
motor (dc): loop of wire in a magnetic field; when current is passed through the loops, the magnetic field exerts torque on the loops, which rotates a shaft; electrical energy is converted…
velocity selector: apparatus where the crossed electric and magnetic fields produce equal and opposite forces on a charged particle moving with a specific velocity; this particle moves through the…
dees: large metal containers used in cyclotrons that serve contain a stream of charged particles as their speed is increased

Chapter 12

Sources of Magnetic Fields

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Summary

The magnetic field created by a current-carrying wire is found by the Biot-Savart law The strength of the magnetic field created by current in a long straight wire is given by B = μ 0 I 2 π R (long straight wire) where I is the current, R is the shortest distance to the wire, and the constant μ 0 = 4 π… The direction of the magnetic field created by a long straight wire is given by right-hand rule 2 (RHR-2): Point the thumb of the right hand in the direction of current, and the fingers curl in the direction of the… The force between two parallel currents I 1 and I 2 , separated by a distance r , has a magnitude per unit length given by F l = μ 0 I 1 I 2 π r

Key terms

long straight wire: given by B = μ 0 I 2 π R (long straight wire) where I is the current, R is the shortest distance to the wire, and the constant μ 0 = 4 π…
force: attractive if the currents are in the same direction, repulsive if they are in opposite directions
center of a circular loop: given by B = μ 0 I 2 R (at center of loop) , where R is the radius of the loop
Biot-Savart law: an equation giving the magnetic field at a point produced by a current-carrying wire
current-carrying wire: found by the Biot-Savart law
Ampère’s law: physical law that states that the line integral of the magnetic field around an electric current is proportional to the current
diamagnetic materials: their magnetic dipoles align oppositely to an applied magnetic field; when the field is removed, the material is unmagnetized
ferromagnetic materials: contain groups of dipoles, called domains, that align with the applied magnetic field; when this field is removed, the material is still magnetized

Chapter 13

Electromagnetic Induction

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Summary

The induced emf in a closed loop due to a change in magnetic flux through the loop is known as Faraday’s law. The direction of an induced emf always opposes the change in magnetic flux that causes the emf, a result known as Lenz’s law An induced emf from Faraday’s law is created from a motional emf that opposes the change in flux The units for magnetic flux are webers, where 1 Wb = 1 T · m 2

Key terms

Lenz’s law: direction of an induced emf opposes the change in magnetic flux that produced it; this is the negative sign in Faraday’s law
Faraday’s law: induced emf is created in a closed loop due to a change in magnetic flux through the loop
induced emf: short-lived voltage generated by a conductor or coil moving in a magnetic field
magnetic flux: measurement of the amount of magnetic field lines through a given area
induced emf from Faraday’s law: created from a motional emf that opposes the change in flux
units for magnetic flux: webers, where 1 Wb = 1 T · m 2
back emf: emf generated by a running motor, because it consists of a coil turning in a magnetic field; it opposes the voltage powering the motor
electric generator: device for converting mechanical work into electric energy; it induces an emf by rotating a coil in a magnetic field

Chapter 14

Inductance

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Summary

The unit of self-inductance and inductance is the henry (H), where 1 H = 1 Ω · s Current changes in a device induce an emf in the device itself, called self-inductance, ε = - L d I d t , where L is the self-inductance of the inductor and d I / d t is the rate of change of current through it. The self-inductance of a solenoid is L = μ 0 N 2 A l , where N is its number of turns in the solenoid, A is its cross-sectional area, l is its length, and μ 0 = 4 π × 10 -7 T · m/A is the permeability of free space Mutual inductance is the effect of two devices inducing emfs in each other

Key terms

inductance: property of a device that tells how effectively it induces an emf in another device
self-inductance of a solenoid: L = μ 0 N 2 A l , where N is its number of turns in the solenoid, A is its cross-sectional area, l is its length, and μ 0 = 4 π × 10 -7 T · m/A is the permeability of fre
inductor: part of an electrical circuit to provide self-inductance, which is symbolized by a coil of wire
mutual inductance: geometric quantity that expresses how effective two devices are at inducing emfs in one another
henry (H): unit of inductance, 1 H = 1 Ω · s ; it is also expressed as a volt second per ampere
self-inductance: effect of the device inducing emf in itself
unit of self-inductance and inductance: the henry (H), where 1 H = 1 Ω · s
inductive time constant: denoted by τ , the characteristic time given by quantity L/R of a particular series RL circuit

Chapter 15

Alternating-Current Circuits

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Summary

Direct current (dc) refers to systems in which the source voltage is constant Alternating current (ac) refers to systems in which the source voltage varies periodically, particularly sinusoidally An ac current is calculated using the peak current (determined by dividing the peak voltage by the resistance), the angular frequency, and the time For capacitors, we find that when a sinusoidal voltage is applied to a capacitor, the voltage follows the current by one-fourth of a cycle.

Key terms

current: found by dividing the voltage by the resistance
sinusoidal voltage: applied to a capacitor, the voltage follows the current by one-fourth of a cycle
ac current: current that fluctuates sinusoidally with time at a fixed frequency
alternating current (ac): flow of electric charge that periodically reverses direction
capacitive reactance: opposition of a capacitor to a change in current
direct current (dc): flow of electric charge in only one direction
bandwidth: range of angular frequencies over which the average power is greater than one-half the maximum value of the average power
power factor: amount by which the power delivered in the circuit is less than the theoretical maximum of the circuit due to voltage and current being out of phase

Chapter 16

Electromagnetic Waves

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Summary

Maxwell’s prediction of electromagnetic waves resulted from his formulation of a complete and symmetric theory of electricity and magnetism, known as Maxwell’s equations The four Maxwell’s equations together with the Lorentz force law encompass the major laws of electricity and magnetism. The first of these is Gauss’s law for electricity; the second is Gauss’s law for magnetism; the third is Faraday’s law of induction (including Lenz’s law); and the fourth is Ampère’s law in a symmetric formulation that… The symmetry introduced between electric and magnetic fields through Maxwell’s displacement current explains the mechanism of electromagnetic wave propagation, in which changing magnetic fields produce changing…

Key terms

displacement current: extra term in Maxwell’s equations that is analogous to a real current but accounts for a changing electric field producing a magnetic field, even when the real current is present
first of these: Gauss’s law for electricity; the second is Gauss’s law for magnetism; the third is Faraday’s law of induction (including Lenz’s law); and the fourth is Ampère’s law in a
Maxwell’s equations: set of four equations that comprise a complete, overarching theory of electromagnetism
radio waves: electromagnetic waves with wavelengths in the range from 1 mm to 100 km; they are produced by currents in wires and circuits and by astronomical phenomena
gamma ray ( γ ray): extremely high frequency electromagnetic radiation emitted by the nucleus of an atom, either from natural nuclear decay or induced nuclear processes in nuclear reactors and…
infrared radiation: region of the electromagnetic spectrum with a frequency range that extends from just below the red region of the visible light spectrum up to the microwave region, or from 0.74 μ…
microwaves: electromagnetic waves with wavelengths in the range from 1 mm to 1 m; they can be produced by currents in macroscopic circuits and devices
Poynting vector: vector equal to the cross product of the electric-and magnetic fields, that describes the flow of electromagnetic energy through a surface