Topic List for Final
Use this list to point out which types of problems you need to work.
This sheet is NOT useful as a “study” sheet!
A) The Zeroth Law of Thermodynamics
If objects A and B are separately in thermal equilibrium with a third object C, then A and B are in thermal
equilibrium with each other.
Note: This is necessary for the use of a thermometer. Why?
B) Unit Conversion
iii) Kelvin (absolute temperature – why?)
Note: Kelvin must nearly always be used. Why?
C) Thermal Expansion
The change in length (or volume) of an object is directly proportional to the initial length (or volume) and
the change in temperature.
D) Ideal Gas Law
PV nRT Nk BT
II. Heat and First Law
Heat is the transfer of energy across the boundary of a system due to a temperature difference between the
system and its surroundings.
The energy transferred to an object (while it is not changing phase) is proportional to the mass and the
temperature change of the object.
C) Latent Heat
i) A system undergoing a phase change does not change temperature
ii) The energy transferred to an object undergoing a phase change is proportional to the mass that
The work done on a gas in a quasi-static process that takes the gas from an initial state to a final stated is
the negative of the area under the curve on a PV diagram, evaluated between the initial and final states.
i) The work done depends on the process (it is path-dependent)
ii) Drawing PV diagrams is very important
iii) Finding the area under the curve often means integration
iv) Common processes to know are: isothermal, isobaric, isovolumetric, adiabatic
E) The First Law of Thermodynamics
This is simply conservation of energy: the change in energy of a system equals the total amount of energy
transferred into it, Eint Q W . Note: Q is energy transferred into the system and W is work on the
F) Thermal Conduction
The rate of energy transfer from one side of a material to another:
i) is greater when the energy difference is greater
ii) is greater for wider objects (larger area)
iii) is less for longer objects
III. Kinetic Theory of Gases
A) Equipartition Theorem
Each degree of freedom contributes 1 kbT to the energy of the system. There are up to 7 degrees of
freedom for a diatomic molecule:
i) 3 translational (motion in x, y, and z)
ii) 2 rotational (Which axis can it not rotate around?)
iii) 2 vibrational (one is kinetic and the other is the potential energy of the spring)
These modes become active in the listed order as temperature increases. Explain.
How many modes does a monatomic molecule have?
B) Molar Specific Heat
i) Constant Volume: Q nCV T . From the First Law, since no work is done, E Q nCV T .
ii) Constant Pressure: Q nCP T . From the First Law, E nCP T PV .
iii) CP CV R
C) Adiabatic Process
i) Remember, this means Q 0 .
ii) PV const. Note: You should be able to use the Ideal Gas Law with this expression if you do
not know P or V.
IV. Heat Engines and the Second Law
Heat engines work in cycles (i.e. the initial and final states of each cycle are the same). Because E 0 for
a cycle, the work by the engine is simply the heat in minus the heat out.
A) Heat Engines
i) The efficiency is the ratio of the work done by the engine to the heat in.
ii) It is impossible to construct a heat engine that, operating in a cycle, produces no effect other
than the input of energy by heat from a reservoir and the performance of an equal amount of work.
In other words, you cannot convert thermal energy completely into work without some waste
B) Heat pumps and Refrigerators
i) The coefficient of performance is the ratio of the heat in either in or out (depending on operation
mode) to the work done on the pump.
ii) It is impossible to construct a cyclical machine whose sole effect is to transfer energy
continuously by heat from one object to another object at a higher temperature without the input of
energy by work.
C) Carnot Engine
This is the most efficient engine possible. Why? How does it work?
D) Otto Cycle: How does it work?
V. Electric Fields
i) Opposites attract.
ii) The total amount of charge in the universe cannot change.
iii) Charge is quantized.
i) A charged object can induce a charge distribution on a neutral object, even without touching it.
C) Coulomb’s Law
i) Fe k e
ii) A positive force causes the objects to repel.
D) Electric Field
i) Fe q0 E
ii) Fields may be added together like any other vector.
E) Field of continuous charge distribution
F) Electric Field Lines
i) The field points in the direction of the lines
ii) The magnitude of the field is proportional to the density of lines
G) Motion in uniform Field
The motion of a particle simply follows Newton’s Laws.
VI. Electric Flux and Gauss’ Law
A) The electric flux is the number of field lines that go through a surface.
B) Gauss’s Law states that the net flux into (or out of) a closed surface depends only on the amount charge
inside the surface.
C) Gauss’s Law can be used to calculate fields of systems with nice symmetry.
VII. Electric Potential
A) Potential is related to potential energy.
B) V E ds depends only on the component of the distance between A and B along the field line.
C) Potential is a scalar, so it can be added just like 2+3=5.
D) We can only talk about the potential difference between two points (there is no such thing as an
absolute potential unless we arbitrarily choose a zero point). It is, therefore, convenient with point charges
to define V 0 .
VIII. Capacitance and Dielectrics
B) Capacitance gets bigger with area and smaller with plate separation. Therefore:
i) Ceq C1 C2 ... when they are in parallel, because the area is added.
1 1 1
ii) ... when they are in series, because the plate separation is added.
Ceq C1 C2
C) Capacitors are used to store energy.
D) Dielectrics decrease the potential across a capacitor.
IX. Direct Current Circuits
A) Current is defined as charge per time: I .
B) Ohm’s Law: V IR
C) Power: P IV
D) Resistance increases with length and decreases with width (area). Therefore:
i) Req R1 R2 ... when they are in series, because the length increases.
1 1 1
ii) ... when they are in parallel, because the width increases.
Req R1 R2
E) Kirchhoff’s Rules
i) At any junction: I in I out
ii) Around any closed loop: V 0
F) RC circuits
i) The charge (and therefore, the current and voltage) on a capacitor in an RC circuit has an
ii) RC Circuits can be analyzed using Kirchoff’s Rules.
X. Magnetic Fields
A) A magnetic field only exerts a force on a charge if the charge has motion perpendicular to the field.
B) A magnetic field does not do work. Why?
C) In the absence of other forces, a particle in a magnetic field will travel in a circle?
ii) How big?
iii) What frequency?
D) Combining E and B fields is useful for things like:
i) velocity selector
ii) mass spectrometer
E) A current-carrying wire in a magnetic field will experience a force. This can cause a torque on a loop.
i) Moving charges produce magnetic fields.
ii) The field lines wrap around the charge.
iii) The field dies off with the square of the radius (like everything else).
iv) Two current-carrying wires will attract/repel. How?
G) Ampere’s Law:
i) the integral of the field around any loop depends only on the current enclosed.
ii) This can be used to find the magnetic field around wire, toroids, and solenoids.
H) Gauss’s Law – the net magnetic flux into (or out of) any closed surface is zero. Why?
XI. Faraday’s Law
A) A changing magnetic flux will produce an emf.
B) Lenz’s Law: the emf will produce a current that counteracts the change in the magnetic flux.
C) The above can be useful for things like:
i) movement of rods
ii) using solenoids to produce current in loops
iii) generators and motors
iv) Eddy currents (kinetic energy of metal sheets can be transformed into electrical energy)
XII. Electromagnetic Waves
A) Explain Maxwell’s Equations
B) What is light in terms of E and B fields?
C) The Poynting vector points in the direction of wave propagation and determines the intensity. Explain.
XIII. Laws of Optics
i) Some or all light reflects at every surface.
ii) The angle of reflection equals the angle of incidence.
i) Light travels slower in some materials than others (it travels fastest in vacuum).
ii) The higher the index of refraction, the slower light travels. Therefore, light transmitted from:
1) Low n to high n bends toward the normal.
2) High n to low n bends away from the normal.
iii) Snell’s Law: n1 sin 1 n2 sin 2
XIV. Image Formation
For everything that follows, the rules for choice of sign are:
1. p is positive if light originates from the object.
2. R, f, and q are positive if they are on the same side as the outgoing light.
3. M should come out positive if the object is upright.
i) Flat Mirrors
1) Image is upright, M = 1. Why?
2) Image is virtual. Why?
3) p = q. Why?
ii) Spherical Mirrors
Ray diagrams are necessary for explanations. All rays should originate from the same point on the
object (usually the point farthest from the principle axis). Some useful rays to draw are:
1) Ray parallel to principle axis reflects along line from focal point.
2) Ray toward focal point reflects parallel to principle axis.
3) Ray toward center reflects back on itself.
4) Ray that hits mirror on principle axis reflects with same angle to principle axis.
All the reflected rays should intersect at some point. This is where the image of the object sits.
iii) Convex Mirrors
1) Image is upright. Why?
2) Image is virtual. Why?
3) q < f. Why?
iv) Concave Mirrors
1) If p < f, image is upright and virtual. Why?
2) If p > f, image is inverted and real. Why?
Below is a list of additional problems you may work.
Note: This is NOT meant to be an exhaustive list, but a good place to start.
How much heat (in kilocalories) is needed to convert 1 kg of ice into steam?
The air in an automobile engine at 20C is compressed from an initial pressure of 1 atm and a volume of 200 cm 3 to a
volume of 20 cm3. Find the temperature if the air behaves like an ideal gas ( = 1.4) and the compression is
A heat engine absorbs 2500 J of heat from a hot reservoir and expels 1000 J to a cold reservoir. When it is run in reverse,
with the same reservoirs, the engine pumps 2500 J of heat to the hot reservoir, requiring 1500 J of work to do so.
Find the ratio of the work done by the heat engine to the work done by the pump.
If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 24 nC in the figure, what is the magnitude of the total electric
force on q?
A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m. Which of the following integrals is correct
for the magnitude (in N/C) of the electric field at
x = +10 m on the x axis?
A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m3) distributed throughout its
column. Determine the magnitude of the electric field 5.0 cm from the axis of the cylinder.
A particle (charge = +2.0 mC) moving in a region where only electric forces act on it has a kinetic energy of 5.0 J at point
A. The particle subsequently passes through point B which has an electric potential of +1.5 kV relative to point A.
Determine the kinetic energy of the particle as it moves through point B.
What is the total energy stored in the group of capacitors shown if the charge on the
30-µF capacitor is 0.90 mC?
In the figure, if I = 80 mA, determine the resistance R.
What is the magnetic force on a 2.0-m length of (straight) wire carrying a current of 30 A in a region where a uniform
magnetic field has a magnitude of 55 mT and is directed at an angle of 20 away from the wire?
What is the magnitude of the magnetic field at point P if a = R and b = 2 R?
A coil is wrapped with 300 turns of wire on the perimeter of a circular frame (radius =
8.0 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is turned on
perpendicular to the plane of the coil. This field changes at a constant rate from 20 to 80 mT in a time of 20 ms.
What is the magnitude of the induced emf in the coil at the instant the magnetic field has a magnitude of 50 mT?
The switch in the figure is closed at t = 0 when the current I is zero. When I = 15 mA, what is the potential difference
across the inductor?
A 100-kW radio station emits EM waves in all directions from an antenna on top of a mountain. What is the intensity of
the signal at a distance of 10 km?
A fish is 80 cm below the surface of a pond. What is the apparent depth (in cm) when viewed from a position almost
directly above the fish? (For water, n = 1.33.)
A concave mirror has a focal length of 20 cm. What is the position (in cm) of the object if the image is upright and is two
times larger than the object?
TF TC 32 F Fe q0 E
TC T 273.15 E ke 2 r ˆ
L Li T
E k e 2 ri
V Vi T i ri
PV nRT Nk BT dq
E ke 2 r ˆ
Q mcT r
Q mL E EA cos
E E dA
Eint Q W q
W P V f Vi E dA in
V U q 0 E d s q 0 V
W nRT ln i A
P kA qq
dx U ke 1 2
P AeT 4
P 2 1 mv 2
mv 2 3 k BT V ke
2 2 r
Eint 3 Nk BT 3 nRT Q
2 2 C
Eint nCV T V
Ceq C1 C 2
CV 3 R
1 1 1
CP 5 R
2 Ceq C1 C 2
C P / CV
PV const. U Q V 1 C ( V ) 2
2C 2 2
Weng Qh Qc C C0
Weng Qc pE
Qh Qh U p E
eC 1 I
qq I av nqvd A
F12 k e 1 2 2 r
r IR V
( V ) 2
P I 2R
Req R1 R2 R 8.31J / K
I e t /
1 1 1 R 1atm 1.013 105
Req R1 R2 1 E 1cal 4.186J
in out c 3.0 108 m / s
V 0 S EB
0 8.85 1012 C 2 / N m 2
loop 0 4 107 T m / A
q (t ) Q 1 e t / RC P e 1.6 1019 C
E Emax cos(kx t ) ke 8.99 109 N m 2 / C 2
I (t ) e t / RC
R B Bmax cos(kx t )
q (t ) Qe t / RC
I (t ) I 0 e t / RC S max
FB qv B S ave S max
FB q vB sin 1 ' 1
FB IL B n1 sin 1 n2 sin 2
dFB Ids B c
B sin c
U B h' q
r h p
qB 1 1 2 1
p q R f
n1 n2 n2 n1
Ids r ˆ
p q R
4 r 2
FB 0 I1 I 2 1 1 1
l 2a f 1 2
B ds 0 I
B 0 I 0 nI
B B dA
B ds 0 I 0 0
B dA 0
1 e t /