220
Lecture PHYSICS 25
Heat Transfer
Transfer
Textbook Sections 14.6 14.8
Lecture 25
Purdue University, Physics 220
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Overview
Last Lecture
Heat is FLOW of energy
Flow of energy may increase temperature
Specific Heat
Heat
T = Q / (c m)
Monatomic IDEAL Gas CV = 3/2 R
Diatomic IDEAL Gas CV = 5/2 R
Latent Heat
Heat associated with change in phase
Today
Thermal Conduction
Thermal Convection
Thermal Radiation
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Quiz 1
On a cool night you make your bed with a thin cotton sheet
covered by thick wool blanket As you lay there all covered
covered by a thick wool blanket. As you lay there all covered
up, heat is leaving your body, flowing though the sheet and the
blanket and into the air of the room. Compare the amount of
heat that flows though the sheet to the amount of heat that
flows through the blanket.
A)More heat flows through sheet than through the blanket.
B)More heat flows through blanket than through the sheet.
C) The same amount of heat flows through sheet as the
bl
blanket.
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Quiz 2
Latent heat is always
A)
B)
C)
D)
part of the specific heat
related to the specific heat
related to the specific heat
the same as the mechanical equivalent of heat
involved in a phase change
in phase change
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Heat Transfer
Heat is the energy that flows between systems at
different temperatures
different temperatures
This transfer can take place in three ways
Conduction
Convection
Radiation
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Heat Conduction
The bar is placed
between two separate
systems at different
temperatures
The bar conducts heat
The bars temperature
varies smoothly from
varies smoothly from
T1 to T2
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Heat Transfer: Conduction
Hot molecules have more KE than cold molecules
High-speed molecules on left collide with lowspeed molecules on right
energy transferred to lower-speed molecules
transferred to lower
molecules
heat transfers from hot to cold
I = rate of heat transfer = Q/t [J/s]
I = A (TH-TC)/d
Q/t = A T/x
= thermal conductivity
Units: J/s-m-C
good thermal conductorshigh
good thermal insulators low
R = d/(A) = thermal resistance
d/(A
thermal resistance
Lecture 25
Purdue University, Physics 220
TH
d = x
TC
Cold
Hot
Area A
7
Heat Conduction
The amount of energy that flows depends on
Th
The area of the bar, A
th
The length of the bar, L
The temperature difference between the two ends
diff
A property of the bar called thermal conductivity,
The rate of heat flow is given by
Q
T
= A
t
L
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Conduction
Which of the following is an example of conductive heat
transfer?
transfer?
A) You stir some hot soup with a silver spoon and notice that
You stir some hot soup with silver spoon and notice that
the spoon warms up.
B) You stand watching a bonfire, but cant get too close
You stand watching bonfire but can get too close
because of the heat.
C) Its hard for central air-conditioning in an old house to cool
Its hard for central air
in an old house to cool
the attic.
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Conduction with 2 Layers
Find I=Q/t in J/s
Key Point: Continuity (just like fluid flow)
I1 = I2
1A(T0-TC)/x1 = 2A(TH-T0)/x2
solve for T0 = temp. at junction
then solve for I1 or I2
answers: T0=2.27 C I=318 Watts
TH-T0 = I R1 and T0-TC = I R2
T = (TH-T0) + (T0-TC) = I (R1 + R2)
I1
I2
Inside: TH = 25C
Outside: TC = 0C
x1 = 0.02 m
A1 = 35 m2 k1 = 0.080 J/s-m-C
x2 = 0.075 m A2 = 35 m2 k2 = 0.030 J/s-m-C
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Purdue University, Physics 220
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ILQ
Touch the metal base of a chair and the top
of a wooden desk in an air-conditioned
room, which feels colder?
A) Base
B) Same
C) Desk
Both must be the same temperature (room
temperature), but metal feels colder because it
it
conducts heat better/faster.
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Metals Feel Cold
If a metal and another material (such as Styrofoam)
are at the same temperature they generally do not
are at the same temperature, they generally do not
feel the same
The metal feels colder
The thermal conductivity of metal is much higher
than that of Styrofoam
The rate of heat flow from your fingers to the metal
is much higher than to the Styrofoam
Therefore, the metal causes your skin to have a
causes you
to
lower temperature and it feels colder
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Convection
Convection is based on
thermal expansion
The warmer material on
the bottom (nearer the
heat source) becomes
less dense
warm low
The warm, low-density
material moves upward
due to the buoyant force
due to the buoyant force
associated with
Archimedes principle
Archimedes principle
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Convection
As the warmer material moves upward, it cools
through conduction to heat the cooler parts of the
through conduction to heat the cooler parts of the
container and the air above
A circular pattern is developed
Convection plays a role in heating and transporting
energy in
A house
Oceans
Atmosphere
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Heat Transfer: Convection
Air heats at bottom
expansion
gets smaller
Thermal expansiondensity 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 T
h = coefficient of convection
Practical aspects
heater ducts on floor
ducts on floor
A/C ducts on ceiling
stove heats water from bottom
riding the thermals
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Convection
Lecture 25
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Convection
Which of the following is an example of convective heat
transfer?
transfer?
A) You stir some hot soup with silver spoon and notice
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
You stand watching bonfire but can get too close
because of the heat.
C) Its hard for central air-conditioning in an old house to
Its hard for central air
in an old house to
cool the attic.
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Convection
Lecture 25
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Radiation
Radiative heat flow involves
energy carried by
electromagnetic (em)
radiation
Electromagnetic radiation is
a type of wave and can be
characterized by frequency,
wavelength and speed
waves carry energy
The waves carry energy
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Radiation
Electromagnetic radiation is generated any time charge an
electric vibrates or undergoes an
electric charge vibrates or undergoes an
acceleration
The vibrations of the atoms generate em radiation
vibrations of the atoms generate em radiation
that carries energy away
The vibration amplitude of the atoms depends on
vibration amplitude of the atoms depends on
the temperature, so the radiated energy depends on
temperature
The energy is absorbed by another object when the
radiation produces a force on the electric charges in
that object
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Electromagnetic Rainbow
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Heat Transfer: Radiation
All things radiate electromagnetic energy
Iemit = Q/t = eAT4
Stefan-Boltzmann Law
e = emissivity (between 0 and 1)
perfect black body has e=1
bl
T is the temperature of the object (in Kelvin)
= Stefan-Boltzmann constant = 5.67 x 10-8 J/s-m2-K4
Stefan
constant 5.67 10
No medium required
All things absorb energy from surroundings
things absorb
from surroundings
Iabsorb = eAT04
good emitters (e close to 1) are also good absorbers
emitters (e close to 1) are also good absorbers
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Heat Transfer: Radiation
All things radiate and absorb electromagnetic
energy
Iemit = eAT4
eA
Surroundings at T0
Iabsorb = eAT04
T
Hot stove
Inet = Iemit - Iabsorb = eA(T4 - T04)
if T > T0, object cools down
if T < T0, object heats up
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Question
One day during the winter, the sun has been shining all day.
Toward sunset a light snow begins to fall. It collects without
melting on a cement playground, but it melts immediately upon
contact on a black asphalt road adjacent to the playground.
How do you explain this.
The black asphalt absorbs more heat from the sun.
The black asphalt has an emissivity of 1 and absorbs
energy from the surrounding (from the sun) compared to
a smaller number for the cement. As a result, it is at a
ll
higher temperature than the cement and melts the
snow
snow.
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Exercise
The Earth has a surface temperature around 270 K and an
emissivity of 0.8, while space has a temperature of around
2 K. What is the net power radiated by the earth into free
space?
space?
(Radii of the Earth and the Sun are RE = 6.38106 m, RS =
7108 m.)
Inet = Iemit - Iabsorb = eA(T4 - T04)
2
= ( 5.67 108 ) ( 4 Rearth ) ( 0.8 ) ( 2704 24 )
= 1.23 1017 Watts
Watts
Lecture 25
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Radiation
Which of the following is an example of radiative heat
transfer?
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
You stand watching bonfire but cant get too close
because of the heat.
C) Its hard for central air-conditioning in an old house to
Its hard for central air
in an old house to
cool the attic.
Lecture 25
Purdue University, Physics 220
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Blackbody
When em radiation bombards an object, some of the
radiation may be absorbed and some reflected
radiation may be absorbed and some reflected
A blackbody is an object that absorbs all em
radiation at all frequencies
di
A perfect blackbody does not exist, but the concept is very
useful
Radiation can be described by two laws
Stefan-Boltzmann
Wiens
Lecture 25
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Radiation Spectrum
Infrared: 100 m - 0.7 m
Visible Light: 0.7 m - 0.4 m
Light:
0.4
Ultraviolet: < 0.4 m
Wiens Law: maxT = 2.898 10-3 mK
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Stefan-Boltzmann Law
The amount of energy radiated by an object depends on its
temperature
If an object has a temperature T and a surface area A, the
rate of energy radiated is given by the Stefan-Boltzmann Law
Q
= AT 4
t
= 5.67 x 10-8 W/m2 is Stefans constant
10
St
is the emissivity of the object
It measures how efficiently it radiates energy
measures how efficiently it radiates energy
= 1 for a blackbody
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Wiens Law
The energy radiated is
distributed as a
function of wavelength
The power is largest
at max where
max
Lecture 25
2.90 x10 3 m K
=
T
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Stefan-Boltzmann and Heat Flow
The total power varies as the fourth power of the
temperature
temperature
Radiated power increases rapidly as T is increased
The power is proportional to the emissivity
power is proportional to the emissivity
= 1 only for a blackbody
It is smaller than 1 for any real object
is smaller than for any real object
Its value depends on the properties of the material and will
be a function of frequency
Many objects are close to being blackbodies and so the
Stefan-Boltzmann Law provides an approximate
description of most radiating objects
description of most radiating objects
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Stefan-Boltzmann and Heat Flow
The Stefan-Boltzmann Law applies to all objects at
all temperatures
all temperatures
Two objects will both radiate energy, but the net transfer
will be from the hotter to the cooler
will be from the hotter to the cooler
The Stefan-Boltzmann Law also describes how heat
is absorbed by an object
Q
= AT 4
t
absorbed
In thermal equilibrium, (Q/t)absorbed = (Q/t)emitted
thermal equilibrium, (Q/t)
(Q/t)
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Sun and Earths Temperature
The Sun has a surface
temperature of
approximately 6000 K
From the StefanBoltzmann Law,
Q/t = 4.6 x 1026 W
This is the rate at
which the energy
leaves the Sun
This produces an
Earth temperature of
~290 K
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Temperature of the Sun
The Sun appear yellowish, i.e., = 0.5 m. What is the
Sun appear yellowish
What is the
temperature at the surface of the Sun?
m T = 2.898 x 10-3 m K
T = 2.898 x 10-3 / 0.5 x 10-6
= 6000 K
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Greenhouse Effect
The atmosphere allows most of
the Suns visible radiation to
reach the surface
It absorbs much of the infrared
absorbs
of the infrared
radiation
The Earth radiates in infrared
Earth radiates in infrared
This energy is absorbed by the
atmosphere and not released to
atmosphere and not released to
space
The trapped infrared radiation
trapped infrared radiation
makes the Earths surface
warmer than it would be without
the atmosphere
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Summary of Concepts
Conduction - contact
I = Q/t = A T/d
Q/t
Convection - fluid motion
I = Q/t = h A T
Radiation - electromagnetic radiation
radiation
Iemit = Q/t = eAT4
Iabsorb = Q/t = eAT04
Q/t eA
Wiens Law: maxT = 2.898 10-3 mK
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