11/21/2013phy 113 c fall 2013 -- lecture 241 phy 113 c general physics i 11 am – 12:15 pm mwf olin...

PHY 113 C Fall 2013 -- Lecture 24 111/21/2013

PHY 113 C General Physics I11 AM – 12:15 PM MWF Olin 101

Plan for Lecture 24:Review: Chapters 17-18, 14, 19-22

1. Sound; Doppler effect & standing waves 2. Physics of fluids; pressure, buoyant

force, Bernoulli’s equation3. Temperature & heat & ideal gas law4. First law of thermodynamics5. Cycles and their efficiency


Comment about Exam 3:

• Part I – take home portion (1 problem): available at end of class today -- 11/21/2013; must be turned in before part II

• Part II – in-class portion (3 problems) --Tuesday 11/26/2013

• Some special arrangements for early exams have been arranged by prior agreement

• Of course, all sections of the exam are to be taken under the guidelines of the honor code


iclicker questionHow are you doing on preparing your equation sheet for Exam 3?

A. It is completedB. It is almost completedC. I am in a panic because there are too

many equations this time


Webassign – Assignment #21

The work done by an engine equals one-fourth the energy it absorbs from a reservoir.

(a) What is its thermal efficiency?

(b) What fraction of the energy absorbed is expelled to the cold reservoir?

4

1

inQ

W

4

3

4

11

in

out

in

outin

in Q

Q

Q

QQ

Q

W



What is the coefficient of performance of a refrigerator that operates with Carnot efficiency between temperatures -3.00°C and +27.0°C?

)315.273(2715.273

315.273

ch

c

ch

cc

TT

T

QQ

Q

W

QCOP



A gasoline engine has a compression ratio of 6.00 and uses a gas for which γ = 1.40. (a) What is the efficiency of the engine if it operates in an idealized Otto cycle?

(b) If the actual efficiency is 16.0%, what fraction of the fuel is wasted as a result of friction and energy losses by heat that could by avoided in a reversible engine? (Assume complete combustion of the air-fuel mixture.)

51.0

6

11

/

11

4.0121

VV

fraction lost= ideal-actual=0.51-0.16=0.35


Webassign – Assignment #21An idealized diesel engine operates in a cycle known as the air-standard diesel cycle shown in the figure below. Fuel is sprayed into the cylinder at the point of maximum compression, B. Combustion occurs during the expansion B → C, which is modeled as an isobaric process. Show that the efficiency of an engine operating in this idealized diesel cycle is given by the following expression.

BCPhADVc

h

c

TTnCQTTnCQ

Q

Q

1

BC

AD

TT

TT

1

1


Comment on adiabatic process (Q=0) --

γγγ

γ

lnln

γ

1γ

ffiii

f

i

f VPVPP

P

V

V

PP

VV

VPPVVP-TnR

TnRVPPV

nRTPV

VPTR-

n

WE

1γ

int


Comment on adiabatic process (Q=0) -- continued

VVP

P

VVP

P

ii

ii

:Isotherm

:Adiabat


Comment on adiabatic process (Q=0) – continued

Suppose you were asked to calculate the final pressure for an expansion process where Vi/Vf=1/10 when Pi=1 atm. and when =1.3?

atm 10.01/10atm 1 : process isothermalFor

atm 05.01/10atm 1 : process adiabaticFor 1.3

fiiff

fiiff

PVPVP

PVPVP


Review of main ideas from Chapters: 17-18 – Sound waves 14 -- Physics of fluids 19-22 – Temperature, heat, thermodynamics


Physics of sound waves

Sound waves are described by the wave equation

2

22

2

2

:,For x

yv

t

ytxy sound

Change of average air density or pressure

position

time

m/s 343

2sin,

: wavesound periodicFor

0

soundvf

ftx

ytxy


1 12 2

Use trig identity again:

sin A sin B 2sin A B cos A B

ft

xytxyft

xytxy leftright λ

π2sin),( λ

π2sin),( 00

right left 02πx

get y (x, t) y (x, t) 2y sin cos 2πftλ

Standing wave:

Standing waves. Two sinusoidal waves, same amplitude, same f, but opposite directions


.....4,3,2,1 2

2sin :shapes spatial Possible

nL

πnxA

n n

2πxStanding wave form: Asin cos 2πft

2L nv f n 1,2,3,4...........

n 2L

Standing waves between reflecting walls


Doppler effect


S

OSO vv

vvff

:effectDoppler sound ofSummary toward

away

R

RSO vv

vvff

: wavesneticelectromagfor effect Doppler

Relative velocity of source toward observer


Typical question concerning Doppler effect:

A driver travels northbound on a highway at a speed of 30.0 m/s. A police car, traveling southbound at a speed of 34.0 m/s, approaches with its siren producing sound at a frequency of 2500 Hz.

(a) What frequency does the driver observe as the police car approaches?

(b) What frequency does the driver detect after the police car passes him?

34343

30343 Hz 2500

S

OSO vv

vvff

34343

30343 Hz 2500

S

OSO vv

vvff


The physics of fluids.

•Fluids include liquids (usually “incompressible) and gases (highly “compressible”).

•Fluids obey Newton’s equations of motion, but because they move within their containers, the application of Newton’s laws to fluids introduces some new forms.

Pressure: P=force/area 1 (N/m2) = 1 Pascal

Density: r =mass/volume 1 kg/m3 = 0.001 gm/ml

PHY 113 C Fall 2013 -- Lecture 24 20

Buoyant force for fluid acting on a solid:

FB=rfluidVdisplacedg

submergedB

topbottomB

gVyAgAyyPyPF

FFF

ygyyPyP

fluidfluid

fluid

ρρ)()(

:forceBuoyant

ρ)()(

11/21/2013

)(ρ (constant) :etc mercury, For water, 00 yygPP

General relationship between P and :r

gdy

dPρ :surface sEarth'near fluids allFor

mg

A

Dy

submergedB gVF fluidρ :forceBuoyant


Bernoulli’s equation:

22222

111

212

1 PgyvPgyv

21

2

1

2222

1

2222

11

212

1

221121

1

PPA

Av

PvPv

vAvAyy


22222

111

212

1 PgyvPgyv Bernoulli’s equation:

2

2

1

01

1122

01212

1

2222

1

1

22

AA

PPghv

vAvA

Pgyv

Pgyv


A hypodermic syringe contains a medicine with the density of water (see figure below). The barrel of the syringe has a cross-sectional area A = 2.40 10-5 m2, and the needle has a cross-sectional area a = 1.00 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force of magnitude 2.65 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle's tip.

52112

2121

22222

111

212

1

104.21000

65.222 /

;/ ; :case In this

A

FvvvaAv

AFPPyy

PgyvPgyv

Webassign questions on fluids (Assignment #17)


Effects of temperature on materials – continued -- ideal gas “law” (thanks to Robert Boyle (1627-1691), Jacques Charles (1746-1823), and Gay-Lussac (1778-1850)

nRTPV

pressure in Pascals

volume in m3 # of moles

temperature in K

8.314 J/(mol K)

1 mole corresponds to 6.022 x 1023 molecules

Notion of temperature:


Notion of heat

Heat can be used to change temperature:

Heat capacity: C = amount of heat which must be added to the “system” to raise its temperature by 1K (or 1o C).

Q = C DT

Heat capacity per mass: C=mc

Heat capacity per mole (for ideal gas): C=nCv

C=nCp


Some typical specific heats

Material J/(kg·oC) cal/(g·oC)

Water (15oC) 4186 1.00

Ice (-10oC) 2220 0.53

Steam (100oC) 2010 0.48

Wood 1700 0.41

Aluminum 900 0.22

Iron 448 0.11

Gold 129 0.03


Heat and changes in phase of materials

Example: A plot of temperature versus Q added to

1g = 0.001 kg of ice (initially at T=-30oC)


Typical question concerning heat:

Suppose you have a well-insulated cup of hot coffee (m=0.3kg, T=100oC) to which you add 0.3 kg of ice (at 0oC). When your cup comes to equilibrium, what will be the temperature of the coffee?

C10.22

J/kg 333000 C) J/(kg 4186

3.0 )(

100

100)(

0)0()100(

o

o

f

icewater

icewaterwatericewater

iceicewaterwaterf

iceicewaterwaterfwatericewater

fwatericeiceicefwaterwater

T

Lc

kgmmcmm

LmcmT

LmcmTcmm

TcmLmTcmQ


Important equations for macroscopic and microscopic descriptions of thermodynamic properties of matter

1 :/ with moleculesFor

3

1

2

1

3

2

2

1

3

2

) massmolar of moles or mass of molecules (assume

:molecules gas of analysis cMicroscopi

:Law Gas Ideal

: WorkmicThermodyna

:micsThermodyna of LawFirst

int

2

220

0

int

nRT

ECC

RTMv

nRTMvnvmNPV

MnmN

nRTPV

PdVW

WQΔE

VP

rms

rmsrms

V

V

f

i


Question from previous exam:


FB

mgT

34

4

/59.979102

8.9/92.1

92.1 0

1028.92000

mkgV

m

NTFmgmgTF

NgVF

ball

BB

submergedfluidB


Question from previous exam:


2211

222211

21 2

1

2

1

AvAv

PgyvPgyv

11/21/2013phy 113 c fall 2013 -- lecture 241 phy 113 c general physics i 11 am – 12:15 pm mwf olin...

Documents

c fall

efficiency slide

expansion b c

gmml slide

yy slide

c general physics

doppler effect slide

honor code slide