Heat Transfer

Lecturer: Professor Stephen T. Thornton

Reading QuizReading Quiz

1 kg of water at 100°C is poured into a

bucket that contains 4 kg of water at

0°C. Find the equilibrium temperature

(neglect the influence of the bucket).

A) 0°C

B) 20°C

C) 50°C

D) 80°C

E) 100°C

Because the cold water mass is greatercold water mass is greater, it will

have a smaller temperature changesmaller temperature change!

The masses of cold/hot have a ratio of 4:1, so

the temperature change must have a ratio of

1:4 (cold/hot).

Reading Quiz Reading Quiz

1 kg of water at 100°C is poured into a

bucket that contains 4 kg of water at

0°C. Find the equilibrium temperature

(neglect the influence of the bucket).

A) 0°C

B) 20°C

C) 50°C

D) 80°C

E) 100°C

QQ11 = = QQ22

mm11ccTT11 = = mm22ccTT22

TT11 TT22 = = mm22 mm11/ /

Last Time

Thermodynamic processesIsothermal, adiabatic

Specific heat of gasesEquipartition

Today

Adiabatic expansion Heat transfer Conduction Convection Radiation

Conceptual Quiz:An ideal monatomic gas has a molar heat capacity Cp at constant pressure. What is

the molar heat capacity at constant volume for an ideal diatomic gas? A) Cp B) Cp + R

C) Cp –R D) Cp + 3 R/ 2

E) Cp - 3R/2

Answer: C

We found CP – CV = R, so CV = CP – R. We found this for monatomic gases, but we also found experimentally it was true for diatomic gases.

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Adiabatic Expansion of a GasFor an adiabatic expansion, dEint = -PdV, since there is no heat transfer, Q = 0.

From the relationship between the change in internal energy and the molar heat capacity, dEint = nCVdT. So –PdV = nCVdT

From the ideal gas law, d(PV) = PdV + VdP = nRdT.

Combining and rearranging gives

(CP/CV)PdV + VdP = 0.

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Define:

Integration of

then gives the result (see textbook):

γ is called the adiabatic gas constant

P

V

CC

0P

V

CPdV V dP

C

constantPV g =

A Comparison Between Isotherms and Adiabats

Do Jug O’Air demo.

Heat Exchange

Conduction – molecules touch each other and exchange energy.

Convection – hot fluids rise Radiation – electromagnetic

radiation like light, infrared,

ultraviolet radiation; all frequencies.

These are very important!!

Heat conduction

If we put a torch to a piece of metal, the molecules in the metal have increased kinetic energy. They collide with adjacent molecules, and the heat moves down the material via these collisions. Start demo.

Some materials transport heat energy more easily than others. Metals are good heat conductors. Wood and plastics are poor.

Heat Conduction Through a Rod

Q is proportional to A and temperatures T2 – T1

Q is proportional to 1/L

T

Q kA tL

is heat flow

through rod

Q

where k is called the thermal conductivity W/(m K)

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The constant k is called the thermal conductivity.

Materials with large k are called conductors; those with small k are called insulators.

Note: materials that are good heat conductors are also good electrical conductors. Why?

Do thermal conductivity demos

Note in the table on thermal conductivities that air is a very poor heat conductor. In fact, we could say it is a good heat insulator.

This is why double pane windows are such good insulators both in the summer and winter. Glass panes are thin and conduct heat much better than air. The layer of air does wonders!

Conceptual Quiz:Which of the following configurations conducts heat more readily?

A) The one on the left. B) The one on the right. C) They both conduct the same.

Answer: A

Remember that heat flow Q is proportional to A/L, which both favors the left side. The rods on the left have the full T, which also helps.

T

Q kA tL

Countercurrent Heat Exchange in the Human Arm

Same phenomenon happens with sea gulls, egrets and other wading birds.

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Building materials are measured using R-values rather than thermal conductivity:

Here, is the thickness of the material./R k=

Heat Exchange

Conduction – molecules touch each other and exchange energy.

Convection – hot fluids rise Radiation – electromagnetic

radiation like light, infrared,

ultraviolet radiation; all frequencies.

These are very important!!

Heat convection

Well known phenomenon because hot fluids rise due to their lower density. We take advantage of this by putting heat ducts on the floor.

Do demo – convection chimney

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Convection occurs when heat flows by the mass movement of molecules from one place to another. It may be natural or forced; both these examples are natural convection.

Heat radiationHave you ever sat in front of a campfire and wondered why your face is so warm, and your behind so cold?

We have not yet studied light, but when we do next semester, you will learn that all objects emit electromagnetic radiation. Waves easily carry energy in the form of light, radar, microwave (cell phone), etc.

Our existence depends on heat radiation from the Sun.

Do light the match (wood) demo. Example of radiation.

Heat radiation is noted in terms of radiated power P

4

-8 2 4

unit W

is called the emissivity and is

between 0 and 1. is area.

= 5.67 10 W/(m K )

Called the Stefan-Boltzmann constant

dQP AT

dt

A

= 1 is a perfect emitter and absorber, and is called a blackbody.

= 0 is an ideal reflector.

Inside of a thermos bottle is shiny and is a good reflector. The heat of the container emits radiation, but it is not absorbed by the outer wall.

e

e

The Thermos Bottle

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If you are in the sunlight, the Sun’s radiation will warm you. In general, you will not be perfectly perpendicular to the Sun’s rays, and will absorb energy at the rate:

21000 cos W/mQ

At

e qD

=D

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This cos θ effect is also responsible for the seasons.

Conceptual Quiz:Which of the following processes of heat transfer is independent of the area exposed? A)   conductionB)   convectionC)   radiationD)   all of these

E) none of these

Answer: E

In one form or the other, all of the heat transfer mechanism depend on the area.

Conceptual QuizConceptual Quiz

You step out of a swimming

pool on a hot day, where the

air temperature is 90°F. Where

will you feel cooler, in Phoenix

(dry) or in Philadelphia

(humid)?

A) equally cool in both places

B) Philadelphia

C) Phoenix

In Phoenix, where the air is dry, more of the water will

evaporate from your skin. This is a phase change,

where the water must absorb the heat of vaporization,

which it takes from your skin. That is why you feel cool

as the water evaporates.

Conceptual QuizConceptual Quiz

You step out of a swimming

pool on a hot day, where the

air temperature is 90°F. Where

will you feel cooler, in Phoenix

(dry) or in Philadelphia

(humid)?

A) equally cool in both places

B) Philadelphia

C) Phoenix

Conceptual Quiz:Do the rods in a previous question transmit an equal amount of heat when in the parallel configuration?

A) No, because they have different heat conductivities.B) Yes, because the temperatures are different at the ends.C) No, because the temperatures are different at the ends.D) Yes, because they have the same areas and lengths.

Answer: A

Look at the equation for thermal conduction. It depends on thermal (heat) conductivity.

T

Q kA tL