PHYSICS 231 Lecture 28: Thermal conduction

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PHYSICS 231Lecture 28 Thermal conduction
ISOLATION

• Remco Zegers
• Walk-in hour Thursday 1130-1330 am
• Helproom

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Previously Phase Change
Solid (low T)
Qcgasm?T
Qcsolidm?T
GAS(high T)
liquid ? solid
Gas ? liquid
liquid (medium T)
QmLv
QmLf
Qcliquidm?T
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How can heat be transferred?
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Conduction
Touching different materials Some feel cold,
others feel warm, but all are at the same
temperature
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Thermal conductivity
metal
T200C
wood
T200C
The heat transfer in the metal is much faster
than in the wood (thermal conductivity)
T370C
T370C
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Heat transfer via conduction
Conduction occurs if there is a temperature
difference between two parts of a conducting
medium
Rate of energy transfer P PQ/?t (unit
Watt) PkA(Th-Tc)/?xkA?T/?x k thermal
conductivity UnitJ/(msoC) metal k300
J/(msoC) gases k0.1 J/(msoC) nonmetals1 J/(msoC)
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Example
A glass window (A4m2,?x0.5cm) separates a
living room (T200C) from the outside (T0oC).
A) What is the rate of heat transfer through the
window (kglass0.84 J/(msoC))? B) By what
fraction does it change if the surface becomes 2x
smaller and the temperature drops to -200C?
A) PkA?T/?x0.84420/0.00513440 Watt B)
PorigkA?T/?x Pnewk(0.5A)(2?T)/?xPorig The
heat transfer is the same
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Another one.
Heat sink
Heat reservoir
An insulated gold wire (I.e. no heat lost to the
air) is at one end connected to a heat reservoir
(T1000C) and at the other end connected to a
heat sink (T200C). If its length is 1m and
P200W what is its cross section (A)?
kgold314 J/(ms0C). PkA?T/?x314A80/125120A2
00 A8.0E-03 m2
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And another
Water 0.5L 1000C
A0.03m2 thickness 0.5cm.
1500C
A student working for his exam feels hungry and
starts boiling water (0.5L) for some noodles. He
leaves the kitchen when the water just boils.The
stoves temperature is 1500C. The pans bottom
has dimensions given above. Working hard on the
exam, he only comes back after half an hour. Is
there still water in the pan? (Lv540 cal/g,
kpan1 cal/(ms0C)
To boil away 0.5L (500g) of water
QLv500270000 cal Heat added by the stove
PkA?T/?x10.0350/0.005 300 cal PQ/?t
?tQ/P270000/300900 s (15 minutes) Hell be
hungry for a bit longer
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Isolation
inside
Tc
Th
L2
L3
L1
A house is built with 10cm thick wooden walls and
roofs. The owner decides to install insulation.
After installation the walls and roof are 4cm
wood2cm isolation4cm wood. If kwood0.10
J/(ms0C) and kisolation0.02 J/(ms0C), by
what factor does he reduce his heating bill?
PbeforeA?T/0.10/0.10A?T PafterA?T/0.04/0.10
0.02/0.020.04/0.100.55A?T Almost a factor of 2
(1.81)!
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Overview of material for exam 8
??I? (compare to ?Fma) Moment of inertia I
I(?miri2) (kgm2) ? angular acceleration
(rad/s2) I depends on the choice of rotation
axis!!
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Chapter 8 Rotational KE
Rotational KEr½I?2
Conservation of energy for rotating
object PEKEtKErinitial PEKEtKErfinal m
gh½mv2½I?2initial mgh½mv2½I?2final
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Ch 8 Angular momentum
?v/r LI? mr2v/r mvr
Conservation of angular momentum If the net
torque equal zero, the angular momentum L does
not change Ii?iIf?f
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Chapter 9 Youngs modulus.
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Chapter 9 Shear modulus
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Chapter 9 Bulk modulus
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Chapter 9 density
?water1.0x103 kg/m3
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Ch. 9 Pascal
Enclosed fluid F1/A1F2/A2
Pascals principle a change in pressure applied
to a fluid that is enclosed is transmitted to
the whole fluid and all the walls of the
container that hold the fluid.
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P0
Pressure at depth h
P P0 ?fluidgh h distance between liquid
surface and the point where you measure P
h
P
Buoyant force for submerged object
B ?fluidVobjectg Mfluidg wfluid The
buoyant force equals the weight of the amount of
water that can be put in the volume taken by the
object. If object is not moving Bwobject
?object ?fluid
Buoyant force for floating object
The buoyant force equals the weight of the amount
of water that can be put in the part of the
volume of the object that is under
water. ?objectVobject ?waterVdisplaced h
?objectVobject/(?waterA)
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Bernoullis equation
P1½?v12?gy1 P2½?v22?gy2 P½?v2?gyconstant
The sum of the pressure (P), the kinetic energy
per unit volume (½?v2) and the potential energy
per unit volume (?gy) is constant at all points
along a path of flow.
Note that for an incompressible
fluid A1v1A2v2 This is called the equation
of continuity.
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Surface tension Fs?L L contact length between
object and liquid ? surface tension
Fs
Fs
?
Fg
Units of ? N/mJ/m2 Energy per unit surface
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Poiseuilles Law
How fast does a fluid flow through a tube?
?R4(P1-P2)
(unit m3/s)
Rate of flow Q ?v/?t
8?L
? coefficient of viscosity
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Ch. 10 Temperature scales
Conversions TcelsiusTkelvin-273.5 Tfahrenheit9/5
Tcelcius32
We will use Tkelvin. If Tkelvin0, the
atoms/molecules have no kinetic energy and
every substance is a solid it is called
the Absolute zero-point.
Celsius
Fahrenheit
Kelvin
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Ch. 10 Thermal expansion
?L
length
?L?Lo?T
surface
?A?Ao?T ?2?
?V?Vo?T ?3 ?
volume
L0
? coefficient of linear expansion different
for each material
Some examples ?24E-06 1/K Aluminum ?1.2E-04
1/K Alcohol
TT0?T
TT0
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Boyle Charles Gay-LussacIDEAL GAS LAW
PV/T nR Nkb n number of particles in the
gas (mol) R universal gas constant 8.31
J/molK N number of atoms/molecules kbboltzmann
s constant 1.38x10-23 J/K nN/NA NAAvogadros
constant 6.02x1023
If no molecules are extracted from or added to a
system
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Pressure
Number of Molecules
Mass of 1 molecule
Averaged squared velocity
Number of molecules per unit volume
Volume
Average translation kinetic energy
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Ideal gases
Average molecular kinetic energy
Total kinetic energy
rms speed of a molecule MMolar mass (kg/mol)
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Ch. 11 Heat transfer to an object
The amount of energy transfer Q to an object with
mass m when its temperature is raised by ?T
Qcm?T
Change in temperature
Mass of object
Energy transfer (J or cal)
Specific heat (J/(kgoC) or cal/(goC)
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Calorimetry
If we connect two objects with different
temperature energy will transferred from the
hotter to the cooler one until their temperatures
are the same. If the system is isolated
Qcold-Qhot mcoldccold(Tfinal-Tcol
d)-mhotchot(Tfinal-Thot) the final temperature
is Tfinal
mcoldccoldTcoldmhotchotThot
mcoldccoldmhotchot
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Phase Change
Solid (low T)
Qcgasm?T
Qcsolidm?T
GAS(high T)
liquid ? solid
Gas ? liquid
liquid (medium T)
QmLv
QmLf
Qcliquidm?T
Make sure to understand ice -gt water -gt steam
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Heat transfer via conduction
Rate of energy transfer P PQ/?t (unit
Watt) PkA(Th-Tc)/?xkA?T/?x k thermal
conductivity UnitJ/(msoC)
For several layers