PHY205s13 Final Exam part 1:
Name: __________________________
Constants: R=8.314J/mole·K k=1.38×10-23J/K NA=6.022×1023 ( to convert: 4.184J/cal, 1atm=1.01×105Pa)
For water: Lf=80cal/gram Lv=540cal/gram c=1cal/gm· 0C
___ 1. A container measures 3 m × 4 m × 2 m and is at 20°C and 1 atm. Assuming that it has only the
monatomic gas He, the amount of kinetic energy in the gas is
A) 3.6 MJ B) 6.1 MJ C) 0.25 MJ D) 0.41 MJ E) none of the above
___ 2. A volume of an ideal gas goes through a temperature change from 20ºC to 60ºC. The relation between
the average molecular kinetic energy at 20ºC (K1) and that at 60ºC (K2) is
A) K1 = K2
D) K1 = 0.88 K2
B) K1 = 0.33 K2
E) K1 = 1.14 K2
C) K1 = 3 K2
___ 3. Two liquids, A and B, are mixed together, and the resulting temperature is 22°C. If liquid A has mass m
and was initially at temperature 35°C, and liquid B has mass 3m and was initially at temperature 11°C,
calculate the ratio of the specific heats of A divided by B.
A) 0.85 B) 2.5 C) 1.2 D) 0.45 E) 0.94
___ 4. A 2.0-kg mass of iron (specific heat = 0.12 kcal/kg · Cº) at a temperature of 430ºC is dropped into 48
kg of water. The water is initially at a temperature of 10ºC. With no heat losses to the surroundings,
the equilibrium temperature of the iron and water is approximately
A) 10.5ºC B) 18.2ºC C) 19.6ºC D) 30.4ºC E) 33.3ºC
___ 5. If the heat capacities of both ice and steam are 0.5 cal/g · Cº, the quantity of heat required to change 1
g of ice at –10ºC to steam at 120ºC is approximately
A) 750 cal B) 735 cal C) 630 cal D) 620 cal E) 555 cal
Use the following to answer question 6:
___ 6. The graph shows the temperature of a 1.0-g sample of material as heat is added to it. The material is
initially a solid at 10ºC. The pressure remains constant, and there is no chemical change. The melting
point temperature is
A) 10ºC B) 100ºC C) 60ºC D) 73ºC E) None of these is correct.
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___ 7. An ideal gas undergoes a cyclic process in which total (positive) work W is done by the gas. What
total heat is added to the gas in one cycle?
A) W B) –W C) zero D) 2W E) W/2
___ 8. The percentage of mechanical energy that can theoretically be turned into heat energy according to the
first law of thermodynamics is
A) 100% B) 90% C) 75% D) 50% E) 0%
___ 9. A gas has a density X at standard temperature and pressure. What is the new density when the absolute
temperature is doubled and the pressure increased by a factor of 3?
A) (2/3)X B) (4/3)X C) (3/4)X D) (6)X E) (3/2)X
___ 10. An ideal gas whose original temperature and volume are 27ºC and 0.283 m3 undergoes an isobaric
expansion. If the final temperature is 87ºC, then the final volume is approximately
A) 0.0340 m3 B) 0.0552 m3 C) 0.170 m3 D) 0.340 m3 E) 1.45 m3
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Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
A
D
B
A
B
E
A
A
E
D
1.5nRT=1.5PV=1.5(1.01×105Pa)(24m3)=3.64×106J
K1/K2=T1/T2=(273+20)K/(273+60)K=.88
mcA(35-22)=3mcB(22-11)
cA/cB=2.54
2kg(.12kcal/kg·K)(430oC-T)=48kg(4.184kcal/kg·K)(T-10oC), T=10.5oC
1g[(.5cal/g· oC)(10oC)+80cal/g+(1cal/g· oC)(100oC)+540cal/g+(.5cal/g· oC)(20oC)]=735cal
melting point is 50oC, thus none
Q=∆Ein+Wby=0+W=W
100%
X=(N/V)1=P1/kT1 (N/V)2=3P1/k2T1=3(N/V)1/2=3X/2
V1/T1=V2/T2 .283m3/(273+27)K=V2/(273+87)K V2=.3396m3
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PHY205s13 Final Exam part 2:
Name: __________________________
___ 1. A steam engine operates between a high and low temperature of 550°C and 180°C. If the steam engine
operates at 40% of its theoretical maximum efficiency and does work at a rate of 1000 W, calculate
how much heat is discharged per hour.
A) 0.8 MJ/hr B) 2.8 MJ/hr C) 3.4 MJ/hr D) 16 MJ/hr E) 12 MJ/hr
___ 2. In a nuclear power plant, heat is taken from the reactor core at 300ºC, work is done to drive an electric
generator, and heat is rejected to the environment at 40ºC. What is the maximum possible thermal
efficiency of this system?
A) 13% B) 27% C) 46% D) 55% E) 87%
___ 3. Entropy is related to probability. An isolated system moves toward
A) a highly ordered state of low probability and high entropy.
B) a highly ordered state of high probability and high entropy.
C) a state of low order, high probability, and high entropy.
D) a state of low order, low probability, and high entropy.
E) a state of low order, high probability, and low entropy.
___ 4. A quantity of heat is removed from a hot reservoir at absolute temperature T and then is added to a
cold reservoir at absolute temperature T/2. The cold reservoir experiences an entropy increase S.
What is the change in the entropy of the universe?
A) S B) zero C) –S D) 2S E) S/2
___ 5. A certain blackbody radiates 100 W at a temperature of 2000 K. How much power would this body
radiate at 3000 K?
A) 150 W B) 225 W C) 338 W D) 506 W E) 759 W
___ 6. Two types of wall separate a refrigerated room from the rest of a building. Wall 1 has half the thermal
conductivity of wall 2. Wall 2 is half as thick as wall 1. The two walls have the same area. The rate
of heat flow through wall 2 compared with the rate of heat flow through wall 1 is
A) four times greater.
D) half as great.
B) twice as great.
E) one-quarter as great.
C) the same.
___7. A traveling wave passes a point of observation. At this point, the time between successive
crests is 0.2 s. Which of the following statements can be justified?
A)
The wavelength is 5 m.
B)
The frequency is 5 Hz.
C)
The velocity of propagation is 5 m/s.
D)
The wavelength is 0.2 m.
E)
There is not enough information to justify any of these statements.
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___8. You have a rope that is 10 m long and has a mass of 0.2 kg. In addition, you have an oscillator
that can generate a 5 Hz wave with an amplitude of 10 cm. What should the tension in the rope be if
you need to transmit 10 W of power along the rope?
A) 102 N B) 205 N C) 320 N D) 51 N E) 250 N
___9. A jet engine emits a whine of frequency 3000 Hz. When the engine is moving directly away
from an observer at half the speed of sound, an observer hears a frequency of
A) 1000 Hz
B) 1500 Hz
C) 2000 Hz
D) 4500 Hz
E) 6000 Hz
___10. A string under tension carries transverse waves traveling at speed v. If the same string is
under four times the tension, what is the wave speed?
A) v
B) 2v
C) v/2
D) 4v
E) v/4
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Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
D ε=.4(1-[273+180]K/[273+550]K)=.1798=W/(Qc+W) Qc=4.56W=4.56(1000J/s)(3600s)=16.4MJ
C 1-(273+40)/(273+300)=.458
C a state of low order, high probability, and high entropy
E ∆Sc=Q/(T/2)=2Q/T≡S, ∆Sh=-Q/T=-S/2, ∆Sc+ ∆Sh=S-S/2=S/2
D 100W(3000K/2000K)4=506W
A Q1/t=(κ2/2)A∆T/L1 Q2/t= κ2A∆T/(L1/2)=4Q1/t
B The frequency in Hz is inverse of the time between the crests
B The power 10 W = (1/2) v (0.2 kg / 10 m) (0.1 m)2 (2π × 5 s-1)2 and v = 101 m/s. The tension FT =
µv2 = 205 N
9. C The observer hears the frequency fo = fs × vs/ (vs + vs/2) = (2/3) vs = 2000 Hz
10. B The speed is proportional to the square root of tension
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PHY205s13 Final Exam part 3 + Chapter 33:
Name__________________________________
____1. If two identical waves with a phase difference of 3π are added, the result is
A)
a wave with the same frequency but twice the amplitude.
B)
a wave with the same amplitude but twice the frequency.
C)
a wave with zero amplitude.
D)
a wave with an intensity equal to the sum of the intensities of the two waves.
E)
This problem cannot be solved without knowing the wavelengths of the two waves.
____2. The fundamental frequency of a vibrating string is f1. If the tension in the string is doubled, the
fundamental frequency becomes A) f1/2 B) f1 / 2 C) f1 D) 2 f1 E) 2f1
___3. A string fixed at both ends is vibrating in a standing wave. There are three nodes between the ends of
the string, not including those on the ends. The string is vibrating at a frequency that is its
A) fundamental. B) 2-d harmonic. C) 3-d harmonic
D) 4-th harmonic.
E) 5-th harmonic
____4. If the refractive index of glass is 1.5 and the refractive index of a particular liquid is 1.38, then
calculate the value for the critical angle of total internal reflection at the liquid-glass interface.
A) 23.1°
B) 66.9°
C) 82.8°
D) 42.6°
E) None of these is correct.
____5. A ray of light strikes a slab of glass (n = 1.55) at an angle of incidence of 35º. The angle of
refraction in the glass is
A) 22º
.
.
B) 63º
C) 27º
D) 90º
E) None of these is correct.
____6. A ray of light passes from air into water, striking the surface of the water with an angle of incidence
of 45º . Which of the following four quantities change as the light enters the water: (1) wavelength,
(2) frequency, (3) speed of propagation, and (4) direction of propagation?
A) 1 and 2 only
B) 2, 3, and 4 only
C) 1, 3, and 4 only
____7. How far must a man's face be located in front of a concave spherical shaving mirror of radius 120
cm for him to see an erect image of his face four times its real size?
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A) –75 cm
B) 45 cm
C) 75 cm
D) 90 cm
E) 150 cm
____8. When a real object is placed just inside the focal point F of a diverging lens, the image is
A)
virtual, erect, and diminished.
B)
real, inverted, and enlarged.
C)
real, inverted, and diminished.
____9. A positive lens has a focal length f. The only way to get a magnification of –1 is to
A)
place a real object at the focal point.
B)
place a real object at a distance 2f from the lens.
C)
place a virtual object at a distance 2f from the lens.
D)
Magnifications can never be negative.
E)
None of these is correct.
____10. Your left eye can focus on objects a great distance away but cannot focus on objects that are
closer than 125 cm to it. The power of the lens in diopters that you need for normal near vision (25 cm) is
A)
+0.8 diopters B) +3.2 diopters C) +4.0 diopters
Page 8
D)
Chapter 33
____1. Which, if any, of the following conditions is not necessary for the light waves from two sources to be
coherent?
A)
They must have the same frequency.
B)
They must have the same amplitude.
C)
They must have the same wavelength.
D)
They must have a constant phase difference.
E)
All of these conditions are necessary.
____2. Two optically flat plates lie one on top of the other. A sheet of paper 0.1 mm thick is inserted between the
plates at one edge. When the plates are illuminated by light of wavelength 589 nm, the number of interference
fringes observed by reflected light is approximately
A) 470
B) 340
C) 294
D) 170
E) 123
____3. A single-slit diffraction pattern is displayed on a screen 0.900 m away from the slit. If the wavelength of the
light is 600 nm and the slit is 1.50 × 10–4 m wide, the distance from the first minimum on the right to the first
minimum on the left is
A) 0.164 mm
B) 1.83 mm
C) 3.99 mm
D) 7.20 mm
E) 7.98 mm
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Unit 3, Chapters 16, 31, 32 + Ch.33
1.
If two identical waves with a phase difference of 3π are added, the result is
A) a wave with the same frequency but twice the amplitude.
B)
a wave with the same amplitude but twice the frequency.
C)
a wave with zero amplitude.
D)
a wave with an intensity equal to the sum of the intensities of the two waves.
E)
This problem cannot be solved without knowing the wavelengths of the two waves.
Ans:
2.
C
The fundamental frequency of a vibrating string is f1. If the tension in the string is doubled, the
fundamental frequency becomes
A) f1/2
Ans:
3.
C) f1
D)
2 f1
E) 2f1
D The fundamental frequency is proportional to the square root of tension
B)
second harmonic.
C)
third harmonic.
E)
fifth harmonic.
D Three nodes on the string means that the string is four half-wavelengths long
If the refractive index of glass is 1.5 and the refractive index of a particular liquid is 1.38, then calculate the
value for the critical angle of total internal reflection at the liquid-glass interface.
A) 23.1° B) 66.9° C) 82.8° D) 42.6° E) None of these is correct.
Ans:
5.
f1 / 2
A string fixed at both ends is vibrating in a standing wave. There are three nodes between the ends of the
string, not including those on the ends. The string is vibrating at a frequency that is its
A) fundamental.
D) fourth harmonic.
Ans:
4.
B)
B sin θc = n2/n1 = 1.38/1.5 = 0.92, θc = 66.9°
A ray of light strikes a slab of glass (n = 1.55) at an angle of incidence of 35º. The angle of refraction in the
glass is
A) 22º
B) 63º
C) 27º
D) 90º
E) None of these is correct.
Page 10
Ans:
A n1 sin θ1 = n2 sin θ2 , sin θ2 = n1 sin θ1/n2 = sin 35º/1.55 = 0.37
6.. A ray of light passes from air into water, striking the surface of the water with an angle of incidence of 45º. Which
of the following four quantities change as the light enters the water: (1) wavelength, (2) frequency, (3) speed of
propagation, and (4) direction of propagation?
A)
1 and 2 only
B)
2, 3, and 4 only
C)
1, 3, and 4 only
Ans:
C
7.
How far must a man's face be located in front of a concave spherical shaving mirror of radius 120 cm
for him to see an erect image of his face four times its real size?
A) –75 cm B) 45 cm C) 75 cm D) 90 cm E) 150 cm
Ans:
8.
A)
B y’/y = 4 = -s’/s; s’ = - 4s; 1/s – 1/4s = 2/r -> s = (3/8)r = 45 cm
When a real object is placed just inside the focal point F of a diverging lens, the image is
virtual, erect, and diminished.
B)
real, inverted, and enlarged.
C)
real, inverted, and diminished.
Ans:
A
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9.
A)
A positive lens has a focal length f. The only way to get a magnification of –1 is to
place a real object at the focal point.
B)
place a real object at a distance 2f from the lens.
C)
place a virtual object at a distance 2f from the lens.
D)
Magnifications can never be negative.
E)
None of these is correct.
Ans:
B m = -1 = y’/y = - s’/s -> s’= s; 1/s’ + 1/s = 2/s = 1/f -> s = 2f
10. Your left eye can focus on objects a great distance away but cannot focus on objects that are closer
than 125 cm to it. The power of the lens in diopters that you need for normal near vision (25 cm) is
A) +0.8 diopters
D) –4.0 diopters
B)
+3.2 diopters
C)
+4.0 diopters
Ans:
E)
None of these is correct.
B The lens should form a virtual image at 1.25 m if the object is placed 0.25 m from the eye. P = 1/f = 1/0.25
– 1/1.25 = 3.2
Chapter 33
Which, if any, of the following conditions is not necessary for the light waves from two sources to be coherent?
A)
They must have the same frequency.
B)
They must have the same amplitude.
C)
They must have the same wavelength.
D)
They must have a constant phase difference.
E)
All of these conditions are necessary.
Ans:
B
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Two optically flat plates lie one on top of the other. A sheet of paper 0.1 mm thick is inserted between the plates at
one edge. When the plates are illuminated by light of wavelength 589 nm, the number of interference fringes
observed by reflected light is approximately
A) 470
B) 340
C) 294
D) 170
E) 123
Ans: B The number of the last fringe at the far edge where the paper is inserted is
-3
-9
m = 2t/λ = 2×10 /589×10 = 340.
A single-slit diffraction pattern is displayed on a screen 0.900 m away from the slit. If the wavelength of the light is
–4
600 nm and the slit is 1.50 × 10 m wide, the distance from the first minimum on the right to the first minimum on
the left is
A) 0.164 mm
Ans:
B) 1.83 mm
C) 3.99 mm
D) 7.20 mm
E) 7.98 mm
D The distance between these two minima is double the distance to the first minimum, i.e.
2y1 = 2L tan(sin-1(λ /a)) = 2 0.9 tan(sin-1(6×10-7/1.5×10-4)) m = 7.2 mm
Page 13