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Virginia Tech - Study Guide - Midterm

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EXAM 1 CHEAT SHEET

Ch 25 / 26 - Geometrical Optics

Ch 15 - Thermodynamics

Law of Reflection

Heat (Joules (Qc cnergy dissipated by work of non-conservative forces (F) Temperature (Kelvins) (T): Heat flows from a high T system to a low T system

Don't forget about the age old question of What are molecular equations?

Spood of light = 0 -3 x 10 m/s Reflection

• Diffuso reflection (rough sic)

Specular reflection (soath sfc) Law of Reflection

Soup

e = angle of incedence e = angle of reflection Normal to sto (all angles measured from normal,

not sic) Virtual image image formed by imagined extension of diverging

rays (cannot be put on a screen) concave converge mirrors convex diverge mirrors Geometrical Optics

Mimor Lenso Equation: We also discuss several other topics like What is stated by the law of supply?

1 = 1 + 1 h = -d valid for all cases Sign convention: d, never neg. for us

d> Oif image is real m> 0 f image is upright (virtual) d 20 if image is virtual m<07 image is inverted (real) h> 0 if image is upright h if image is inverted f> 0 for converging mirrors / lenses

fc0 for divcrging mirrors / lenses Magnification

m-h/

h m = m.m.m....m, If you want to learn more check out How are microbes cultured?

• **If you put object on focal point - no image (d **** Smells LowIndex of Refraction s Don't forget about the age old question of Epistemology is the study of what?

n.sin(e) = n, sin(e) – nuoly =n21 air - vacuum, son..1 e. - arcsini n./n) He increases e, also increases Max value of e. = 90 If you want to learn more check out What is the most dramatic force shaping the destiny of markets and marketing?

1st Law of Thermodynamics - Extension of E conservation theorem to include heat AU - Q.W We also discuss several other topics like Most mayan instruments are gendered musical performance is for what gender?

u "internal energy = totall energy (previously E) Q: heat that goes into system

> if heat anders system

Q20 if heat loaves system W: work done by a system

W> 0 system does work to environment

W207 environment does work to system Heal Gas La PV = nRT U = 32 RT P: pressure [p] = Pa = Nim

PV Dizaram: V: volume M=m

Expansion: V. V W O T: temp IT = Kelvins

Compression: V, V W<0 in: number of moles Rideal gas constant = 8.31 J/molk Constant Pressure Process ischaria) Constant Volure Process WE|F|| Arcase

W = 0 noarca under curve W= P.MAX AXEV

ist law: U = 0-W W-P AV

AU = 0 1st law: AU = 0 W=0 - PAV Constant Templeathermal

Adiabatic Process PV = nRT

O = 0 (no heat exchange b/w system & enviro) RT is a constant

Adiabatic compression: V.<V W 0 P = cors:/V

Adiabatic curves are siceger than isothermals W = nRT In(V/V)

PV = constant PVSP.V. AT = T.T- O for an isothermal AU - 32 nRAT 1st law: AU = Q - W = 0

Convex converging Concave divorging Con Lense Tracing: mirror lense eq is the same = real, inverted image Div LT: d <0,01 <hch - m 1 - virtual, upright image Simole Ostical Devices (Eye /Camcral Eye:

Image must be real = lens must be converging Mirror / lense equation applies, d, is variable & d is fixed

Is there a maxd,? d. - *, & all rey's become horizontal & fed

TV Molar Specific Heats We can only do this at const VIP

Cons! W =0

32 AT We want Q = CnAT

. = 32 R (true for ideal gases) , reminds us of constant volume 1st law: AU = 0-W

AU = Q = BECOMES = 3/2 RAT - QnAT But, W=0

So. AU = 0 Const : We want Q = c.AT

9 - 52 R

AU = PAV - BECOMES - 1st law: AU = Q-W

32 RAT + QR41 = NAT = 5/2 nRAT But, W = PAV

So AU = Q - PAV Heat Cycles

Hoa: Enaires Process whose PV Diagram is a closed curve heat work AU for an ideal gas in one cycle = ?

Efficiency: c = Wi AU -0 = 3/2 ARAT

0, +2, + W AT - T.-T=0 1st law: AU = 0 - W=0

Cara

Must have a real image converging lens Lens must be able to move

Constraint: fis fixed

• dis variable, d must be variable Multiple Lenses / Mirrors

1) Form image of object using only firs: lens / mirror. Ignore the rest. 2) Use this image as object of second lens / mirror Ignore the rest. 3) Repeat as needed. For Lenses Image forms on same side as observer real image

Converging lensa Image forms on opposite sido as observer - virtual image

Diverging lense Far Mirrors Image forms on same side as observer real image

Concave mirror Image forms on opposite side as observer - virtual image

Convex mirror

EXAM 1 CHEAT SHEET

Ch 18 - Electric Forces & Fields

Free Space!

Electric charge - new force/indetinable quantity (+ / .)

- q: typical symbol for charge

SI:[] = C (Coulomb] |F..I - 19.9.1 | F | - 11 Coulomb's low

F = FMI = (4., 11 ) | F. 1 = k[19.4 ) k: Coulomb's constant Sl: k = 8.99x10 Nm/c Electric Fields

. LF, I = k (|Q9|77)

Fal=k(|Q4|17) Red part depends only on Q and r Tako k(01) Ed

o Magnitude of E dua to Q at distancer Definition: F-qE

0

0 is a test charge that is small and positive E due to a point.chside

0 . E: radially outward 0 ) E: radially inward E[P) = ?

. F. = E(P) Pi

• E[P) = E. + E, + E, Gauss's Lave

is in Nmc How much E is interrupted by A?

O of Ethrough A Definition: 0.-IELA

0 El = 1 Ecoste)

. : angle blw E and nomal to sfa, no

contribution to through A Definition: 0. - 1E Acos(e) How much of E, is intercepted by S?

1.

Study Sou

o fqis outside, : = 0

o lqis inside: 0-10 Gauss's Law

0 - 9in /

E = constant = 8.85x10-11 CNm Vaing G: Law to find E due to sufficierry mctric charge distributions

Use symmetry to estimate (roughly) force of clectric field (E) Choose a convenient closed sfo

0 Gaussian sto Apply Gauss's law: 0.- 9 in /& 4. Solve for E to an infinite sheet of charge uniformly charged

E(P) = ? g=QIA E, is first estimace, but E, is a better estimate At most, E depends ond

through side wall = 0 = 2 E Aa=9in /

0 By Gauss's law 20 E 4a = Sin/ & = oda /

• So,E /2€, is constant Parald Plate Capacitor

• E. | = E| = c/20,

• El = a/E

Points from # to biw plates is constant 2 EL = 9in/e, = c /e

o E= 0 /2€, is constant

EXAM 1 CHEAT SHEET

Ch 25/26 Formulas / Constants

Speed of light = C -3x 10 m/s (large but finite)

= e = angle of incedence @ = angle of reflection Normal to sfc (all angles measured from normal, not sfc)

| 1

=

1

+

1

m = h/h. Snell's Law

o n

0

, sin(e)= n,sin(e)

= arcsiná n./n)

Ch 15 Formulas / Constants

AU = Q - W

• Ideal gases: PV = nRT U = 3/2 nRT

o R: ideal gas constant = 8.31 J/ molik

o n number of moles Constant Pressure: W = PAV

1 st law: AU = Q-W=Q - PAV Constant Volume: W = 0

1st law: AU = 0 Isothermal: W = nRT In(V/V)

Q = W Adiabatic: WSO AU = -W

PV*= constant PV = P.7, Molar Specific Heats:

o Constant Volume

. We want Q = CnAT

. = 3/2 R W = 0 + AU = Q

3/2 RAT = C NAT Constant Pressure

We want an expression of the type: Q = C NAT

*

= 5/2 R

AU = Q - PAV

312 RAT + RAT = c AT = 5/2 RAT Heat Cycles

Q = W Heat Engines

0 Efficiency: e = WIQ.

Definition: Q,+Qc+W e = (Q.-Q.)/Q. or e = 1 - Q./Q..

o

Ch 18 Formulas / Constants

. [F] = k (19.911)

• k: Coulomb's constant

O SI: k = 8.99x10Nm,c? Definition: F. = qE

E = F/9

qis a test charge that is small and positive Definition: 0= E A

0 E = E + E, O TEI= Ecos(e)

- O: angle bw E and normal to sfo, no contribution to è through A Definition: $ = | E | Acos(0)

= 4,/E

o e = constant = 8.85x10-12 c m ? g=QIA . E|= 0/2€, is constant