Question

1
Question

• An ice cube is removed from the freezer and put
  in a cup of hot chocolate. Which
• statement is most accurate?
• A) Cold flows from the ice cube into the hot
  chocolate.
• B) Heat flows from the hot chocolate into the
  ice cube.
• C) The cold from the ice cube mixes with the
  heat from the hot chocolate.

2
Question

• If the kinetic energy of an average ideal gas
  molecule in a sample at 20ºC doubles, its final
  temperature must be _______.
• A) 10ºC
• B) 40ºC
• C) 313ºC
• D) none of the above

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Heat and Heat Transfer

• Where would you rather go for break, Montreal or
  Southern France?

4
Heat Capacity

• Why do you burn your
• mouth (but not your
• hand) when you eat hot
• pie or pizza?

5
Why do we go to the beach to cool off?

• All because water has a high heat capacity!

6
Which heats up more quickly?

• Put a pot of water on the stove 15 minutes to
  boil
• Put same mass of iron 2 minutes to reach 100o
  C
• Substances have different ability to absorb or
  lose heat.

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Heat Capacity and Specific Heat
For many substances, under normal circumstances
?T?Q. Example heat pot of water Or Q C?T
where C is the heat capacity. Takes more Q to
boil 2 cups than 1 cup The specific heat
capacity, or just specific heat, of a substance
is the heat capacity per unit mass.
or
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• Which has a higher specific heat iron or water?
  A) Iron B) water
• Which has a higher specific heat water or sand?
  A) water B) sand

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Water has a very high specific heat
12
Example (text problem 14.12) If 125.6 kJ of heat
are supplied to 5.00?102 g of water at 22 ?C,
what is the final temperature of the water?
13
Example (text problem 14.19) A 0.400 kg aluminum
teakettle contains 2.00 kg of water at 15.0 ?C.
How much heat is required to raise the
temperature of the water (and kettle) to 100 ?C?
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Example (text problem 14.19) A 0.400 kg aluminum
teakettle contains 2.00 kg of water at 15.0 ?C.
How much heat is required to raise the
temperature of the water (and kettle) to 100 ?C?
The heat needed to raise the temperature of the
water to Tf is
The heat needed to raise the temperature of the
aluminum to Tf is
Then Qtotal Qw QAl 732 kJ.
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Can we predict any specific heats? Specific Heat
of Ideal Gases
The average kinetic energy of a molecule in an
ideal gas is
And the total kinetic energy of the gas is
16
Define the molar specific heat at constant
volume this is the heat capacity per mole.
Heat is allowed to flow into a gas, but the gas
is not allowed to expand. If the gas is ideal
and monatomic, all the heat goes into increasing
the average kinetic energy of the particles.
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The amount of added heat is
If the gas is diatomic
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Rotational motions of a 2-atom molecule
Internal energy will be distributed equally among
all possible degrees of freedom (equipartition of
energy). Each degree of freedom contributes ½kT
of energy per molecule and ½R to the molar
specific heat at constant volume.
19
Example (text problem 14.26) A container of
nitrogen gas (N2) at 23 ?C contains 425 L at a
pressure of 3.5 atm. If 26.6 kJ of heat are
added to the container, what will be the new
temperature of the gas?
T1 23 V1 425 L P1 3.5 atm Q 26.6
T2 ?
Change to standard units Absolute T, V in m3 and
P in N/m2 T 296oK V 425 x 10-3 m3 P 3.5
x 1.01 x105 N/m2
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Example (text problem 14.26) A container of
nitrogen gas (N2) at 23 ?C contains 425 L at a
pressure of 3.5 atm. If 26.6 kJ of heat are
added to the container, what will be the new
temperature of the gas?
For a diatomic gas,
The number of moles n is given by the ideal gas
law
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The change in temperature is
The final temperature of the gas is Tf Ti ?T
317 K 44 ?C.
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Thermal Conduction
Through direct contact, heat can be conducted
from regions of high temperature to regions of
low temperature. Energy is transferred by
collisions between neighboring atoms or
molecules.
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The rate of energy transfer by conduction is
where ? is the thermal conductivity, A is the
cross-sectional area, and ?T/d is the temperature
gradient, the temperature change per unit
distance. ? depends on the material. Some
materials conduct heat better than others
25
Also
where R is the thermal resistance.
This is convenient when heat is conducted through
multiple layers because
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Example (text problem 14.51) For a temperature
difference of 20 ?C, one slab of material
conducts 10.0 W/m2 another of the same shape
conducts 20.0 W/m2. What is the rate of heat
flow per m2 of surface when the slabs are placed
side by side with a total temperature difference
of 20 ?C?
For each slab, calculate the thermal resistance
per square meter
27
Example continued
When the materials are placed in series,
When the materials are placed in series, the rate
of heat flow is
28
Final

• Exam IV just like all exams. Covers all material
  since Thanksgiving including material covered
  only in lecture.
• Final-Separate exam. Comprehensive, all material
  until Thanksgiving.
• 8 MC 3 problems. Only from text material
• Recommend studying HW most important .
• Curve exams and many lab grades
• Promods lab (3-5)
• I am in my office TW 2-5

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Question

• You are making macaroni and cheese for dinner,
  again. Which is the best choice for stirring the
  noodles in the pot of boiling water?
• A) a wooden spoon
• B) a metal spoon
• C) any kind of spoon
• D) your finger, but really fast

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Example (text problem 14.48) A metal rod with a
diameter of 2.30 cm and a length of 1.10 m has
one end immersed in ice at 0 ?C and the other end
in boiling water at 100 ?C. If the ice melts at
a rate of 1.32 grams every 175 s, what is the
thermal conductivity of the metal? Assume no
heat loss to the surrounding air.
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We are given geometrical information, A and
d ?T Rate of ice melting which is related to
rate of heat transfer Find ?
32
Example (text problem 14.48) A metal rod with a
diameter of 2.30 cm and a length of 1.10 m has
one end immersed in ice at 0 ?C and the other end
in boiling water at 100 ?C. If the ice melts at
a rate of 1.32 grams every 175 s, what is the
thermal conductivity of the metal? Assume no
heat loss to the surrounding air.
Heat is conducted to the ice at a rate of Qc is
the heat necessary to melt the ice.
The heat conducted to the ice in a time period ?t
is
The heat needed to melt a given mass of ice is Lf
333 x 103 J/kg
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Example continued
Since all the heat conducted by the rod is
absorbed by the ice,
34
Question

• You are trying to transfer heat from a hot
  reservoir to a cold reservoir. You have at your
  disposal an aluminum rod and a copper rod of the
  same size. Which should you choose to have the
  highest rate of energy transfer?
• A) The copper rod alone
• B) The aluminum rod only
• C) The rods in parallel.
• D) The rods in series.

35
Question

• You are in the doctor's office and notice that
  the metal instrument tray feels much colder than
  the exam table you are sitting on. This is
  because
• A) the tray actually is colder than the table.
• B) the exam table has a cushion inside, which
  is a good insulator.
• C) the metal conducts heat away from your hand
  more quickly than does the table.

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Thermal Convection
Hot air rises. We can see the ripples in the air
above a hot road. The rising air transfers heat.
Convection is the movement of heat by fluid
currents. Material is transported from one place
to another.
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Convection can set up convection cells. Hot
fluids rise and cool fluids sink. Important for
cooking, weather, Sun, Ocean currents etc
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Fig. 14.12
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Fig. 14.16
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Thermal Radiation
The most important source of heat on Earth is
the Sun. How can the heat get here? There is
nothing (vacuum between us and Sun) Not by
conduction or convection. Heat gets here by
radiation
44
Radiation is a an electromagnetic (EM)
wave. Light is one example of EM radiation Even
if I turn out the lights this room is full of EM
radiation
45
Examples of radiation
All bodies emit electromagnetic (EM) radiation.
The perfect absorber and emitter of EM radiation
is called a blackbody. The amount and type of
radiation emitted depends on the temperature of
the object.
46
Why do we call them blackbodies?
47
Question

• A wood-burning fireplace has a chimney which
  allows the heated air to rise and escape the
• house. How then does a fireplace then heat the
  room?
• A) convection
• B) conduction
• C) radiation
• D) all of the above

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The rate of energy emission by a blackbody is
(Stefans Law)
where A is the surface area of the emitting body,
T is its temperature, and ? 5.670?10?8 W/m2
K4 is the Stefan-Boltzmann constant.
49
Since an ideal blackbody does not exist, Stefans
law is written as
where e is the emissivity e 0 for a perfect
reflector of EM radiation and e 1 for perfect
blackbody.
50
A spectrum shows the amount of radiation emitted
at a particular wavelength. For a blackbody, the
peak of the spectrum is determined only by its
temperature.
Wiens law
51
The net energy gained or lost by a blackbody at a
temperature T is
where Ts is the temperature of the surroundings.
52
Example (RS 14) A sphere with a diameter of 80
cm is held at a temperature of 250 ?C and is
radiating energy. If the intensity of the
radiation detected at a distance of 2.0 m from
the spheres center is 102 W/m2, what is the
emissivity of the sphere?
The power emitted by a point source is This is
the total power passing through a sphere of
radius d
The emissivity is Notice absolute T
53
Thermos bottle and heat transfer
Vacuum
Silvered surface
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Thermos and heat transfer

• No Heat transfer by conduction. (Vacuum doesnt
  conduct). Small losses through stopper.
• No convection (Vacuum)
• No heat transfer by radiation
• Silvered surface reflects
• heat radiation back into
• bottle

55
Question

• Which of the following do not emit radiant
  energy?
• A) Sun
• B) Earth
• C) Cup of hot chocolate
• D) Ice cube
• E) all of the above emit radiation

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• Good luck on all your finals!
• Especially Physics