213 P213Fnl
Form
A
PHYSICS - Final Exam
Fall 2007
READ THIS
This exam is worth 100 points. It consists of 25 multiple-choice questions worth 4 points each. Indicate
your answers to the multiple-choice questions in the appropriate spaces on the answer sheet. Choose the
best answer for each question from among the choices provided.
Don't get hung up on the questions. They should only take a few minutes each. If you find yourself
spending more than a few minutes on a question you are probably looking at it the wrong way. You
should skip it for now and come back to it later.
Enter your student number on the scantron sheet prior to answering the first question. You will
not be given time at the end of the exam to do so.
Do not begin the examination until you are instructed to do so.
GOOD LUCK
Read and sign this brief memorandum of confidentiality.
I will not reveal any portion of this test or the answers thereto to anyone who has not yet taken the exam, nor to
anyone who I have reasonable expectation may then communicate the information to someone who has not taken
the exam. I have not solicited in any sense any information from others about any previous administrations of this
exam in this semester. I will hand in this entire printed copy of the exam at the end of the exam session and I will
make no copies of any of the material herein. At the end of the exam I will cease writing when instructed to put
my pencil down and follow all subsequent instructions. I understand that violation of this agreement
constitutes academic dishonesty and is subject to disciplinary action.
______________________________
Sign Name here
______________________________
Print name
Check the appropriate sect # if you wish to have your exam booklet returned to you
Sect 101 - Thu 8:00 AM
Sect 105 - Fri 8:00 AM
Sect 102 - Thu 10:10 AM
Sect 106 - Fri 10:10 AM
Sect 103 - Thu 12:20 PM
Sect 107 - Fri 12:20 PM
Sect 104 - Thu 3:35 PM
Sect 108 - Thu 6:30 PM
Sect 109
Fri 2:30 PM
Failure to sign and return this copy may result in zero credit for this exam.
1. A Carnot heat engine and an irreversible heat engine both operate between the same high temperature and low
temperature reservoirs. They absorb the same energy from the high temperature reservoir as heat. The irreversible
engine:
A. transfers more energy to the low temperature reservoir as heat.
B. cannot absorb the same energy from the high temperature reservoir as heat without violating
the second law of thermodynamics.
C. has the greater efficiency.
D. does more work.
E. has the same efficiency as the reversible engine.
2. Heat is:
A.
B.
C.
D.
E.
energy transferred by virtue of a temperature difference.
energy transferred by macroscopic work.
energy content of an object.
a property objects have by virtue of their temperatures.
a temperature difference.
3. The energy given off as heat by 300 g of an alloy as it cools by 50 C raises the temperature of 300 g of water from
30 C to 40 C in an insulated container. The specific heat of the alloy (in cal/g C) is:
A.
B.
C.
D.
E.
0.20
0.15
0.10
0.015
0.50
Page 1
4. A highly compressed gas that was initially at room temperature is suddenly released into the atmosphere. Describe
what happens.
A. The gas cools down because some of its internal energy is converted into heat.
B. The gas remains at room temperature since it neither does work nor does it exchange heat
with the surroundings.
C. The gas gets hotter because it does work while expanding.
D. The gas cools down because some of its internal energy is converted into the work required
for expansion.
E. The gas gets hotter because it absorbs heat from the surroundings.
5. Three gases, one consisting of monatomic molecules, one consisting of diatomic molecules, and one consisting of
polyatomic molecules, are in thermal equilibrium with each other and remain in thermal equilibrium as the temperature
is raised. All have the same number of molecules. The gases with the least and greatest change in internal energy are
respectively:
A.
B.
C.
D.
E.
polyatomic, monatomic
monatomic, polyatomic
the change in internal energy is the same for each gas
diatomic, monatomic
monatomic, diatomic
6. The heat capacity at constant volume and the heat capacity at constant pressure have different
values because:
A.
B.
C.
D.
E.
the system does work at constant pressure but not at constant volume.
the system does more work at constant volume than at constant pressure.
heat increases the temperature at constant volume but not at constant pressure.
heat increases the temperature at constant pressure but not at constant volume.
the system does work at constant volume but not at constant pressure.
Page 2
7. A train is approaching a highway crossing at a speed of 40 m/s. A driver stopped at the crossing hears the train's
whistle at a frequency of 1000 Hz. What frequency would the driver hear if the train stopped? The speed of sound in
air is 343 m/s.
A.
B.
C.
D.
E.
883 Hz
791 Hz
896 Hz
1132 Hz
1117 Hz
8. An iron stove, used for heating a room by radiation, is more efficient if:
A.
B.
C.
D.
E.
its outer surface is covered with aluminum paint.
its inner surface is covered with aluminum paint.
its outer surface is black.
its outer surface is highly polished.
its inner surface is highly polished.
9. Calculate the change in entropy of a 1 kg block of ice that melts into water at 0C. The latent heat of fusion of ice =
3.33 x 105 J/Kg.
A.
B.
C.
D.
E.
1.22 x 103 J/K
3.33 x 103 J/K
3.33 x 102 J/K
-1.22 x 103 J/K
-3.33 x 103 J/K
Page 3
10. An ideal gas, consisting of n moles, undergoes a reversible isothermal process during which the volume changes from
Vi to Vf . The change in entropy of the thermal reservoir in contact with the gas is given by:
A.
B.
C.
D.
E.
nR ln(Vf - Vi)
nR(Vf - Vi)
nR ln(Vf/Vi)
nR ln(Vi/Vf )
none of the above (entropy cant be calculated for a reversible process)
11. An ideal gas of molecules (of mass 3.3 x 10-27 kg) is at temperature 400 K and density 0.1 kg/m3. The gas is confined
within a cube of side length 2 m. What is magnitude of the average force experienced by one of the walls of this cube
due to the collisions and reflections of this confined gas?
A.
B.
C.
D.
E.
0.021 N
3.2 x 105 N
6.7 x 105 N
4.0 x 105 N
0
12. A cold body (at Tc) is placed in contact with a hot body (Th). During a brief time interval, heat of magnitude dQ is
exchanged between the bodies and negligible work is done. What can be said about the entropy increase ( S) of the
universe, assuming no heat transfer elsewhere?
A.
B.
C.
D.
E.
S > 0, with dQ < 0 for the hot body and dQ > 0 for the cold body.
S = 0, because the process is reversible.
S < 0, because the process is irreversible.
S < 0, because heat flows from the hot to the cold body.
S > 0, with dQ > 0 for the hot body and dQ < 0 for the cold body.
Page 4
13. Water (density = 1.0 103 kg/m3) flows through a horizontal tapered pipe. At the wide end its speed is 4.0m/s. The
difference in pressure between the two ends is 4.5. 103 Pa. The speed of the water at the narrow end is:
A.
B.
C.
D.
E.
4.5m/s
3.4m/s
4.0m/s
2.6m/s
5.0m/s
14. The P-V diagram shows when one mole of He is taken through a reversible cycle. Process ab is constant volume, bc
is isothermal and ca is constant pressure. Use R = 8.314 J/mol.K in the calculations. Calculate the work done by the
gas the during isothermal process bc.
b
Pressure
8p0
P0
P0= 831.4 N/m2
V0 = 1m3
Isothermal
c
a
V0 Volume
A.
B.
C.
D.
E.
8V0
-8730 J
+5820J
0J
+13831 J
-5814 J
Page 5
15. A column of argon is open at one end and closed at the other. The shortest length of such a column that will resonate
with a 200 Hz tuning fork is 42.5 cm. The speed of sound in argon
must be:
A.
B.
C.
D.
E.
340 m/s
85.0 m/s
170 m/s
470 m/s
940 m/s
16. The figure shows a closed cycle for a gas (the figure is not drawn to scale). The change in the internal energy of the gas
as it moves from a to c along the path abc is -210 J. As it moves from c to d, 185 J must be transferred to it as heat.
An additional transfer of 70 J as heat is needed as it moves from d to a. How much work is done by the gas as it
moves from c to d?
A.
B.
C.
D.
E.
-95 J
95 J
45 J
0J
-45 J
Page 6
17. Ultrasound devices used in hospitals utilize very high frequency sound waves to produce images of the internal
structure of the body by observing reflections from surfaces and density gradients. The level of detail that can be
observed is limited to structures no smaller than the wavelength of the ultrasound waves. If ultrasound travels with a
speed of 1500 m/s through the body and we wish to observe structures 1 mm in size, what minimum frequency must
the ultrasound device use?
A.
B.
C.
D.
E.
2.4 x 105 Hz
1.5 x 106 Hz
3.4 x 105 Hz
9.4 x 106 Hz
1.5 x 105 Hz
18. A box contains 6 gas molecules. Microstates are distinguished by whether a given molecule is in the left or right half of
the box. What percentage of time is the gas in the central configuration, where there are 3 molecules in each half of the
box?
A.
B.
C.
D.
E.
81.4%
9.38%
5.00%
85.7%
83.3%
19. If you can breathe while lying flat on the floor with a 400N weight on your chest, roughly how far below the surface of
a body of water could your chest be such that you could continue to breathe through a flexible snorkel tube poking out
of the water? Assume your chest has a frontal area of 0.09m2.
A.
B.
C.
D.
E.
45 cm
35 cm
4.5 cm
4.5 m
60 cm
Page 7
20. When an ideal gas undergoes a slow isothermal expansion:
A.
B.
C.
D.
E.
the increase in internal energy is the same as the work done by the environment.
the increase in internal energy is the same as the energy absorbed as heat.
the increase in internal energy is the same as the work done by the gas.
the work done by the environment is the same as the energy absorbed as heat.
the work done by the gas is the same as the energy absorbed as heat.
21. The Stanford linear accelerator contains hundreds of brass disks tightly fitted into a steel tube (see figure). The
coefficient of linear expansion of the brass is 2.00 10-5 per C. The system was assembled by cooling the disks in
dry ice (-57 C) to enable them to just slide into the close-fitting tube. If the diameter of a disk is 80.00 mm at 43 C,
what is its diameter in the dry ice?
A.
B.
C.
D.
E.
80.16 mm
79.84 mm
78.40 mm
79.68 mm
none of these
22. A certain wire stretches 1 cm when a force F is applied to it. The same force is applied to a wire of the same material
but with twice the diameter and twice the length. The second wire stretches:
A.
B.
C.
D.
E.
0.25 cm
1 cm
0.5 cm
4 cm
2 cm
Page 8
23. A sample of argon gas (molar mass 40 g) is at four times the absolute temperature of a sample of hydrogen gas (molar
mass 2 g). The ratio of the rms speed of the argon molecules to that of the hydrogen is:
A.
B.
C.
D.
E.
1/5
5
5
1
1
5
24. An ideal engine consists of an isothermal expansion at 600 K and an isothermal compression at 300 K. If the engine is
to produce 1000 J of work each cycle, the heat it has to absorb from the heat reservoir at high temperature is
A.
B.
C.
D.
E.
4000 J
2000 J
1000 J
3000 J
5000 J
25. You are standing midway between two speakers, A and B, which are 8.0 m apart. Each speaker emits sound waves,
in phase, with a frequency of 1 kHz. How far must you walk, if at all, directly toward speaker A in order to find a
point of destructive interference?
A.
B.
C.
D.
E.
34.3 cm
0m
17.2 cm
2.0 m
8.6 cm
Page 9
Physics 213
Final Exam
Fall 2007
IMPORTANT:
Please enter your ID number and your section number onto the scantron form provided.
Constants:
Young's Modulus for aluminum: E = 70x109 N/m2
Young's Modulus for brass: E = 91x109 N/m2
Young's Modulus for steel: E = 200x109 N/m2
Shear Modulus for wood: G = 5x106 N/m2
Bulk Modulus for lead: B = 7.7x109 N/m2
Bulk Modulus for water: B = 2.0x109 N/m2
Bulk Modulus for steel: B = 170x109 N/m2
1 atm = 1.01 x 105 Pa
Density of water = 1000 kg/m3
Density of wood = 700 kg/m3
Density of air = 1 kg/m3
Coefficient of linear expansion of steel
= 11 x 10-6 /K
Thermal conductivity of steel k = 14 W/mK
Thermal conductivity of copper k = 401 W/mK
Thermal conductivity of white pine k = 0.11 W/mK
Specific heat of water = 1 cal/gK or 4186 J/kgK
Specific heat of aluminum = 900 J/kgK
Latent heat of fusion for water = 80 cal/g or 333 kJ/kg
Latent heat of Vaporization for water = 540 cal/g or 2256 kJ/kg
g = 9.8 m/s2
Speed of sound = 343 m/s
R = 8.31 J/mol K
NA = 6.02 x 1023
kB = 1.38 x 10-23 J/K
1 cal = 4.186 J
c = 3 x 108 m/s
Tc = T - 273.15
TF = 9/5 Tc + 32
Equations:
F
L
=E
A
L
=
F
x
=G
A
L
m
V
p+
v = /T = f
=
V
V
F
A
p = p0 + gh
12
v + gh = const.
2
= vT
p=
Av = const.
p=B
y(x,t) = ymsin(kx-t)
2
= 2f
T
v=
k=
P=
2
1
v 2 y 2
m
2
1
1
sin + sin = 2 sin ( + ) cos ( )
2
2
y(x,t) = y1 (x,t) + y2 (x,t)
1
1
cos + cos = 2 cos ( + ) cos ( )
2
2
y1(t ) = y m sin( kx t )
Interference:
y2 (t ) = ym sin(kx t + )
1
1
y (t ) = y1 + y 2 = 2 ym cos sin kx t +
2
2
= m(2 )
Constructive:
1
Destructive: = m + (2 )
2
m=0,1,2, ...
y1( x , t ) = ym sin(kx t )
Standing Waves:
y2 (x, t ) = y m sin(kx + t )
y (x , t ) = y1 + y2 = [2 ym sin kx ]cos t
Nodes: x =
n
2
fn =
nv
2L
v=
B
s(x,t) = smcos(kx-t)
I=
= (10dB)log
1
Antinodes: x = n +
2 2
n = 0,1,2,...
I
I0
Constructive: L = m
P1
22
= v sm
A2
I 0 = 10 12 W/m 2
1
Destructive: L = m +
2
n = 0,1,2,...
p = p m sin(kx t )
P
P
I = s = s2
A 4r
=
L
2
fn =
nv
2L
fn =
nv
4L
Beats: s = s1 + s2 = [2 sm cos t ]cost
=
f=
1
( 1 2 )
2
=
(v vD ) f
(v m vS )
1 2
1
(1 + 2 )
2
fbeat = f1 f2
+ vD: toward S
- vD: away from S
+ vS: away from D
- vS: toward D
V = V T
= 3
L = LT
Q = cm T
Q =mL
Vf
W = p dV
Eint = Q W
H=
Vi
Pr = AT 4
K=
vrms =
=
CV = Cp R
3 RT
M
kB =
R
NA
Eint = nCV T
CV
=
QC
W
=1
QH
QH
K=
dQ
TC
(ideal refrigerator) dS = r
T
TH TC
K=
2N
K
3V
Cp
pV = const.
For adiabatic processes:
P=
3
kB T
2
1
2
mv rms
2
1
2 d 2 N / V
K=
=
PV = nRT
Q
dT
= kA
t
dx
QC
QC
=
Won
QH QC
S = S f Si = nR ln
Vf
T
+ nCv ln f
Vi
Ti
TV
= 1
1
= const.
TC
(ideal engine)
TH
f
f
dQr
T
i
S = dS =
i
Answer Key for Test "P213FnlFa07.tst", 10/11/2007
No. in
No. on
Q-Bank
Test
20.Sec04 16 1
18.Sec06 1 2
18.Sec07 8 3
19.Sec03 6 4
19.Sec08 19 5
18.Sec07 5 6
17.Sec09 23 7
18.Sec11 10 8
20.Sec03 5 9
20.Sec02 11 10
19.Sec03 2 11
20.Sec03 4 12
14.Sec10 24 13
19.Sec03 11 14
17.Sec07 14 15
18.Sec10 3 16
16.Sec05 16 17
20.Sec08 2 18
14.Sec07 14 19
19.Sec11 9 20
18.Sec05 4 21
12.Sec07 14 22
19.Sec04 12 23
20.Sec05 8 24
17.Sec05 5 25
Correct Answer
A
A
A
D
B
A
A
C
A
D
C
A
E
D
A
C
B
A
A
E
B
C
E
B
E
Page 1