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
PHY 113 C Fall 2013 -- Lecture 24 211/21/2013
PHY 113 C Fall 2013 -- Lecture 24 311/21/2013
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
PHY 113 C Fall 2013 -- Lecture 24 411/21/2013
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
PHY 113 C Fall 2013 -- Lecture 24 511/21/2013
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?
41
inQ
W
43
411
in
out
in
outin
in QQ
QQQ
QW
PHY 113 C Fall 2013 -- Lecture 24 611/21/2013
Webassign – Assignment #21
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(2715.273315.273
ch
c
ch
cc
TTT
QQQ
WQ
COP
PHY 113 C Fall 2013 -- Lecture 24 711/21/2013
Webassign – Assignment #21
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
611
/11 4.01
21
VV
fraction lost= ideal-actual=0.51-0.16=0.35
PHY 113 C Fall 2013 -- Lecture 24 811/21/2013
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
1
BC
AD
TTTT
11
PHY 113 C Fall 2013 -- Lecture 24 911/21/2013
Comment on adiabatic process (Q=0) --
γγγ
γ
lnln
γ
1γ
ffiii
f
i
f VPVPPP
VV
PP
VV
VPPVVP-TnR
TnRVPPVnRTPV
VPTR-n
WE
1γ
int
PHY 113 C Fall 2013 -- Lecture 24 1011/21/2013
Comment on adiabatic process (Q=0) -- continued
VVPP
VVPP
ii
ii
:Isotherm
:Adiabat
PHY 113 C Fall 2013 -- Lecture 24 1111/21/2013
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
PHY 113 C Fall 2013 -- Lecture 24 1211/21/2013
Review of main ideas from Chapters: 17-18 – Sound waves 14 -- Physics of fluids 19-22 – Temperature, heat, thermodynamics
PHY 113 C Fall 2013 -- Lecture 24 1311/21/2013
Physics of sound waves
Sound waves are described by the wave equation
2
22
2
2
:,For xyv
tytxy sound
Change of average air density or pressure
positiontime
m/s 343
2sin,
: wavesound periodicFor
0
soundvf
ftxytxy
PHY 113 C Fall 2013 -- Lecture 24 1411/21/2013
1 12 2
Use trig identity again:
sin A sin B 2sin A B cos A B
ftxytxyftxytxy 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
PHY 113 C Fall 2013 -- Lecture 24 1511/21/2013
.....4,3,2,1 2
2sin :shapes spatial Possible
n
LπnxA
n n
2πxStanding wave form: Asin cos 2πft
2L nv f n 1,2,3,4...........
n 2L
Standing waves between reflecting walls
PHY 113 C Fall 2013 -- Lecture 24 1611/21/2013
Doppler effect
PHY 113 C Fall 2013 -- Lecture 24 1711/21/2013
S
OSO vv
vvff
:effectDoppler sound ofSummary toward
away
R
RSO vv
vvff
: wavesneticelectromagfor effect Doppler Relative velocity of source toward observer
PHY 113 C Fall 2013 -- Lecture 24 1811/21/2013
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?
3434330343 Hz 2500
S
OSO vv
vvff
3434330343 Hz 2500
S
OSO vv
vvff
PHY 113 C Fall 2013 -- Lecture 24 1911/21/2013
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 PascalDensity: 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
FFFygyyPyP
fluidfluid
fluid
ρρ)()(
:forceBuoyant ρ)()(
11/21/2013
)(ρ (constant) :etc mercury, For water, 00 yygPP r
General relationship between P and r:
gdydP ρ :surface sEarth'near fluids allFor
mg
A
y
submergedB gVF fluidρ :forceBuoyant
PHY 113 C Fall 2013 -- Lecture 24 2111/21/2013
Bernoulli’s equation:
22222
111
212
1 PgyvPgyv rrrr
21
2
1
2222
1
2222
11
212
1
221121
1
PPAAv
PvPv
vAvAyy
r
rr
PHY 113 C Fall 2013 -- Lecture 24 2211/21/2013
22222
111
212
1 PgyvPgyv rrrrBernoulli’s equation:
2
2
1
01
1122
01212
1
2222
1
1
22
AA
PPghv
vAvAPgyv
Pgyv
r
r
rr
rr
PHY 113 C Fall 2013 -- Lecture 24 2311/21/2013
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
104.2100065.222 /
;/ ; :case In this
AFvvvaAv
AFPPyyPgyvPgyv
r
rrrr
Webassign questions on fluids (Assignment #17)
PHY 113 C Fall 2013 -- Lecture 24 2411/21/2013
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:
PHY 113 C Fall 2013 -- Lecture 24 2511/21/2013
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 T
Heat capacity per mass: C=mc
Heat capacity per mole (for ideal gas): C=nCv
C=nCp
PHY 113 C Fall 2013 -- Lecture 24 2611/21/2013
Some typical specific heats
Material J/(kg·oC) cal/(g·oC)Water (15oC) 4186 1.00Ice (-10oC) 2220 0.53Steam (100oC) 2010 0.48Wood 1700 0.41Aluminum 900 0.22Iron 448 0.11Gold 129 0.03
PHY 113 C Fall 2013 -- Lecture 24 2711/21/2013
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)
PHY 113 C Fall 2013 -- Lecture 24 2811/21/2013
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
PHY 113 C Fall 2013 -- Lecture 24 2911/21/2013
Important equations for macroscopic and microscopic descriptions of thermodynamic properties of matter
1 :/ with moleculesFor
31
21
32
21
32
) 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
nRTECC
RTMv
nRTMvnvmNPV
MnmN
nRTPV
PdVW
WQΔE
VP
rms
rmsrms
V
V
f
i
PHY 113 C Fall 2013 -- Lecture 24 3011/21/2013
Question from previous exam:
PHY 113 C Fall 2013 -- Lecture 24 3111/21/2013
FB
mgT
34
4
/59.979102
8.9/92.192.1 0
1028.92000
mkgVm
NTFmgmgTF
NgVF
ball
BB
submergedfluidB
r
r
PHY 113 C Fall 2013 -- Lecture 24 3211/21/2013
Question from previous exam:
PHY 113 C Fall 2013 -- Lecture 24 3311/21/2013
2211
222211
21 2
121
AvAv
PgyvPgyv
rrrr