Heat and Waves

1
Heat and Waves

• Chapters 5 6

2
Reading Memo Insights

• How do you convert Fahrenheit to Celsius?
• C 5/9 (F - 32)
• Why is it that water stays the same temp when it
  hits its boiling point no matter how long you
  keep heat on it?
• What is an Absolute Zero?
• Heat passes through a vacuum and heats through
  radiation?
• Are wave movements always symmetrical?

3
Summary of Important Equations to understand for
the HW

1. ?l a l ?T
2. CHANGE in Internal Energy ?U W Q
3. Q m c ?T
4. v v(F/?)
5. v f ? (for light, c ? f)

4
Temperature

• Intimately tied to the idea of Energy (see intro
  to analogy for energy)
• Three scales
• Fahrenheit, Celsius, and Kelvin
• Kelvin Temperature is a measure of the average KE
  of particles ? particles have KE!
• Higher temperature ? particles move faster ?
  higher KE
• http//plabpc.csustan.edu/general/tutorials/temper
  ature/temperature.htm
• Liquids/Solids are bound (solids bound more
  tightly than liquids
• Imagine connected with springs) ? some particles
  also have PE!
• Vibrate through greater distance when Temperature
  goes up
• This vibrational/elastic PE is important in phase
  changes
• PE is negative when bound
• http//hyperphysics.phy-astr.gsu.edu/hbase/thermo/
  inteng.htmlc3

5
Temperature vs. Internal Energy

• (Kelvin) Temperature is a property of a typical
  molecule of a substance -- how many molecules
  there are doesn't matter
• Internal Energy, on the other hand, is the total
  energy of all the particles
• E.g., you can have a few high speed particles in
  a very dilute gas, giving it a high temperature
  but little total energy, or many low speed
  particles in a dense liquid, giving it a low
  temperature but a greater total energy overall.
  The high temperature dilute gas would not be able
  to transfer much heat to a cooler substance but
  the lower temperature liquid would!
• Absolute Zero (-273.15 oC)
• Average KE almost zero
• Cannot be reached HUP
• Low temperatures superfluids, superconductors,
  etc.
• High temperatures KE high so no binding so no
  liquids/solids
• Above 20,000 K electrons break free plasmas only

6
Thermal Expansion

• Unconstrained substances expand with increased
  temp
• Bridges expand in summer, contract in winter
• In gases, higher temp ? higher speeds
• In liquids/solids, more heat added ? vibrate
  through larger distance
• ?l a l ?T
• a ? coefficient of linear expansion

7
In Class Exercise 1

• In summer, lbridge 1,000 m when T 35 oC.
• Calculate change in length on a winter day when
  Tf -5 oC
• a 12 x 10-6/oC (see Example 5.1 on p. 171)

Known Unknown




lbridge, summer 1,000m
?lwinter ?m
Ti, summer 35oC
Tf, winter -5oC
a 12 x 10-6/oC

• ?T is negative
• ?l is also negative
• This expansion/contraction used in bimetallic
  strips in thermostats (Fig 5.9 on p. 172)

8
Expansion

• Liquids also expand/contract
• Exception Dice lt Dwater (water expands upon
  freezing)
• Gases expand too V µ T
• Gases expand 10, liquids 5, and solids 1 with
  temperature
• Ideal Gas Law PV nRT
• Increasing Temp ? Increasing Volume ? DECREASING
  mass ( weight) density
• Temperature does not change mass or weight itself!

9
Two ways to increase Temp (or energy, since T
KE)

• 0th Law of Thermodynamics
• Temp measures thermal equilibrium (Ta Tb Tc
  so Ta Tc) and heat flows from TH to TL
• Expose to reservoir at higher Temp (HEAT
  TRANSFER)
• Doing Work on it (WORK TRANSFER)
• Experiment by James P. Joule established
  established relationship between mechanical work
  and heat
• Temperature depends on average KE of atoms and
  molecules
• 1st Law of Thermodynamics
• Internal Energy (of atoms molecules) U (KE
  PE)atomic
• Gases only have KE
• Liquids/solids also have PE (since they're bound
  and oscillate)

10
U increases with increasing Temp

• Heat, Q, is a form of energy that flows from TH
  to TL
• As Heat flows, energy is transferred (like work
  in mechanics)
• As work is done, energy is transferred/transformed
  in mechanics
• Q and W are energy in transition while U and PE
  are stored energy
• What quantities are measured in units of Joules?
• Energy (KE, PE, and U), which is changed by
• Work
• Heat
• That's because they're all different forms of
  energy (stored or in transition)

In Energy in Transition Stored Energy
Mechanics Work transfers energy to/from ? Mechanical Energy (KE PE)
Thermodynamics Heat transfers energy to/from ? Internal Energy
11
Review the story so far...

• Atoms have KE and PE ? Internal Energy, U
• We know Work (W) can change the energy (U) and is
  energy in transition
• We also know that Heat (Q) changes Temperature
  (T) ? which is equal to the average KE of the
  particles
• Therefore, Q also changes energy and is also
  energy in transition
• So if we can somehow find both Q W, we can
  figure out exactly how much the energy of a
  system changes and don't need to know anything
  about the microscopic U of each atom!

12
1st Law CHANGE in Internal Energy

• CHANGE in Internal Energy ?U W Q
• http//hyperphysics.phy-astr.gsu.edu/hbase/thermo/
  inteng.htmlc3
• W means work done on gas (W -pdV -p?V) and
  Q means heat flowing into gas
• W F d but if something is dropped from a
  building, the distance is just the ?h So W
  F?h. But p F/A so F pA. Now Work becomes W
  pA?h. But Ah is Volume so W p?V. Now, since
  Volume is decreasing (e.g., dropped from a higher
  height to a lower height), this is actually
  negative of that W -p?V
• Restatement of conservation of energy
• Internal Energy is essential to understanding
  phase transitions
• When Heat is transferred but Temp. remains same ?
  Heat goes to PE (to break bonds)
• We already know how to calculate work so if we
  can now quantify heat, we can figure out ?U
  without knowing anything about the microscopic
  nature of U!!!

13
Heat Transfer Conduction(Solids Liquids)

• Conduction transfer of energy via direct contact
• Takes place at boundary between 2 substances
• Via collision of atoms and molecules
• Conduction poor in gases (direct contact rare)
• Materials with trapped air become good thermal
  insulators
• A rug is not warmer than cold floor
• Poorer conductor ? less heat conducted away from
  feet
• Metals are good thermal conductors
• Conduction electrons carry U from hot to cold
  areas (valence electrons available for bonding)

14
Heat Transfer Convection(Fluids Liquids
Gases)

• Convection transfer of energy by buoyant mixing
  in a fluid
• Thermal Buoyancy when fluid is heated, it's
  Density decreases
• Hotter, less dense fluid rises
• Cooler, denser surrounding fluid pushes it up ?
  FB, just like in the Law of Archimedes we studied
  in the last chapter
• Conduction occurs between warm, rising fluid and
  cold, static fluid
• Cools and falls back down mixing leads to
  convection currents
• Examples
• Convection happens in the atmosphere oceans
• Sun warming Earth leads to sea/land breezes and
  thermals
• Sun warms water at Equator leads to underwater
  currents

15
Heat Transfer Radiation(EM Waves)

• Radiation transfer of energy via electromagnetic
  waves
• Can operate in a vacuum
• Emission is mainly in the IR part of the spectrum
  (for substances with T lt 430oC)
• U of atoms converted to EM energy radiation
• Radiation carries the energy through space until
  it's absorbed
• Upon absorption, converted to U of atoms of
  absorbing substance
• Everything emits EM Radiation
• Hotter things emit more IR and Visible light
• Emission of radiation cools absorption warms
• Cooling by emission is similar to cooling by
  evaporation (which is analogous to a baseball
  team's batting average going down when its best
  hitters are traded)
• Hold hand to side of lightbulb radiation warms
• Place above, both radiation and convection of
  heated air warms

16
Summary

• Atoms have both KE PE ? Internal Energy (U)
• We know Work (W) is energy in transition and can
  change U
• Since Heat (Q) changes the Temperature (T ? is
  equal to the average KE of the constituent
  particles), we know that Q is also energy in
  transition
• So if we can find both Q W, we can get the
  change in Internal Energy (?U) without any
  reference whatsoever to the microscopic U of each
  individual atom/molecule
• Since we already know how to calculate (or
  quantify) Work, all we need to do is figure out
  how to quantify Heat (Q) now...

17
Specific Heat Capacity Q m c ?T

• Heat is transfer of energy
• Units of Joules and c has units of J/kg-oC
• Amount of Q needed to raise T of 1 kg by 1 oC
• Larger c ? more Q needed to raise T by 1oC
• cwater is really high can absorb or release
  large amounts of Q (that's why it's used in
  radiators, power plants, etc.)

18
In Class Exercise 2

• How much heat must be added to 1 cup (0.3 kg) of
  water to boil it (raise it from 20 oC to 100 oC)?
  
• Note cwater 4.18 kJ/kg-oC (see example 5.2 on
  p. 186)

Known Unknown




m 0.3kg
Q ? J
Ti 20oC
Tf 100oC
cwater 4.18 kJ/kg-oC

• Q mc ?T 0.3kg 4.18kJ/kg-oC 80oC

19
Mechanical Energy can be converted into Heat
Energy

• Mechanical Energy (PE or KE) can be converted
  into Heat (Q) through Friction
• This extra Heat Energy raises the Temperture ?
  which raises the Internal Energy
• But ?T is tiny (e.g., if you assume all KE goes
  to Q, even then KE Q m c ?T -- see p. 156)
• Usually Mech Energy isn't large enough to change
  T significantly (satellite re-entry exception)
• James P. Joule established equivalence of
  mechanical energy and heat
• 1 cal 4.184 J (1 food cal 1 kcal)

20
Phase Transition

• Particles "trapped" in a bound state have
  negative PE
• http//hyperphysics.phy-astr.gsu.edu/hbase/thermo/
  phase.htmlc4
• Negative energy compared to free particles
• Bound atoms are also said to have negative PE
• Answer to reading memo Adding heat to boiling
  water no longer increases KE
• Instead, heat energy goes into breaking the bonds
  
• Thus, increases PE from negative to 0 (breaking
  of bonds)
• Molecule becomes water vapor and leaves liquid
  water
• Same thing happens in melting
• Heat energy goes to increasing PE
• Makes bonds "looser" than they are in a solid
• Temperature remains constant
• Transparency Figure 5.34 on p. 190

PE0
- PE
21
Phase Transitions (contd.)

• Transparency Figure 5.34 on p. 190
• Phase transitions also depend on pressure (more
  pressure higher T)
• Heat needed for transitions is latent heat of
  fusion (solid-to-liquid) and latent heat of
  vaporization (liquid-to-gas)

Temperature
Gas
Boiling
Liquid
Melting
Heat
Solid
22
The Second Law of Thermodynamics (Skip)

• Heat engine transforms heat energy into
  mechanical energy
• 2nd Law Some heat has to go to a reservoir at TL
  
• Efficiency (Work/QH) 100 Carnot eff (TH
  - TL)/TH 100
• Heat Movers (e.g., refrigerators) use Energy
  Input and Phase Transitions to reverse process
• Alternative form of 2nd Law dS dQ/T ? i.e.,
  there is Entropy

23
Wave Types Properties

• Waves move and carry energy but do not have mass
• A wave is a disturbance that travels through a
  medium (for material waves) from one location to
  another. Waves are said to be an energy transport
  phenomenon. As a disturbance moves through a
  medium from one particle to its adjacent
  particle, energy is being transported from one
  end of the medium to the other. A pulse is a
  single disturbance moving through a medium from
  one location to another location. The repeating
  and periodic disturbance which moves through a
  medium from one location to another is referred
  to as a wave. (see also http//www.glenbrook.k12.i
  l.us/gbssci/phys/Class/waves/u10l4a.html)
• Like Q and W, waves can also be thought of as
  energy in transition!
• It's a wave if1) energy moves from one place to
  another and 2) matter doesn't move from one place
  to another (for the most part)
• Transverse waves oscillations are perpendicular
  (transverse) to direction of wave travel (EM)
  (http//id.mind.net/zona/mstm/physics/waves/par
  tsOfAWave/waveParts.htm)

24
Wave Anatomy Properties

• Longitudinal waves oscillations are along
  direction of travel (Sound)
• Pulse single wavefront Continuous wave many
  wavefronts
• Wave properties and Wave Anatomy
  http//www.sciencejoywagon.com/physicszone/lesson/
  09waves/introwav/sld003.htm
• Energy is proportional to amplitude squared
  (recalling the definitions of KE -- 1/2 times
  velocity squared -- and spring PE -- 1/2 k times
  x squared -- should give some feel for this)
• Answer to Reading Memo Some waveforms aren't
  symmetrical (e.g., in noise, which isn't
  periodic)
• But you can always measure the amplitude, even if
  you can't determine the equilibrium position, by
  using a technique called peak to peak amplitude
  measurement, which measures the entire height of
  a waveform, top to bottom
• As wavefront spreads out more and more, material
  waves' amplitude decreases (since amplitude is
  directly related to energy and energy is spread
  over the whole wavefront, as the wavefront
  expands, the amount of energy per unit length
  decreases as it has to spread out more)
• As wavefront spreads out more and more, it begins
  to look flat becomes a plane wave (wavefronts
  become straight planes rays become parallel)

25
Wave Propagation

• Speed of wave rate of movement of disturbance
  (depends only on medium for material waves)
• v v(F/?), where F is the Tension in the string
  and ? m/L (using properties of the medium)
• Changes in tension and length alter the frequency
  of the pulse's back and forth oscillation, just
  like tuning a string or pressing a guitar string
  against a fret does the same.
• v f ? (using properties of the wave)
• higher frequency shorter wavelength

26
In Class Exercise 3

• What is the frequency of light of wavelength 700
  nm? Similar to Example 6.3 on p. 213

Known Unknown


? 700nm
f ?Hz
c 3 x 108m/s

• c f? ? f c/?

27
The Doppler Effect

• Doppler Effect wavelength shorter than when
  source is at rest (in direction of motion)
• http//surendranath.tripod.com/Doppler/Doppler.htm
  l
• Diffraction wave bends around edges if plane
  wave hits opening smaller than wavelength, starts
  to bend around, as if new wave originating from
  that spot
• Interference constructive and destructive when
  overlap is ½ wavenlength, destructive when
  multiple of whole wavelength, constructive
  (http//www.glenbrook.k12.il.us/gbssci/phys/Class/
  waves/u10l3c.html)