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PHY 113 A Fall 2012 -- Lecture 33 111/26/2012
PHY 113 A General Physics I9-9:50 AM MWF Olin 101
Plan for Lecture 32:Review of Chapters 14, 19-22
1. Advice about preparing for exam2. Review of the physics of fluids and of
thermodynamics3. Example problems
PHY 113 A Fall 2012 -- Lecture 33 211/26/2012
PHY 113 A Fall 2012 -- Lecture 33 311/26/2012
Format of Wednesday’s exam
What to bring:1. Clear, calm head2. Equation sheet (turn in with exam)3. Scientific calculator4. Pencil or pen(Note: labtops, cellphones, and other electronic equipment must be off or in sleep mode.)
Timing:May begin as early as 8 AM; must end ≤ 9:50 AM
Probable exam format 4 problems similar to homework and class examples; focus
on Chapters 14 & 19-22 of your text. Full credit awarded on basis of analysis steps as well as
final answer
PHY 113 A Fall 2012 -- Lecture 33 411/26/2012
Examples of what to include on equation sheet
Given information on exam paper
Suitable for equation sheet
Universal or common constants (such as g, R, ..)
Basic physics equations from earlier Chapters: Newton’s laws, energy, momentum,…
Particular constants (density of fluid, heat capacity of fluid, latent heat for phase change …)
Relationship between pressure and force; fluid density; pressure within fluids; buoyant force; Bernoulli’s equation
Unit conversion factors such atm to Pa, Cal to J, oC to K, …
Concept of temperature and its measurement scales; ideal gas law
Definition of thermodynamic heat and work; first law of thermodynamics
Molecular model of ideal gas law; internal energy of ideal gas
Thermodynamic cycles and their efficiency
PHY 113 A Fall 2012 -- Lecture 33 511/26/2012
General advice for preparing for exam• Prepare equation sheet, including basic
equations* from each chapter• Work example problems from class notes,
textbook examples, webassign, other sources using your equation sheet
• During your review, you may develop new questions. Make an effort to get answers by consulting with your instructor, physics TA, etc.
*Note: One of the challenges is to distinguish the basic equations/concepts from particular examples
PHY 113 A Fall 2012 -- Lecture 33 611/26/2012
iclicker question:Which of the following equations concerning the physics of fluids can be safely omitted from your equation sheet?
2222
121
212
11
01
B
E.
22
D.
C.
B.
A.
gyvPgyvP
ghPP
v
gVFA
P
V
M
displacedfluid
F
PHY 113 A Fall 2012 -- Lecture 33 711/26/2012
Problem solving steps
1. Visualize problem – labeling variables2. Determine which basic physical principle(s) apply3. Write down the appropriate equations using the
variables defined in step 1. 4. Check whether you have the correct amount of
information to solve the problem (same number of knowns and unknowns). Note: in some cases, there may be extra information not needed in the solution.
5. Solve the equations.6. Check whether your answer makes sense (units,
order of magnitude, etc.).
PHY 113 A Fall 2012 -- Lecture 33 811/26/2012
iclicker question:A. I would like to have two extra review sessions
one on Monday and one on Tuesday to go over the material
B. I would like to have one extra review session on Tuesday to go over the material
C. I would like to schedule individual or small group meetings in Olin 300 to go over the material
D. I am good
PHY 113 A Fall 2012 -- Lecture 33 911/26/2012
Review: Physics of fluids
APA
V
MVM
FF
: area of surface aon forceby exerted Pressure
: volumeand mass with fluid a ofDensity
PHY 113 A Fall 2012 -- Lecture 33 1011/26/2012
Review: Physics of fluids -- continued Pressure exerted by fluid itself due to gravity:
yrgDy = mg/A
P(y+Dy)
P(y)
gdydP
dydP
yyPyyP
ygyyPyPAmg
AyyF
AyF
mgyyFyF
y
ρ
)()(lim
ρ)()(
)()(
)()(
0
r
y2
y1 1221 )()(
:fluid ibleincompressFor
yygyPyP
PHY 113 A Fall 2012 -- Lecture 33 1111/26/2012
Review: Physics of fluids -- continued Buoyant force
displacedB gVF fluidρ :forceBuoyant
rfluid
mg
FBN 0 mgFN B
PHY 113 A Fall 2012 -- Lecture 33 1211/26/2012
Review: Physics of fluids -- continued Bernoulli’s equation Continuity condition
2211
2222
121
212
11
vAvA
gyvPgyvP
P2
=P1
1
212121
velocity fluidfor Solve
:,,,,,,Given
v
yyAAPP
PHY 113 A Fall 2012 -- Lecture 33 1311/26/2012
Review: Temperature -- notion of “absolute” Kelvin scale
TC=TK-273.15
PHY 113 A Fall 2012 -- Lecture 33 1411/26/2012
Effects of temperature on materials –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
Review: Ideal gas law
PHY 113 A Fall 2012 -- Lecture 33 1511/26/2012
Review: Notion of internal energy of a system
Eint(T,V,P….)
The internal energy is a “state” property of the system, depending on the instantaneous parameters (such as T, P, V, etc.).
),,(),,( intintint iiifff PVTEPVTEE DEint can also include phase change of a material (solidliquid, liquidgas, etc.)
PHY 113 A Fall 2012 -- Lecture 33 1611/26/2012
Review: First law of thermodynamics
WQE int
Ei Ef
Q W
Q: heat added to system W: work on system
PHY 113 A Fall 2012 -- Lecture 33 1711/26/2012
Review: First law of thermodynamics – continued
Examples with W=0 DEint = Q
Changing temperature in a given phase
Changing phase at given temperature
K)J/(kg 4186 :for water Example,
massunit per capacity heat
c
cTTmccdTmQf
i
T
T
if
J/kg 333000 K, 273.15at melting icefor Example,
massunit per heat latent
L
LmLQ
PHY 113 A Fall 2012 -- Lecture 33 1811/26/2012
Review: First law of thermodynamics – continued
1γ
11γ
)0( conditions adiabaticAt
/ln )( emperatureconstant tAt
)( pressureconstant At
0 )( olumeconstant vAt
: gas idealfor Examples
:system on the doneWork
f
iii
ifiiif
ifiif
if
V
V
V
VVPWQ
VVVPWTT
VVPWPP
WVV
nRTPV
PdVWf
i
PHY 113 A Fall 2012 -- Lecture 33 1911/26/2012
Review: First law of thermodynamics – continued
Eint for ideal gas
..............................
diatomicfor
monoatomicfor
1
1
57
35
int
nRTE
PHY 113 A Fall 2012 -- Lecture 33 2011/26/2012
Review: First law of thermodynamics – continued
Translational kinetic energy for ideal gas molecules:
M
RTv
RTMv
i
i
3
2
3
2
221
PHY 113 A Fall 2012 -- Lecture 33 2111/26/2012
Review thermodynamic cycles for designing ideal engines and heat pumps
P (
1.01
3 x
105 )
Pa
Vi Vf
Pi
Pf
A
B C
Din
eng
outin
eng
Q
W
QQQ
WW
:Efficiency
:system input toHeat
:engine ofWork
Engine process:
PHY 113 A Fall 2012 -- Lecture 33 2211/26/2012
Review thermodynamic cycles -- Carnot cycle
AB Isothermal at Th
BC AdiabaticCD Isothermal at Tc
DA Adiabatic
h
c
in
out
in
outin
T
Tε
Q
Q
Q
1
1
cycleCarnot of Efficiency
PHY 113 A Fall 2012 -- Lecture 33 2311/26/2012
Review thermodynamic cycles – continued Other examples of thermodynamic cycles
Thermodynamic work: W = –(shaded area) For simple graph, can use geometry to calculate area; first law of thermo and ideal gas laws also apply.