thermo, optics and waves review

Temperature and Kinetic Theory

Temperature

Relates how relatively hot or cold objects are

Scales

Celsius, Fahrenheit and Kelvin

°C = 5/9 (°F -32)

°F = (9/5)°C + 32

K = °C + 273.15


Thermal Equilibrium

Two objects in contact with initially different temperatures will eventually reach the same temp.

No net heat energy flows between the objects

Final temperature will fall between the two initial temperatures


Thermal Expansion

Temperature changes can result in changes of length and/or volume

Linear Expansion

ΔL = αL0ΔT

α = coefficient of linear expansion (unique to material)

ΔT must be in °C

Volume Expansion

ΔV = βV0ΔT

β = coefficient of volume expansion (unique to material)


Gas Laws

Boyle’s Law – volume is inversely proportional to pressure (constant temperature)

Charles’s Law – volume is directly proportional to temperature (constant pressure)

Gay-Lussac’s Law – pressure is directly proportional to temperature (constant volume)


Ideal Gas Law – three laws combine to

PV = nRT

n = # moles

R = 8.315 J/mol·K

Alternate equation

PV = NkT

N = # molecules

k = 1.38e-23 J/K


Kinetic Theory

All matter is composed of atoms in random motion

Pressure is defined as a measure of the collisions of molecules against the walls of their container

Kinetic energy of a gas, KE = 3/2kT

Can find the root-mean-square velocity of molecules

vrms = sqrt(3kT/m)



Multiple Choice Questions – TIMED!

Quietly answer the questions on your own.

Multiple Choice Answers

1. C

2. B

3. B

4. A

5. D

6. B

7. C

8. E

9. E

10. D

Heat as Energy Transfer

Heat flows naturally from a warm body to a cool body until they reach thermal equilibrium

Good to know:

calorie – amount of heat to be added to increase temp of 1 gram of water by 1 °C

kilocalorie – (kcal or Calorie) amount of heat to be added to increase temp of 1 kilogram of water by °C

Mechanical equivalent of heat: 4.186 J = 1 cal

Heat

Internal Energy/Thermal Energy

The aggregate energy of an object’s molecules

U = 3/2nRT = 3/2NkT

Heat

Energy transferred between objects seeking thermal equilibrium

Measured in Joules

Temperature

Not the same as heat!

Depends on average kinetic energy of molecules

Heat

Specific Heat

Relates transfer of heat to change in temperature of a given material

Heat

Q = mcΔT

Calorimetry

Works on concept of conservation of energy

Two objects in contact will transfer energy, one ultimately

losing heat and the other gaining

Qgained + Qlost = 0

Heat

Phase Changes

Heat of fusion – Lf, energy needed per unit mass to change from solid to liquid, and vice versa

Heat of vaporization – Lv, energy needed per unit mass to change from liquid to gas, and vice versa

Heat required

Q = mL

Heat

Conduction

Transfer of heat by touch (molecular collisions)

Rate of heat transfer

ΔQ/Δt = kAΔT/l

k = thermal conductivity

A = cross-sectional area

l = distance between two collisions

High values of k = material is a good conductor of heat

Low values of k = material is a good insulator

Heat

Convection

Heat transfer due to motion of fluids

Heated molecules move in swirls

Bring cool molecules to heating element

Newly heated molecules then move in swirls

Repeat

Heat

Radiation

Heat transfer as electromagnetic waves (no medium necessary)

Rate of heat transfer

ΔQ/Δt = eσAT4

σ = Stefan-Boltzmann constant, 5.67e-8 W/m2K4

e = emissivity (unique to material being radiated)

Heat

Heat




1. A

2. E

3. A

4. E

5. B

6. E

7. A

8. C

9. A

10. C

Thermodynamics

First Law of Thermodynamics (cons. of energy)

ΔU = Q + W

+W = work done on system

-W = word one by system

When work is done, volume must change

When internal energy changes, temperature must change

Isothermal – constant temp.

Since ΔT = 0, ΔU = 0

Work must equal heat, W = Q

Thermodynamics

Adiabatic – no heat exchanged

Internal energy and temperature will change

Since Q = 0, ΔU = W

Isobaric – constant pressure

W = PΔV

Isochoric/Isovolumetric – constant volume

No work is done

ΔU = Q

Thermodynamics

Thermodynamics

Isobaric and Isochoric graphs are self-explanatory.

Isothermal and Adiabatic Differences

Final pressure is larger for isothermal – as gas expands, energy is lost to surrounding by doing work, and heat flows back in to replace lost energy.

For adiabatic, heat cannot flow to replace lost energy so pressure and temp. drop more.

Second Law of Thermodynamics

Several ways

Clausius Statement – heat flows from a warm body to a cool body, but not the converse

Kelvin-Planck Statement – no engine can turn all heat into work

Entropy – measure of disorder of a system

ΔS = Q/T (temp. in Kelvins)

Naturally, overall entropy of a system increases

Thermodynamics

Thermodynamics




1. E

2. D

3. A

4. A

5. B

6. B

7. E

8. E

9. E

10. C

Waves and Sound

Simple Harmonic Motion (SHM)

Vocab to know – amplitude, cycle, period, frequency, hertz

Cyclic vibrations or oscillations – repeating motion

Recall mass-spring system and pendulum

Object is displaced and a restoring force acts to return the object to the equilibrium position

For mass-spring system, restoring force is spring force F = -kx Period T = 2pi*sqrt(m/k)

For pendulum, x-component of gravity is the restoring force Period T = 2pi*sqrt(l/g)

Waves and Sound

Waves and Sound

Energy in SHM In absence of friction,

energy is being converted between kinetic and potential

Setting up a CoE equation can help you find a variety of variables Total energy remains

the same, so compare energies at different points in the motion

Waves and Sound

Accounting for Friction in SHM

Damped Harmonic Motion – amplitude decreases as a function of time

Other cases to know:

Overdamped, underdamped, critical damping

Wave Motion

Waves are disturbances that carry energy – not matter itself

More vocab – pulse, periodic wave, wavelength, wave velocity

Types of Waves

Transverse – particles move perpendicular to wave motion

Longitudinal – particles move parallel to wave motion

Waves and Sound

Waves and Sound

Transverse Wave Longitudinal Wave

Energy Carried by Waves

Quantified by intensity, which is energy per second per unit area

Intensity, I = P/(4πr2)

Speed of a Wave

v = λf

Speed of a Wave on a String as a Function of Tension

v = sqrt[FT/(m/L)]

Waves and Sound

Waves and Sound

Reflection of a Wave at a Boundary of Very Different Densities Fixed End (less dense to

more dense) Reflected pulse will be

inverted Energy is lost as heat,

and some transferred to wall

Free End (more dense to less dense) Reflected pulse will be on

the same side as incident pulse

Waves and Sound

Reflection of a Wave at a Boundary of Similar Densities

Some of the energy will be transmitted and some will be reflected

Watch and note the differences

Waves and Sound

Interference of Waves

Constructive – when pulses in phase interact, their amplitudes add

Destructive – when pulses out of phase interact, their amplitudes subtract

Waves and Sound

Standing Waves

When two ends of a cord are fixed, certain vibrations can produce a wave that appears not to move.

Vocab – nodes, antinodes, fundamental frequency, harmonics

Waves and Sound

Sound

Longitudinal waves

Require a medium to propagate

Speed depends on medium

Pitch – perception of frequency

Audible range of 20 to 20,000 Hz

Loudness – perception of intensity

Measured in decibels

β = 10log(I/I0)

I0 is reference level, usually 1.0e-12 W/m2

Quality – known as timbre

Waves and Sound

Standing Waves on Stringed Instruments

Harmonics given by

fn = nv/2L

n indicates harmonic

Antinodes at both ends

Standing Waves in Pipes

Open at both ends (like a flute)

fn = nv/2L

Nodes at both ends

Open at one end (like a clarinet)

fn = nv/4L

Antinode at one end

Waves and Sound

Beats

Interference of two sources of similar frequency produce audible recurring intensity changes (beats)

Beat Frequency

fB = |f1 – f2|

Technical name: the wah wahs ok, not really

Waves and Sound

Doppler Effect

The perceived shift in frequency due to the relative motion of source and observer

fo = fs[(v+vo)/(v-vs)]

v = speed of sound

vo = observer

vs = source

Waves and Sound




1. C

2. A

3. A

4. A

5. D

6. D

7. A

8. B

9. E

10. E

Optics

Optics

Law of Reflection

Incident angle is equal to the reflected angle

Measured relative to normal, not surface of mirror

Optics

Types of Reflection

Diffuse – rough surfaces

Specular – smooth surfaces

Spread – dominate direction, partially diffuse

Optics

Images Created by Mirrors and Lenses Vocab to know: Image distance

Object distance

Virtual image

Real image

Convex

Concave

Focus

Principal axis

Focal point

Focal length

Magnification

1/f = 1/p + 1/q

M = h’/h = -q/p

Images Created by Mirrors Shiny side of the mirror is the positive side, dull side is

negative

Real images always form on the positive side, virtual on the negative

Negative values of h’ and M indicate the image is inverted

Converging (concave) mirrors have a positive focal length

Diverging (convex) mirrors have a negative focal length

Optics

Optics

Refraction

The bending of light due to the transmission of light into a new medium

Snell’s Law

n1sinθ1 = n2sinθ2

n = index of refraction (unique to medium)

Optics

If the critical angle is met, total internal reflection occurs

θc = n2/n1, n1>n2

This is why diamonds are awesome

Images Created by Lenses

Images formed on the side opposite the object are real images (positive q)

Images formed on the same side as the object are virtual images (negative q)

Converging lens (convex) has a positive focal length

Diverging lens (concave) has a negative focal length

Optics

Optics




1. C

2. A

3. D

4. B

5. B

6. E

7. A

8. C

9. B

10. B

Wave Nature of Light


Young’s Double-Slit

Monochromatic light though two slits

Pattern of bright and dark spots

Created by constructive and destructive interference

Constructive dsinθ = mλ

Destructive dsinθ = (m + ½)λ

d = slit separation

m = order


Single Slit Diffraction

Bright and dark spots due to interference

Dark spots

Dsinθ = mλ

D = width of slit

m = order


Diffraction Gratings

Tons of single slits

dsinθ = mλ

d = distance btn slits


1. E

2. C

3. B

4. E

5. B

6. D

7. B

8. C

9. A

10. D

thermo, optics and waves review

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