PHYSICS 149: Lecture 26

PHYSICS 149: Lecture 26• Chapter 14: Heat

– 14.1 Internal Energy– 14.2 Heat– 14.3 Heat Capacity and Specific Heat– 14.5 Phase Transitions– 14.6 Thermal Conduction– 14.7 Thermal Convection– 14.8 Thermal Radiation

Lecture 26 Purdue University, Physics 149 1

Final Exam• Wednesday, December 15, 8:00 – 10:00 AM• Place: MSEE B012• Chapters 1 – 15 (only the sections we covered)• The exam is closed book.• The exam is a multiple-choice test.• There will be 30 multiple-choice problems.

– Each problem is worth 10 points.

• You may make a single crib sheet.– you may write on both sides of an 8.5” × 11.0” sheet.

• Review session on Monday• Course Evaluation:

– courseval.itap.purdue.edu/etw/ets/et.asp?nxappid=WCQ&nxmid=start&s=8– open until 12/12/2010

Lecture 10 2Purdue University, Physics 149

ILQ 1The intensity of a sound wave is directly proportional to

A) the frequencyB) the square of the speed of soundC) the amplitudeD) the square of the amplitude


ILQ 2An open pipe (open at both ends) has a length of 50 cm. What is the wavelength of the second harmonic frequency?

A) 25 cmB) 50 cmC) 75 cmD) 100 cm


Internal Energy• The internal energy of a system is the total energy of all of the

molecules in the system except for the macroscopic kinetic energy (kinetic energy associated with macroscopic translation or rotation) and the external potential energy (energy due to external interactions).

• Internal energy includes– Translational kinetic energy of the molecules

• the average translational kinetic energy of the molecules of an ideal gas <Ktr> = (3/2)⋅k⋅TSI (Note: TSI in K)

– Rotational and vibrational kinetic energy of the molecules– Potential energy between molecules– Chemical and nuclear binding energy of the molecules

• Internal energy does not include– any energy related to outside or macroscopic sources or motions, like

• overall translational energy of the system• potential energy due to external fields such as gravity.


Energy Conversion: Joule’s Experiment

As the two masses fall, they cause paddles to rotate.– Gravitational potential energy is converted into kinetic energy

of the paddle wheel.As the paddles agitate the water, it causes water’s temperature rise.– Kinetic energy of the paddle wheel is converted into internal

energy.



Heat

• Definition: Flow of energy between two objects due to difference in temperature– Note: similar to WORK– Object does not “have” heat (it has energy)

• Units: calorie– Amount of heat needed to raise 1g of water 1ºC– 1 Calorie = 1 kcal = 1000 cal = 4186 Joules

• Heat flows from a system at higher temperature to one at lower temperature

The Cause of Thermal Expansion

• Objects expand when their temperatures increase because the vibrational energy of their molecules increases; this makes the average distance between molecules increase.– Example: liquid-in-glass thermometer relies on thermal

expansion of the mercury or alcohol.



• When temperature rises– molecules have more kinetic energy

• they are moving faster, on the average

– consequently, things tend to expand• Amount of expansion depends on…

– change in temperature– original length– coefficient of thermal expansion

• L0 + ΔL = L0 + α L0 ΔT• ΔL = α L0 ΔT (linear expansion)• ΔA = 2αA0 ΔT (area expansion)• ΔV = β V0 ΔT (volume expansion)

Thermal Expansion

Temp: T

Temp: T+ΔTL0

ΔL


Expansion Coefficients


Thermal Expansion


Amazing WaterWater is very unusual in that it has a maximum density at 4 degrees C. That is why ice floats, and we exist!

ρ (kg m-3)

T (C)


Stuck Lid ILQA glass jar (α = 3x10-6 K-1) has a metal lid (α = 16x10-6 K-1) which is stuck. If you heat them by placing them in hot water, the lid will beA) Easier to openB) Harder to openC) Same

Copper lid expands more, making a looser fit, and easier to open!


Jar ILQA cylindrical glass container (β = 28x10-6 k-1) is filled to the brim with water (β = 208x10-6 k-1). If the cup and water are heated 50C what will happen?

A) Some water overflowsB) SameC) Water below rim

Water expands more than container, so it overflows.

Heat Capacity, C• If no mechanical work is done either on or by a system,

its change in internal energy is equal to the heat energy transferred into the system.

• For many substances, the change in temperature is proportional to the change in heat energy; the constant of proportionality is called the heat capacity. In other words, the heat capacity of the system is the ratio of heat flow into a system to the temperature change of the system:

– Heat capacity depends on both the substance and also on the amount of the substance which is present.

– Heat capacity is a scalar quantity.– Units: J/K or J/˚C– Q > 0 for heat flow into the system, which causes ΔT > 0– Q < 0 for heat flow out of the system, which causes ΔT < 0


Specific Heat, c• The specific heat capacity (or specific heat) of a substance is the

heat capacity per unit mass.

– Specific heat means the amount of heat necessary to change the temperature of 1 kg of a substance by 1˚C

– Specific heat depends only on the substance (since we divide the heat capacity by the mass).

– Specific heat is a scalar quantity.– Units: J/(kg⋅K) or J/(kg⋅˚C)

• If more than two substances are in contact, heat energy is transferred until they are all in thermal equilibrium. The final temperature and the changes in temperature of the various substances depend on the specific heats and the amounts of the substances that are present.

• The heat required to produce a temperature change in a system is:

– Q > 0 for heat flow into the system, which causes ΔT > 0– Q < 0 for heat flow out of the system, which causes ΔT < 0



Specific Heat• Heat adds energy to object/system• IF system does NO work then:

– Heat increases internal energy: Q = ΔU– Heat increases temperature: Q = C ΔT

• Q = c m ΔT– Heat required to increase T depends on

amount of material (m) and type of material (c)

• Q = cmΔT : “Cause” = “inertia” x “effect” (just like F=ma)– cause = Q– effect = ΔT– inertia = cm (mass x specific heat capacity)– c … specific heat

• ΔT = Q/cm (just like a = F/m)

Phase Transitions• Phase transitions occur when a substance goes from one phase

(solid, liquid, or gas) to another. • Phase transitions occur at constant temperature. During a phase

transition, heat flow continues, but the temperature of the substance does not change.

• The latent heat is the heat energy required per unit mass of effect a phase change.

– The latent heat of fusion Lf: The heat per unit mass that must flow to melt a solid or to freeze a liquid (that is, Lf is for the solid-liquid transition).

– The latent heat of vaporization Lv: The heat per unit mass that must flow to change the phase from liquid to gas or from gas to liquid (that is, Lv is for the liquid-gas transition).

– Latent heat is a scalar quantity.– Unit: J/kg

• Phase transitions can go in either direction, the latent heat is the same (but the heat energy flows the opposite way, of course).


Example: Ice Water Steam

Q = miceciceΔT = 1 kg × 2.1 kJ/kg⋅K × 25 K = 52.3 kJ Q = mi+wLf = 1 kg × 333.7 kJ/kg = 333.7 kJ

Q = mwatercwaterΔT = 1 × 4.19 × 100 = 419 kJQ = mw+sLv = 1 × 2256 = 2256 kJ

Q = msteamcsteamΔT = 1 × 2 × 25 = 50 kJ

m = 1 kgPhase Transitions


Evaporation

• Liquids evaporate due to the spread in kinetic energy of their molecules; the highest-energy molecules are able to escape (because it can break loose from the molecular bonds at the surface of the water), which reduces the average energy of those that are left (thereby cooling the liquid).


Molecular Picture of Gas• Gas is made up of many individual molecules• Number density is number of molecules/volume

– N/V = ρ/m– ρ is the mass density– m is the mass for one molecule

• Number of moles n = N / NA– NA = Avogadro’s number = 6.022×1023 mole-1

– NA= number of molecules per mole– 1 mole = amount of substance that contains as many

elementary entities as there are atoms in exactly 12 grams of carbon-12



Atoms, Molecules and Moles• 1 mole = 6.022 × 1023 molecules (NA = Avogadro’s Number)• NA = Number of atoms or molecules that make a mass equal

to the substance's atomic or molecular mass in grams.• 1 u = 1 atomic mass unit = (mass of 12C atom)/12

– Approximately # of neutrons + # of protons– Atomic weight W

• 1 u = 1.66 × 10-27 kg = 1gram/NA• Mass of 1 mole of “stuff” in grams = molecular mass in u

– E.g. 1 mole of N2 has mass of 2 × 14 = 28 grams


The Ideal Gas Law

• P V = N kB T– P = pressure in N/m2 (or Pascals)– V = volume in m3

– N = number of molecules– T = absolute temperature in K– k B = Boltzmann’s constant = 1.38 x 10-23 J/K– Note: P V has units of N-m or J (energy!)


Ideal Gas Law

You inflate the tires of your car so the pressure is 30 psi, when the air inside the tires is at 20 degrees C. After driving on the highway for a while, the air inside the tires heats up to 38 C. Which number is closest to the new air pressure?

A) 16 psi B) 32 psi C) 57 psi

Careful, you need to use the temperature in K

P = P0 (38+273)/(20+273)


Balloon ILQ

What happens to the pressure of the air inside a hot-air balloon when the air is heated? (Assume V is constant)

A) Increases B) Same C) Decreases

Balloon is still open to atmospheric pressure, so it stays at 1 atm

Transfer of Heat Energy

• There are three ways in which heat energy can be transferred:

– Conduction– Convection– Radiation

For each case, we will study the rate of heat flow (that is, power).



Heat Transfer: Conduction • Hot molecules have more KE than cold molecules

• High-speed molecules on left collide with low-speed molecules on right– energy transferred to lower-speed molecules– heat transfers from hot to cold

• I = rate of heat transfer = Q/t [J/s] – I = κ A (TH-TC)/d

• Q/t = κ A ΔT/Δx– κ = thermal conductivity

• Units: J/s-m-C• good thermal conductors…high κ• good thermal insulators … low κ

– R = d/(Aκ) = thermal resistance

TH

Hot

TC

Cold

d = Δx

Area A


Heat Transfer: Convection • Air heats at bottom• Thermal expansion…density gets smaller• Lower density air rises

– Archimedes: low density floats on high density• Cooler air pushed down• Cycle continues with net

result of circulation of air• I = Q/t = h A ΔT

– h = coefficient of convection• Practical aspects

– heater ducts on floor– A/C ducts on ceiling– stove heats water from bottom– “riding the thermals”


Convection


Heat Transfer: Radiation• All things radiate electromagnetic energy

– Iemit = Q/t = eAσT4

• e = emissivity (between 0 and 1)– perfect “black body” has e=1

• T is Kelvin temperature• σ = Stefan-Boltzmann constant = 5.67 x 10-8 J/s-m2-K4

– No “medium” required• All things absorb energy from surroundings

– Iabsorb = eAσT04

• good emitters (e close to 1) are also good absorbers

Thermal Radiation• Thermal radiation does not (have to) travel through a

material medium (unlike convection) and does not have to be in direct contact (unlike conduction).

• The energy is carried by electromagnetic waves that travel at the speed of light. All bodies emit energy through electromagnetic radiation.

• All materials radiate electromagnetic waves whose frequency depends on their temperature; some radiate in the visible spectrum, such as the Sun and glowing coals, while others radiate in the infrared. – Ex) The Earth is warmed by the Sun’s heat, which is transferred

via radiation.



All things radiate and absorb electromagnetic energy– Iemit = eAσT4

– Iabsorb = eAσT04

– Inet = Iemit - Iabsorb = eAσ(T4 - T04)

if T > T0, object cools downif T < T0, object heats up

T

Surroundings at T0

Hot stove

Heat Transfer: Radiation


RadiationWhich of the following is an example of radiative heat transfer?

A) You stir some hot soup with a silver spoon and notice that the spoon warms up.B) You stand watching a bonfire, but cant get too close because of the heat.C) Its hard for central air-conditioning in an old house to cool the attic.

Blackbody• An idealized body that absorbs all the radiation incident

on it is called a blackbody. • A blackbody emits more radiant power per unit surface

area than any real object at the same temperature. – Note that a good absorber is also a good emitter of radiation,

because it has to emit the same amount of radiation to keep the same temperature.

• It emits a unique radiation spectrumwhich depends only on its temperature and size, and not on the material it is made of or its shape.



Radiation Spectrum

Wien’s Law: λmaxT = 2.898 × 10-3 mK

Infrared: 100 μm - 0.7 μmVisible Light: 0.7 μm - 0.4 μmUltraviolet: < 0.4 μm


Greenhouse Effect

PHYS 149 Students

You guys are great!

Good luck for the exam

Thank you for being my students.


Documents

PHYSICS 149: Lecture 26