# EQUATIONS Flashcards Preview

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Flashcards in EQUATIONS Deck (91)
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1
Q

Circuits

RESISTANCE

(of a material used as a resistor in a circuit)

UNITS=?

A

R=ρL/A

UNITS: Ω (Ohms)

• ρ=resistivity of the material
• L=length of material
• A=cross-sectional area

2
Q

INTENSITY of a wave

A

=waves/m2

3
Q

VELOCITY of a wave

A

V=λf

4
Q

VOLTAGE in a circuit (3)

A

V=PE/q

V=Ed

V=Kq/r

5
Q

KINETIC ENERGY

A

KE=½mv2

6
Q

HARMONICS

FOR:

1. String or pipe with MATCHING ends–
• both nodes or antinodes
2. String or pipe open at ONE end –
• with one node and one antinode

λ=?

A

λ = 2L/n

λ = 4L/n

7
Q

Snell’s Law

A

n1sinθ1 = n2sinθ2

8
Q

Young’s Double Slit Experiment

A

x = λL/d

• x is the distance between fringes
• λ is the wavelength of light used
• d is the distance between the two slits
• L is the distance between the “double slit” and the final screen
9
Q

TORQUE (3)

A

T=Fl

T=mgl

T=Frsinθ

10
Q

GRAVITATIONAL PE

IN SPACE

A

PEgrav= - Gmm/r

11
Q

PEELASTIC

A

PEelastic=½kx2

12
Q

PEELECTRICAL (3)

A

PEelec=Kqq/r

PEelec=qEd

PEelec=qV

13
Q

POTENTIAL ENERGY STORED IN A CAPACITOR (3)

A

PEcapacitor=½QV

PEcapacitor=½CV2

PEcapacitor=½Q2/C

14
Q

MECHANICAL ENERGY (ME)

A

ME=KE+PE

15
Q

WORK (2)

A

W=Δ ENERGY

W=Fdcosθ

16
Q

RAMPS

A

Fm=mg (h/d)

• h is the height of the ramp
• d is the distance along its hypotenuse

17
Q

LEVERS

A

Fm=mg( L1 / L2 )

• L1 is the lever arm for the mass
• L2 is the lever arm for the applied force

18
Q

PULLEYS

A

Fm= mg / ( # of vertical ropes directly lifting the mass)

19
Q

POWER (4)

A

P=ΔE/t

P=W/t

P=Fdcosθ

P=Fvcosθ

20
Q

HYDRAULIC LIFTS (2)

A

Fm=mg (h1/h2)

Fm=mg (A1/A2)

h1=distance traveled by the large plunger

h2=distance traveled by the small plunger

A1 =cross-sectional area of the small plunger

A2 cross-sectional area of the large plunger

21
Q

FORCE FOR A CONSTANT ELEC. FIELD

A

F=qE

22
Q

FORCE FOR A POINT CHARGE ELEC. FIELD

A

F=Kqq/r2

<span>(Coulomb’s Law)</span>

23
Q

STRENGTH OF FIELD (“E”) FOR A CONSTANT ELEC. FIELD (2)

A

E=F/q

E=V/d

24
Q

STRENGTH OF FIELD (“E”) FOR A POINT CHARGE ELEC. FIELD

A

E=Kq/r2

25
Q

ELEC. POTENTIAL ENERGY FOR A CONSTANT ELEC. FIELD

A

PEelec=qEd

26
Q

ELEC. POTENTIAL ENERGY FOR A POINT CHARGE ELEC. FIELD

A

PEelec= (+/-) Kqq/r

27
Q

VOLTAGE FOR A CONSTANT ELEC. FIELD

A

V=Ed

28
Q

VOLTAGE FOR A POINT CHARGE ELEC. FIELD

A

V=Kq/r

29
Q

Fmagnetic EXERTED ON A CHARGED PARTICLE,q, MOVING IN A MAGNETIC FIELD,B

A

F=qvBsinθ

30
Q

CURRENT

A

I=Δq/Δt

31
Q

OHM’S LAW

A

V=IR

32
Q

ELECTRICAL POWER (3)

A

P=IV

P=I2R

P=V2/R

33
Q

VELOCITY OF A WAVE

A

V=λf

34
Q

THE BEAT FREQUENCY

A

fbeat= |f1 - f2|

35
Q

THE DOPPLER EFFECT (2)

A

Δf/fsource= v/c

Δλ/λsource= v/c

36
Q

HARMONICS FOR A STRING OR PIPE WITH MATCHING ENDS–BOTH NODES OR BOTH ANTINODES

A

L= nλ/2

or λ=2L/n

37
Q

HARMONICS FOR A PIPE OPEN AT ONE END ONLY–ONE NODE AND ONE ANTINODE

A

L=nλ/4

OR λ=4L/n

38
Q

ENERGY OF A PHOTON

A

E=hf

39
Q

INDEX OF REFRACTION, “n”

A

n=c/v

40
Q

FOCAL POINT

FOR MIRRORS ONLY

A

f=½r

41
Q

THIN LENS EQUATION

A

1/p + 1/q = 1/f

42
Q

MAGNIFICATION

A

M= -q/p

43
Q

OPTICAL POWER

A

P= 1/f

44
Q

TWO LENS SYSTEMS:

MAGNIFICATION

A

M=m1m2

45
Q

TWO LENS SYSTEMS:

POWER

A

P=p1+p2

46
Q

FRICTION (2)

A

Fkkmgcosθ

Fssmgcosθ

47
Q

THE CHARGE OF AN ELECTRON=

(in Coulombs)

A

-1.6 x 10-19C

48
Q

THE IDEAL GAS LAW

A

PV=nRT

49
Q

THE FUNDAMENTAL THERMODYNAMIC RELATION

A

ΔG=ΔH-TΔS

50
Q

EQUATION RELATING KEQ TO GIBBS FREE ENERGY (2 VARIATIONS)

SPONTANEOUS IF ΔG IS (+/-)?

A

ΔG= -RTlnKeq

OR

Keq=e-ΔG/RT

SPONTANEOUS IF ΔG IS NEGATIVE

(“EXERGONIC”)

51
Q

HEAT CAPACITY

A

c =ΔQ/ΔT

52
Q

SPECIFIC HEAT

A

q=McΔT

53
Q

FREEZING POINT DEPRESSION

A

The freezing point of a liquid is depressed when a non-volatile solute is added according to:

∆T = kfmi

kf is a constant

54
Q

RAOULT’S LAW

Vapor Pressure w/ a Non-Volatile Solute =

A

Vapor Pressure w/ a Non-Volatile Solute = (mole fraction of the pure solvent, X)*(Vp of the pure solvent, Vp°)
Vp = XVp°

x=mole fraction of pure solvent

Vp=Vapor pressure of pure solvent

55
Q

RAOULT’S LAW

TOTAL Vapor Pressure w/ a Volatile Solute =

A

Vptotal

= Vpsolvent + Vpsolute

( Xsolvent Vp°solvent) + (Xsolute Vp°solute)

(mole fraction, X, of solvent* Vp° of the solvent) + (mole fraction of the solute* Vp° of the solute)

56
Q

OSMOTIC PRESSURE, Π

A

Π= iMRT

i = # of ions formed in solution
M is the solute molarity
R is the gas constant
T is the absolute temperature

57
Q

BOILING POINT ELEVATION

A

∆T = kbmi

• where kb is a constant,
• m is MOLALITY (NOT molarity)
• i is the number of ions formed per molecule

58
Q

NERNST EQUATION

A

Ecell = E° - (.06/n) * log ([lower]/[higher])

n=# moles of electrons transferred

Fe3+(aq)→Fe(s)

=3 e’s transferred

59
Q

GIBBS FREE ENERGY

A

ΔG=ΔH-TΔS

60
Q

GIBBS FREE ENERGY #3

in association with:

Free energy and Cell potentials

(+/-) ∆G = SPONTANEOUS/ FAVORABLE?

A

∆G = -nFE

n is the number of moles of electrons transferred

F is Faraday’s constant

E is the emf of the cell

NEGATIVE ∆G = SPONTANEOUS/ FAVORABLE?

^^OR A POSITIVE^^

61
Q

GIBBS FREE ENERGY #2

in association with:

Free energy and Equilibrium Constants

(+/-) ∆G = SPONTANEOUS/ FAVORABLE?

A

∆G = - RTlnKeq

∆G = free energy at any moment
∆G° = standard-state free energy
R = ideal gas constant = 8.314 J/mol-K
T = temperature (Kelvin)
lnQ = natural log of the reaction quotient

(+/-) ∆G = SPONTANEOUS/ FAVORABLE?

DEPENDS ON VALUE OF Keq

SPONTANEOUS:

∆G < 0
K > 1

NON-SPONTANEOUS:

∆G > 0
K < 1

62
Q

GIBBS FREE ENERGY #1

in association with:

TEMPERATURE and Free Energy

(+/-) ∆G = SPONTANEOUS/ FAVORABLE?

A

∆G =∆H -T∆S

NEGATIVE ∆G= SPONTANEOUS / FAVORABLE

63
Q

Gases

DALTON’S LAW OF PARTIAL PRESSURES

A

Ptotal=P1+P2+P3

64
Q

Gases

GRAHAM’S LAW

(EFFUSION & DIFFUSION)

A

E1/E2=√MW2/√MW1

65
Q

Density & Specific Gravity

DENSITY, ρ

A

ρ=m/v

66
Q

Give Units–No equation here

DENSITY OF WATER=?

(2)

A

1000 kg/m3 OR 1.0 g/cm3

REMEMBER:

1 cm3 = 1mL

1 L H2O=1 kg

1 mL H2O=1 g

67
Q

SPECIFIC GRAVITY

FOR OBJECTS FLOATING IN LIQUIDS:

WHAT IS SIGNIFICANCE OF THE FRACTION OF THE OBJECT THAT IS SUBMERGED IN WATER?

A

SG= ρsubstancewater

ρ=density, m/v

ρwater=1 g cm3 or 1000 kg/m3

FOR OBJECTS FLOATING IN WATER:

FRACTION OF OBJECT SUBMERGED IS EQUAL TO THE SPECIFIC GRAVITY!

68
Q

BUOYANT FORCE, Fbuoyant

A

Fbuoyant=ρvg

69
Q

Fluid Pressure

GENERAL PRESSURE FORMULA

A

P=F/A

70
Q

Fluid Pressure

FLUID PRESSURE

A

P=ρgh

71
Q

Fluid Flow

FLOW RATE

A

Q=AV

A=total cross-sectional area

72
Q

Fluid in motion

BERNOULLI’S EQUATION

A

K=P+ρgh+½ρv2

• P=random vibrational energy of the fluid molecules
• ρgh= PEgravitational per volume of the fluid
• h=height (NOT depth)
• ½ρv2 = KE per volume of moving fluid molecules

73
Q

Energy Levels

WORK FUNCTION, φ

A

KE=E-φ

74
Q

Energy Levels

ENERGY OF A PHOTON, “E”

A

E=hf

75
Q

Chemistry

PERCENT % MASS

A

% MASS=

Mass of ONE element/TOTAL mass of cpd

x 100%

76
Q

Equilibrium

LAW OF MASS ACTION

Keq=?

A

Keq=

[products]X<span> </span>/ [reactants]Y

77
Q

Le Chatelier’s Principle

Qeq

MORE___ THAN ___

RXN PROCEEDS TO THE ___

A

MORE REACTANT THAN PRODUCT

RXN PROCEEDS TO THE RIGHT

78
Q

Le Chatelier’s Principle

Q>Keq

MORE___ THAN ___

RXN PROCEEDS TO THE ___

A

MORE PRODUCT THAN REACTANT

RXN PROCEEDS TO THE LEFT

79
Q

Evolution & Populations

HARDY-WEINBERG EQUILIBRIUM (2)

A

p2+2pq+q2=1

p+q=1

p is the frequency of the “A” allele in the population

q is the frequency of the “a” allele in the population

p2** represents the frequency of the **homo**zygous genotype **AA

q2** represents the frequency of the **homo**zygous genotype **aa

2pq** represents the frequency of the **hetero**zygous genotype **Aa

80
Q

Ochem

“FORMAL CHARGE”

A

FORMAL CHARGE=

VALENCE - ASSIGNED

81
Q

HÜCKEL’S RULE

A

4n + 2π

To exhibit aromaticity, a ring system must have exactly 4n + 2π electrons

82
Q

Circuits

CAPACITANCE

A

C= Q/V

83
Q

Waves-The dB System

INTENSITY IN dB

A

=10*log (I/Io)

I=intensity of wave (in W/m2)

Io=threshold of human hearing (given)

84
Q

Chromatography

PAPER OR THIN LAYER CHROMATOGRAPHY (TLC)

Rf=?

A

Rf= DIST. TRAVELED BY COMPONENT /DIST. TRAVELED BY SOLVENT

85
Q

MICHAELIS-MENTEN EQUATION

A

Vo= Vmax [S] / Km+[S]

86
Q

MICHAELIS CONSTANT, Km

Km IS A MEASURE OF…?

A

Km=[S] at ½Vmax

Km= MEASURE OF AN ENZYME’S AFFINITY FOR ITS SUBSTRATE

87
Q

Types of Enzyme Inhibition

LINEWEAVER-BURKE PLOTS

Y-INTERCEPT=?

A

1/Vmax

88
Q

Types of Enzyme Inhibition

LINEWEAVER-BURKE PLOTS

X-INTERCEPT=?

A

-1/Km

89
Q

Types of Enzyme Inhibition

LINEWEAVER-BURKE PLOTS

SLOPE=?

A

Km/Vmax

90
Q

Circuits

CAPACITANCE**

(NOT PEcapacitor !)

How do Capacitance and PEcapacitor relate?

A

C=Q/V

Once solving for C, plug that into one of the 3 PEcapacitor formulas:

=½QV

=½CV2 OR

=½Q2/C

91
Q

Circuits

CAPACITANCE

wrt AREA OF OVERLAP, A b/t plates

and DISTANCE, D b/t plates

A

C=εA/d

• C is the capacitance (Farads)
• A is the area of overlap of the two plates (m2)
• ε is the dialectric constant of the material between the plates
• for a vacuum, εr = 1
• d is the separation between the plates (m)