Keep This Page Attached to the Exam
Physics 7A (A/B) Winter 2007 Final Cover Sheet
INSTRUCTIONS:
Right now, as soon as you get this part of the exam:
1. Fill in this cover sheet completely.
2. Put your name, DL section number, and the first three letters of your last name on each
page of the exam. This is important!!!! The pages are separated for grading!
3. Count the pages of the final exam. There should be 9 pages total, including problems
and questions on pages 2 - 8. If you find this is not the case, inform the proctor
IMMEDIATELY. It is your responsibility to have a complete exam -- any missing
problems or questions will be given the lowest grade.
Remember:
*
You will probably not know the answer or immediately know what to do when you first read a question.
You are being tested on your ability to think. So think about how you can apply the general models and
methods you have learned to the particular situations discussed in the questions.
Then do it. *
Do Your Own Work!
We automatically report anyone suspected of cheating to Student Judicial Affairs!
I certify by my signature below that I have read the above and below instructions and that I will abide by
the UC Davis Code of Academic Conduct. This includes
• not copying from anyone else’s final
• not letting any other student copy from my final
• not discussing this final exam with any student who has not yet taken it, nor providing any information,
written or oral, that might get to a student who has not yet taken it.
Circle the room you are taking this final exam in:
1100 Social Sciences
198 Young Hall
158 Roessler
Count from the front row which number (or letter) row you are sitting in: Enter the row number/letter here:
Name (Print Clearly):
Last
DL Section Number:
first
(This is a number between 1 and 11) Lecture Section:
(A, B)
Signature:______________________________________
You may begin the final as soon as you have completed this and the following 7 pages: put your name, DL
section number, and first three letters of your last name on this and each of the following six pages.
Tear off the formula page stapled to the back of the exam (page 9); remove it from the exam in order to use it
(you do not have to return the formula sheet).
7A-1 W07 Final
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Problem 1. (14% of exam)
Assume that we have two separate physical systems: one mole of Gas 1 and one mole of Gas 2. Each gas
undergoes a reversible, constant-pressure process that takes it from an initial state to a final state, as
represented in the two state diagrams below.
The two gases have the same initial values of H and T (Ha and T1), and the same final values of T (T2), but the
final value of H is greater for the Gas 2 (Hc > Hb). Assume that both gases behave as ideal gases.
Enthalpy (H)
Enthalpy (H)
Gas 1
Gas 2
Hc
Hb
Ha
final
final
Ha
initial
T1
T2
Temperature (T)
initial
T1
T2
Temperature (T)
1a. Compare the magnitudes and direction (in/out) of the heat transferred for the two processes. You must
explain your response!
1b. A student says that Gas 1 is N2 (nitrogen) and Gas 2 is He (helium). Explain if this is possible using the
concept of modes.
7A-1 W07 Final
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Problem 2 (16%)
2a. A solid substance has a structure that allows each atom to have 6 nearest
neighbors (called simple cubic packing: 4 nearest neighbors in the same
plane, one above, and one below). Calculate the bond energy for 2
moles of this solid. Refer to PE (r) plot for more information. The
vertical scale of the graph is in units of 10-21 Joules. Briefly comment
whether your estimation of bond energy is an underestimation,
overestimation, or neither. Explain.
Horizontal scale: units of 10-10 m
m
Lennard-Jones PE(r) for
an atom-atom pair
2b. A heat pack (HP), like the ones in DL, is initially in liquid phase at room temperature. The HP is then
triggered and as it becomes a solid it gives off heat to the environment. The final state of the HP is a solid
at room temperature. Describe the change in entropy (S) for the HP from a statistical (microstates) view.
Is S for the HP positive, negative, or zero?
7A-1 W07 Final
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Problem 3. (16% of exam)
3a. Inside a sealed, insulated container (where no work or heat can be exchanged with the environment) are
three moles of neon gas [Ne(g); 20.2 g/mole] containing 14, 965 J of thermal energy, and in a separate
sealed, insulated container are two moles of ammonia gas [NH3(g); 17 g/mole] containing 23,279 J of
thermal energy. Both gases can be considered ideal, and both are at 400 K. Which gas molecule, if either,
has the greater average translational kinetic energy? Briefly, but completely, explain your answer.
3b. In an experimental measurement of heat capacity, the internal energy of an unknown quantity of an ideal
gas increases by 561 Joules when 925 Joules of heat are added to the gas (no heat is allowed to leave the
gas). The initial temperature of the gas (just before the heat is added) is 250 K. The final temperature of
the gas is 265 K. There are no phase changes during this process. This is either a measurement of C V or of
CP. From the given information, which is it? Explain.
7A-1 W07 Final
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Problem 4. (16%)
A mass (m = 0.20 kg) has an initial horizontal speed of 3.0 m/s. The mass slides through a distance of 30 cm
across a horizontal surface where it collides with a stationary, horizontal spring (which has spring constant,
k = 180 J/m2). The spring is initially at its equilibrium position (x = 0 cm). Its final position is the compressed
position as seen in the figure below (x = xfinal). [Watch your units!].
The mass is not attached to the spring. The mass compresses the spring and momentarily comes to rest.
Initial:
v = 3.0 m/s
x = 0 cm
x = -30 cm
Final:
v = 0 m/s
xfinal = + ? cm
Assume that the horizontal surface is frictionless and that no energy is transferred to or from thermal systems.
4a. Write out an expression for ETOT in terms of the energy systems, and then find its value in units of Joules.
4b. Find the final position of the spring, xfinal.
4c. On the axis below sketch a graph of the kinetic energy (KE) of the block as a function of the block's
distance from the equilibrium position of the spring (which is at x = 0 cm), and sketch the potential energy
of the spring (PES) as a function of the block's distance from x = 0 cm. Make your plot go from x = - 30
cm to xfinal. Clearly identify the two kinds of energies (KE & PE S) on your graph, and label all axes with
values. On your plot, clearly show where the KE max and the PES, max are.
Energy (Joules)
x=0
x (cm)
Distance from
equilibrium
(cm)
7A-1 W07 Final
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Problem 5. (8% of exam)
Calculate the binding energy (BE) of a Polonium-210 nucleus (84210Po). The mass of the 84210Po nucleus is
209.93 u (excluding electrons). Make it clear to the grader what the steps are in your calculation.
7A-1 W07 Final
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Problem 6. (16% of exam)
6a. An ideal gas is taken from state A to state B by an adiabatic (Q = 0) process as
shown in the PV state diagram at right. How does the temperature at state B
compare to the temperature at state A? Explain the steps of your answer.
P

A
B
V
6b. A student who has not taken Physics 7A says that bonds store energy and release that energy when they
break. Using any relevant concepts, models, and/or examples, explain whether you agree or disagree. Use
only the space provided here.
7A-1 W07 Final
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Problem 7. (14%)
Heat is added to a sample of material at a constant rate. The sample starts off as a solid at a temperature of
60 K, and as heat is added the sample melts, and then vaporizes. The temperature as a function of energy
added to the sample is shown on the plot.
T [K]
300
K
200
K
100
K
60 K
0J
150 J
450 J
1050 J
1500 J
1800 J
Energy
added [J]
7a. From the information provided, determine which is greater, the heat of vaporization or the heat of melting?
Explain how you know.
7b. From the information provided, determine in which phase, solid, liquid or gas, the sample has the greatest
heat capacity? Explain and support your answer with calculations.
7A-1 W07 Final
p9
Physics 7A-A/B Winter 2007 Final Exam Formulae and Constants
Separate this sheet from the exam packet. You may keep this page after the final.
1
2
m v 
2
∆U = Q + W
∆U = ∆Eth + ∆Ebond + ∆Eatomic + ∆Enuclear
H = U + PV
∆H = Q (at constant pressure)
G = H + TS
PEgrav  mgy
G = H - TS (at constant T & P)
∆G < 0 if spontaneous
∆G = 0 if in equilibrium
∆G > 0 if not spontaneous
gEarth  10 N/kg = 10 m/s2
W = –  Fdr  Favg∆r
kB = 1.38 x 10-23 J/K
KE 
PEspring 
1
2
kx 
2
NA = 6.02 x 1023 molecules (or atoms)/mole
R = NA kB = 8.31 J / K•mol
W = –  PdV  Pavg∆V
Q =  TdS  Tavg∆S
Patm = 1 atm = 105 Pa (= 105 J/m3)
Q =  CdT  C∆T
1,000 g = 1 kg
4.18 J = 1.0 cal
PV = nRT
1 kcal = 1000 cal
Suniverse  0
1 kJ = 1,000 J = 1000 Nm = 1000 kgm2/s2
S  k B ln
Ssystem
1 W = 1 J/s
Q

T
1 N = 1 kgm/s2
1 eV = 1.602 x 10-19 J
∆Ssystem = C ln(Tf / Ti)
1 u = 1 amu = 1.6605 x 10-27 kg = 1 g/mole
C = Q/∆T
A( nucleons)
Z(protons)
C = cmassm = cmn
mproton = 1.007276 u
CV = dEth/dT
Cp = Cv + nR
X(element)
or
cp = cv + R
mneutron = 1.008665 u
Ethermal/mode = 1/2kBT (on average)
E = mc2
Ethermal = (# of modes/molecule) 1/2nRT
c = 3 x 108 m/s (speed of light)
c2 = 932 MeV/amu
Ethermal/mole = NA (# of modes/molecule) 1/2kBT
Ethermal  CT
Ebond = all pairs (PEpair-wise)
Ebond  -N(# nn/2) or  -nNA(# nn/2)
nn = nearest neighbors pairs
|Ebond| =  ∆mHvap 
|Ebond| =  ∆mHmelt 
Area of rectangle = heightbase
Area of triangle = (1/2)heightbase
Area of parallelogram = heightbase
Prob (state) =  State / Total
7A-1 W07 Final