Heat and WavesChapters 5 & 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

http://plabpc.csustan.edu/general/tutorials/temperature/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.html#c3

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

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 α = 12 x 10-6/oC (see Example 5.1 on p. 171)

Known Unknown

lbridge, summer= 1,000m

Ti, summer = 35oC

Δlwinter = ?m

•ΔT is negative

•Δl is also negative

•This expansion/contraction used in bimetallic strips in thermostats (Fig 5.9 on p. 172)

Tf, winter = -5oC

α = 12 x 10-6/oC

Expansion 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!

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)

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?

1. Energy (KE, PE, and U), which is changed by:

2. Work

3. 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

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 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(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)

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

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

< 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

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...

Specific Heat Capacity: Q = m c ΔT

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.)

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)

Q = mc ΔT = 0.3kg * 4.18kJ/kg-oC * 80oC

Known Unknown

m = 0.3kg Q = ? J

Ti = 20oC

Tf = 100oC

cwater = 4.18 kJ/kg-oC

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 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)

Phase Transition Particles "trapped" in a bound state have negative PE

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/phase.html#c4

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

PE=0

- PE

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)

Heat

Tem

pera

ture

Melting

Boiling

Solid

Liquid

Gas

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

The Second Law of Thermodynamics (Skip)

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! It's a wave if:

1) 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/partsOfAWave/waveParts.htm)

Wave Types & Properties

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)

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 wavelength

In Class Exercise #3: What is the frequency of light of wavelength 700

nm? Similar to Example 6.3 on p. 213

c = fλ f = c/λ

Known Unknown

λ = 700nm f = ?Hz

c = 3 x 108m/s

The Doppler Effect Doppler Effect: wavelength shorter than

when source is at rest (in direction of motion) http://surendranath.tripod.com/Doppler/Doppler.html

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)