Using the

1
Using the Clicker

• If you have a clicker now, and did not do this
  last time, please enter your ID in your clicker.
• First, turn on your clicker by sliding the power
  switch, on the left, up. Next, store your student
  number in the clicker. You only have to do this
  once.
• Press the button to enter the setup menu.
• Press the up arrow button to get to ID
• Press the big green arrow key
• Press the T button, then the up arrow to get a U
• Enter the rest of your BU ID.
• Press the big green arrow key.

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Temperature

• What is temperature?

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Temperature

• Temperature is a measure of the average internal
  energy of an object or a system.
• Internal energy is energy associated with motion
  of atoms and/or molecules.
• Temperature is thus a measure of the average
  kinetic energy of the atoms and molecules making
  up an object or a system.
• (More on this next time)

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Temperature scales

• On the worksheet, see how much you know about the
  various temperature scales and how to convert
  between them.

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Temperature scales

• A change by 1C is the same as a change by 1K.
  The Celsius and Kelvin scales are just offset by
  about 273.
• A change by 1C is the same as a change by 1.8F.
  To convert between Celsius and Fahrenheit we use

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Equations involving temperature

• If the equation involves T, use an absolute
  temperature (we generally use a Kelvin
  temperature).
• If the equation involves ?T, we can use Celsius
  or Kelvin.

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Measuring temperature

• A device used to measure temperature is called a
  thermometer, and all thermometers exploit the
  fact that properties of a material depend on
  temperature. Examples of temperature-dependent
  properties include
• the pressure in a sealed container of gas
• the volume occupied by a liquid
• the voltage generated across a junction of two
  different metals
• All these effects, and plenty of others, can be
  used in thermometers.

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Thermal expansion

• Linear expansion
• Most materials expand when heated. As long as the
  temperature change isn't too large, each
  dimension of an object experiences a change in
  length that is proportional to the change in
  temperature.
• or, equivalently,
• where L0 is the original length, and is the
  coefficient of linear expansion, which depends on
  the material.

Material ( 10-6/C) Material ( 10-6/C)
Aluminum 23 Glass 8.5
Copper 17 Iron 12
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Thermal expansion

• Volume expansion
• For small temperature changes, we can find the
  new volume using
• or, equivalently,
• where V0 is the original volume.

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Bimetallic strip

• A bimetallic strip is made from two different
  metals that are bonded together. The strip is
  straight at room temperature, but it curves when
  it is heated. How does it work?
• What is a common application of a bimetallic
  strip?

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Bimetallic strip

• A bimetallic strip is made from two different
  metals that are bonded together. The strip is
  straight at room temperature, but it curves when
  it is heated. How does it work?
• The metals have equal lengths at
• room temperature but different
• expansion coefficients, so they have
• different lengths when heated.
• What is a common application of a bimetallic
  strip?
• A bimetallic strip can be used as a switch in a
  thermostat. When the room is too cool the strip
  completes a circuit, turning on the furnace. The
  furnace goes off when the room (and the strip)
  warms up.

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What happens to holes?
When an object is heated and expands, what
happens to any holes in the object? Do they get
larger or smaller? 1. The holes get smaller
2. The holes stay the same size 3. The holes
get larger
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Holes expand, too

• Holes expand as if they were filled with the
  surrounding material.
• If you draw a circle on a disk and then heat the
  disk, the whole circle expands.
• Removing the material inside the circle before
  heating produces the same result the hole
  expands.

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Holes expand, too
15
Thermal Stress

• If an object is heated or cooled and it is not
  free to expand or contract, the thermal stresses
  can be large enough to cause damage. This is why
  bridges have expansion joints (check this out
  where the BU bridge meets Comm. Ave.). Even
  sidewalks are built accounting for thermal
  expansion.
• Materials that are subjected to thermal stress
  can age prematurely. For instance, over the life
  of a airplane the metal is subjected to thousands
  of hot/cold cycles that weaken the airplane's
  structure.
• Another common example occurs with water, which
  expands by 10 when it freezes. If the water is
  in a container when it freezes, the ice can exert
  a lot of pressure on the container.

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Heat

• What is heat?

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Heat

• Heat is energy transferred between a system and
  its surroundings because of a temperature
  difference between them.

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Specific heat

• The specific heat of a material is the amount of
  heat required to raise the temperature of 1 kg of
  the material by 1C.
• The symbol for specific heat is c.
• Heat lost or gained by an object is given by

Material c (J/(kg C)) Material c (J/(kg C))
Aluminum 900 Water (gas) 1850
Copper 385 Water (liquid) 4186
Gold 128 Water (ice) 2060
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A change of state

• Changes of state occur at particular
  temperatures, so the heat associated with the
  process is given by
• Freezing or melting
• where Lf is the latent heat of fusion
• Boiling or condensing
• where Lv is the latent heat of vaporization
• For water the values are
• Lf 333 kJ/kg
• Lv 2256 kJ/kg
• c 4.186 kJ/(kg C)

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Which graph?

• Simulation
• Heat is being added to a sample of water at a
  constant rate. The water is initially solid,
  starts at -10C, and takes 10 seconds to reach
  0C.
• You may find the following data helpful when
  deciding which graph is correct
• Specific heats for water cliquid 1.0 cal/g C
  and
• cice csteam 0.5 cal/g C Latent heats for
  water heat of fusion Lf 80 cal/g and heat of
  vaporization Lv 540 cal/g
• Which graph shows correctly the temperature as a
  function of time for the first 120 seconds?

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Which graph?
Which graph shows correctly the temperature as a
function of time for the first 120 seconds? 1.
Graph 1 2. Graph 2 3. Graph 3 4. Graph 4
5. Graph 5 6. None of the above
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Ice water

• 100 grams of ice, with a temperature of -10C, is
  added to a styrofoam cup of water. The water is
  initially at 10C, and has an unknown mass m. If
  the final temperature of the mixture is 0C, what
  is the unknown mass m? Assume that no heat is
  exchanged with the cup or with the surroundings.
• Use these approximate values to determine your
  answer
• Specific heat of liquid water is about 4000 J/(kg
  C) Specific heat of ice is about 2000 J/(kg C)
  Latent heat of fusion of water is about 3 x 105
  J/kg

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Ice water

• One possible starting point is to determine what
  happens if nothing changes phase. How much water
  at 10C does it take to bring 100 g of ice at
  -10C to 0C? (The water also ends up at 0C.)
• You can do heat lost heat gained or the
  equivalent method
• Plugging in numbers gives
• Lot's of things cancel and we're left with
• 100 g 2m, so m 50 g. So, that's one possible
  answer.

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Ice water

• Challenge for next time find the range of
  possible answers for m, the mass of the water.

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Whiteboard