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

QQ

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.