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Physics 207: Lecture 30, Pg 1
Lecture 30Goals:Goals:
• Review for the final.Review for the final.
• Final exam on Monday, Dec 20, at 5:05 pm, at Sterling 1310, Graham 19.
• HW 11 due tonight.
Physics 207: Lecture 30, Pg 2
The figure shows a snapshot graph D(x, t = 2 s) taken at
t = 2 s of a pulse traveling to the left along a string at a speed of 2.0 m/s. Draw the history graph D(x = −2 m, t) of the wave at the position x = −2 m.
Waves
Physics 207: Lecture 30, Pg 3
History Graph:
2 3 64 7time (sec)
2
-25
Physics 207: Lecture 30, Pg 4
A concert loudspeaker emits 35 W of sound power. A small microphone with an area of 1 cm2 is 50 m away from the speaker.
What is the sound intensity at the position of the microphone?
How much sound energy impinges on the microphone each second?
Physics 207: Lecture 30, Pg 5
R
I Psource4R2
Psource=35 WR=50 m
The power hitting the microphone is:
Pmicrophone= I Amicrophone
Physics 207: Lecture 30, Pg 6
Intensity of sounds
If we were asked to calculate the intensity level in decibels:
10log10
I
I0
I0: threshold of human hearing
I0=10-12 W/m2
Physics 207: Lecture 30, Pg 7
Suppose that we measure intensity of a sound wave at two places and found them to be different by 3 dB. By which factor, do the intensities differ?
1 10log10
I1I0
2 10log10
I2I0
1 2 10log10
I1I2
3
I1I2
100.3 2
Physics 207: Lecture 30, Pg 8
Engines
For the engine shown below, find, Wout, QH and the thermal efficiency. Assume ideal monatomic gas.
Pi
4Pi
Vi 2Vi
Q=90J
Q=25J
Physics 207: Lecture 30, Pg 9
First, use the ideal gas law to find temperatures
Pi
4Pi
Vi2Vi
Q=90J
Q=25JTi
4Ti8Ti
2Ti
From the right branch, we have:
nCVΔT=90 J
n(3R/2)6Ti=90JnRTi=10J
Physics 207: Lecture 30, Pg 10
Work output is the area enclosed by the curve:
Pi
4Pi
Vi2Vi
Q=90J
Q=25JTi
4Ti8Ti
2Ti
Wout=area=3PiVi=3nRTi=30J
Physics 207: Lecture 30, Pg 11
From energy conservation:
Wout=QH-QC
Wout=30JQC=115J
η=0.2
The thermal efficiency is:
QH=145J
Physics 207: Lecture 30, Pg 12
The Carnot Engine
All real engines are less efficient than the Carnot engine because they operate irreversibly due to the path and friction as they complete a cycle in a brief time period.
Carnot showed that the Carnot showed that the thermal efficiency of a thermal efficiency of a Carnot engine is:Carnot engine is:
hot
coldcycleCarnot T
T1
Physics 207: Lecture 30, Pg 13
For which reservoir temperatures would you expect to construct a more efficient engine?
A) Tcold=10o C, Thot=20o C
B) Tcold=10o C, Thot=800o C
C) Tcold=750o C, Thot=800o C
Physics 207: Lecture 30, Pg 14
Kinetic theory A monatomic gas is compressed isothermally to 1/8 of its
original volume. Do each of the following quantities change? If so, does the
quantity increase or decrease, and by what factor? If not, why not?
a. The temperature
b. The rms speed vrms
c. The mean free path
d. The molar heat capacity CV
Physics 207: Lecture 30, Pg 15
1
4 2 N /V r2
N/V: particles per unit volume
Mean free path is the average distance particle moves between collisions:
The average translational kinetic energy is:
εavg=(1/2) mvrms2=(3/2) kBT
CV=3R/2 (monatomic gas)
The specific heat for a monatomic gas is:
Physics 207: Lecture 30, Pg 16
The average kinetic energy of the molecules of an ideal gas at 10°C has the value K1. At what temperature T1 (in degrees Celsius) will the average kinetic energy of the same gas be twice this value, 2K1?
(A) T1 = 20°C
(B) T1 = 293°C
(C) T1 = 100°C
Suppose that at some temperature we have oxygen molecules moving around at an average speed of 500 m/s. What would be the average speed of hydrogen molecules at the same temperature?
(A) 100 m/s
(B) 250 m/s
(C) 500 m/s
(D) 1000 m/s
(E) 2000 m/s
Physics 207: Lecture 30, Pg 17
Simple Harmonic Motion
A Hooke’s Law spring is on a horizontal frictionless surface is stretched 2.0 m from its equilibrium position. An object with mass m is initially attached to the spring however, at equilibrium position a lump of clay with mass 2m is dropped onto the object. The clay sticks.
What is the new amplitude?
km
km
-2 20(≡Xeq)
2m
2m
Physics 207: Lecture 30, Pg 18
½ k A2=½ m vmax2
vmax=ωA
The speed when the mass reaches the equilibrium position:
The speed after clay sticks can be found using momentum conservation:
m vmax=(m+2m)vnew
vnew=vmax/3
The new amplitude can be found using energy conservation:
½ (m+2m)vnew2=½ k Anew
2
Anew=A/√3
Physics 207: Lecture 30, Pg 19
Fluids
What happens with two fluids??
Consider a U tube containing liquids of density 1 and 2 as shown:
Compare the densities of the liquids:
(A) 1 < 2 (B) 1 = 2 (C) 1 > 2
1
2
Physics 207: Lecture 30, Pg 20
Fluids
What happens with two fluids??
Consider a U tube containing liquids of density 1 and 2 as shown:
At the red arrow the pressure must be the same on either side. 1 x = 2 y
Compare the densities of the liquids:
(A) 1 < 2 (B) 1 = 2 (C) 1 > 2
1
2
x
y