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Physics 214: General Physics
Professor: Ricky J. Sethi Instructor Info

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Lecture Notes for Chapters 5 and 6

  • 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?
  • Summary of Important Equations to understand for the HW:
    1. Δl = α l ΔT
    2. CHANGE in Internal Energy = ΔU = W + Q
    3. Q = m c ΔT
    4. v = √(F/ρ)
    5. v = f λ (for light, c = λ f)
  • 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
      • Liquids/Solids are bound (solids bound more tightly than liquids; imagine connected with springs) → some particles also have PE!
      • Remember: (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
          • For example, 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
  • 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
    • Δl = α l ΔT
      • α → coefficient of linear expansion
    • 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 if α = 12 x 10-6/oC (see Example 5.1 on p. 171)
      Known Unknown
      lbridge, summer= 1,000m Δlwinter = ?m
      Ti, summer = 35oC
      Tf, winter = -5oC
      α = 12 x 10-6/oC
      • ΔT is negative
      • Δl is also negative
      • This expansion/contraction used in bimetallic strips in thermostats (Fig 5.9 on p. 172)
    • Liquids also expand/contract
      • Exception: Dice < Dwater (water expands upon freezing)
    • Gases expand too: V ∝ 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!
  • First Law of Thermodynamics
    • Two ways to increase temperature:
      • 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
      • Doing Work on it
        • Experiment by James P. Joule established established relationship between mechanical work and heat
    • Temperature depends on average KE of atoms and molecules
    • Internal Energy (of atoms & molecules): U = (KE + PE)atomic
      • Gases only have KE but liquids/solids also have PE (since they're bound and oscillate)
    • U increases with increasing Temp
      • Heat, Q, is 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:
        • In Energy in Transition Stored Energy
          Mechanics Work transfers energy to/from → P.E.
          Thermodynamics Heat transfers energy to/from → Internal Energy
        • What quantities are measured in units of Joules?
          1. Energy (KE and PE)
          2. Work
          3. Heat
        • That's because they're all different forms of energy (stored or in transition)
    • 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!
    • 1st Law: CHANGE in Internal Energy = ΔU = W + Q (http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/inteng.html#c3)
      • W means work done on gas (+W = -pdV = -pΔV) and +Q means heat flowing into gas
        • W = F • d; but if something is dropped from a building, the distance is just the Δh; So W = F•Δh. But p = F/A so F = pA. Now Work becomes W = pA•Δh. But A•h is Volume so W = pΔV. Now, since Volume is decreasing (e.g., dropped from a higher height to a lower height), this is actually negative of that: +W = -pΔV
      • 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 ΔU without knowing anything about the microscopic nature of U!!!
  • Heat Transfer
    • Conduction: transfer of energy via direct contact (SOLIDS & LIQUIDS)
      • 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
      • Metals are good thermal conductors
        • Conduction electrons carry U from hot to cold areas (valence electrons available for bonding)
      • A rug is not warmer than cold floor
        • Poorer conductor → less heat conducted away from feet
    • Convection: transfer of energy by buoyant mixing in a fluid (FLUIDS: LIQUIDS & GASES)
      • 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
      • Convection happens in atmosphere
        • Sun warming Earth leads to sea/land breezes and thermals
      • Convection happens in oceans, too
        • Sun warms water at Equator; leads to underwater currents
    • Radiation: transfer of energy via electromagnetic waves (EM WAVES)
      • Can operate in a vacuum
      • Emission is mainly in the IR part of the spectrum (for substances with T < 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
  • Specific Heat Capacity
    • 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 (ΔU) 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...
    • Q = m c ΔT
      • Heat is transfer of energy so 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 oC
    • 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
    • Mechanical Energy (PE or KE) can be converted into Q (which raises T → Internal Energy)
      • But ΔT is tiny (e.g., if you assume all KE goes to Q, even then: KE = Q = m c ΔT -- 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)
    • cwater is really high: can absorb or release large amounts of U (that's why it's used in radiators, power plants, etc.)
  • Phase Transition
    • Particles "trapped" in a bound state have negative PE
    • Answer to reading memo: Adding heat to boiling water no longer increases KE
      • Instead, heat energy goes to break bonds
      • Thus, increases PE from negative to 0 (breaking of bonds)
      • Molecule becomes water vapor and leaves liquid water
    • Same thing in melting
      • Heat energy goes to increasing PE
      • Makes bonds "looser" than they are in a solid
      • Temp. remains constant
        • Transparency: Figure 5.34 on p. 190
    • Also depends 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)
  • Second Law of Thermodynamics
    • 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
  • Wave Types and 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.il.us/gbssci/phys/Class/waves/u10l4a.html)
    • Like Q and W, waves can also be thought of as energy in transition!
    • Transverse waves: oscillations are perpendicular (transverse) to direction of wave travel (EM) (http://id.mind.net/~zona/mstm/physics/waves/partsOfAWave/waveParts.htm)
    • 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)
  • Wave Propagation
    • Speed of wave = rate of movement of disturbance (depends only on medium for material waves)
    • v = √(F/ρ), where F is the Tension in the string and ρ = 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 λ (using properties of the wave)
    • higher frequency == shorter wavelengths
      • In-class Exercise 3: What is the frequency of light of wavelength 700 nm? Similar to Example 6.3 on p. 213
        Known Unknown
        λ = 700nm f = ?Hz
        c = 3 x 108m/s
    • Doppler Effect: wavelength shorter than when source is at rest (in direction of motion)
    • 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.