Physics 207 Lecture 30. Lecture 30. Final exam on Monday, Dec 20, at 5:05 pm, at Sterling 1310, Graham 19. HW 11 due tonight

Physics 207 – Lecture 30 Lecture 30 Goals: • Review for the final. • Final exam on Monday, Dec 20, at 5:05 pm, at Sterling 1310, • Graham 19. HW 1...
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Physics 207 – Lecture 30

Lecture 30 Goals:

• 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 1

Waves  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.

Physics 207: Lecture 30, Pg 2

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Physics 207 – Lecture 30

 History Graph:

2

-2

2

3

4

6 5 time (sec)

7 Physics 207: Lecture 30, Pg 3

 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 4

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Physics 207 – Lecture 30

I= R

Psource 4 πR 2

Psource=35 W R=50 m  The power hitting the microphone is:

Pmicrophone= I Amicrophone Physics 207: Lecture 30, Pg 5

Intensity of sounds  If we were asked to calculate the intensity level in

decibels:

I β = 10log10    I0  I0: threshold of human hearing I0=10-12 W/m2

Physics 207: Lecture 30, Pg 6

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Physics 207 – Lecture 30

 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?

 I1   I2  β1 = 10log10  β 2 = 10log10   I0   I0   I1  β1 − β 2 = 10log10  = 3  I2  I1 = 10 0.3 = 2 I2 Physics 207: Lecture 30, Pg 7

Engines  For the engine shown below, find, Wout, QH and

the thermal efficiency. Assume ideal monatomic gas.

4Pi Q=90J

Pi

Q=25J

Vi

2Vi Physics 207: Lecture 30, Pg 8

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Physics 207 – Lecture 30  First, use the ideal gas law to find temperatures

4Pi

8Ti

4Ti

Q=90J

Pi

2Ti

Ti

Q=25J

2Vi

Vi

 From the right branch, we have:

nCV T=90 J n(3R/2)6Ti=90J

nRTi=10J Physics 207: Lecture 30, Pg 9

 Work output is the area enclosed by the curve:

4Pi

8Ti

4Ti

Q=90J

Pi

2Ti

Ti

Q=25J

2Vi

Vi

Wout=area=3PiVi=3nRTi=30J

Physics 207: Lecture 30, Pg 10

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Physics 207 – Lecture 30

 From energy conservation:

Wout=QH-QC Wout=30J QC=115J

QH=145J

 The thermal efficiency is:

=0.2 Physics 207: Lecture 30, Pg 11

The Carnot Engine 

Carnot showed that the thermal efficiency of a Carnot engine is:

ηCarnot cycle = 1−

Tcold Thot

 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. Physics 207: Lecture 30, Pg 12

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Physics 207 – Lecture 30



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 13

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 14

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Physics 207 – Lecture 30



The average translational kinetic energy is: avg=(1/2)



mvrms2=(3/2) kBT

Mean free path is the average distance particle moves between collisions:

λ=

1 4 2π (N /V )r 2

N/V: particles per unit volume 

The specific heat for a monatomic gas is: CV=3R/2 (monatomic gas) Physics 207: Lecture 30, Pg 15

 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 16

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Physics 207 – Lecture 30 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? 2m 

k

m

2m m

k -2

0( Xeq)

2 Physics 207: Lecture 30, Pg 17



The speed when the mass reaches the equilibrium position:

½ k A 2=½ m vmax2 vmax=A 

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)v new2=½ k A new2  Anew=A/ 3 Physics 207: Lecture 30, Pg 18

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Physics 207 – Lecture 30

Fluids  What happens with two fluids??  Consider a U tube containing liquids of

ρ2

density ρ1 and ρ2 as shown:

ρ1

Compare the densities of the liquids: (A) ρ1 < ρ2

(B) ρ1 = ρ2

(C) ρ1 > ρ2

Physics 207: Lecture 30, Pg 19

Fluids 

What happens with two fluids??



Consider a U tube containing liquids of density ρ1 and ρ2 as shown:



ρ2

x ρ1

At the red arrow the pressure must be the same on either side. ρ1 x = ρ2 y  Compare the densities of the liquids: (A) ρ1 < ρ2

(B) ρ1 = ρ2

y

(C) ρ1 > ρ2

Physics 207: Lecture 30, Pg 20

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