Temperature and Heat

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Temperature and Heat
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Temperature Scales
NOTE K0 is absolute zero, meaning (almost)
zero KE/molecule
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Temp Scales Question

• Two cups of coffee are heated to 100 degrees
  Fahrenheit. Cup 1 is then heated an additional
  20 degrees Centigrade, cup 2 is heated an
  additional 20 Kelvin. Which cup of coffee is
  hotter?
• A) One B) Two C) Same

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Thermal Expansion

• When temperature rises
• molecules have more kinetic energy
• they are moving faster, on the average
• consequently, things tend to expand
• amount of expansion depends on
• change in temperature
• original length
• coefficient of thermal expansion
• L0 ?L L0 ? L0 ?T
• ?L ? L0 ?T (linear expansion)
• ?V ? V0 ?T (volume expansion)

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Density Question

• As you heat a block of aluminum from 0 C to 100 C
  its density
• A. Increases
• B. Decreases
• C. Stays the same

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Example concrete sidewalk

• A concrete (a12x10-6 /K) sidewalk is 10m long
  when poured on a cold day (0o C) How much will
  the length of the sidewalk increase on a hot day
  (35o C)?

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Example gas tank

• A steel (ß36x10-6 /K) gas tank has a volume of
  75 lit. You fill it up with gasoline (ß950x10-6
  /K) early in the morning when it is cool During
  the day the temperature increases by 20o C. How
  much gas will spill out?

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Differential Expansion Demo

• A bimetallic strip is made with aluminum
  a16x10-6 /K on the left, and iron a12x10-6 /K
  on the right. At room temperature, the lengths of
  metal are equal. If you heat the strips up, what
  will it look like?

A B C
Aluminum gets longer, forces curve so its on
outside
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Amazing Water

• Water is very unusual in that it has a maximum
  density at 4 degrees C. That is why ice floats,
  and we exist!

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Tight Fit

• An aluminum plate has a circular hole cut in it.
  An aluminum ball (solid sphere) has exactly the
  same diameter as the hole when both are at room
  temperature, and hence can just barely be pushed
  through it. If both the plate and the ball are
  now heated up to a few hundred degrees Celsius,
  how will the ball and the hole fit ?
• A. The ball wont fit through the hole any more
• B. The ball will fit more easily through the hole
  
• C. Same as at room temperature

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• Why does the hole get bigger when the plate
  expands ???

Imagine a plate made from 9 smaller pieces. Each
piece expands. If you remove one piece, it will
leave an expanded hole
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Stuck Lid Question

• A glass jar (a 3x10-6 K-1) has a metal lid (a
  16x10-6 K-1) which is stuck. If you heat them by
  placing them in hot water, the lid will be
• A. Easier to open
• B. Harder to open
• C. Same

Copper lid expands more, making a looser fit, and
easier to open!
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Heat

• Definition Flow of energy between two objects
  due to difference in temperature
• Note similar to WORK
• Object does not have heat (it has energy temp)
• Units Joule
• 4186 Joules 1 Calorie 1000 calories
• calorie Amount of heat needed to raise
• 1g of water 1ºC

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Example Sears Tower

• You decide to take the stairs to the top of the
  Sears tower (442m). If you have a weight of 670N
  and your body was 100 efficient in converting
  food into mechanical energy. How many Calories
  would you need to eat to replenish your body

Whopper with Cheese 696 Cal Big Mac with
Cheese 560 Cal
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Specific Heat

• Heat adds energy to object/system
• IF system does NO work then
• Heat increases internal energy. Q DU
• Heat increases temperature!
• Q c m DT
• Heat required to increase Temp depends on amount
  of material (m) and type of material (c)
• Q cm?T Cause inertia x effect (just
  like Fma)
• cause Q
• effect ?T
• inertia cm (mass x specific heat capacity)
• ?T Q/cm (just like a F/m)

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Question

• After a grueling work out, you drink a liter of
  cold water (0 C). How many Calories does it take
  for your body to raise the water up to body
  temperature of 36 C?
• 1) 36 2) 360 3) 3,600 4) 36,000

1 liter 1,000 grams of H20 1000 g x 1
calorie/(gram degree) x (36 degree) 36,000
calories 36,000 calories 36 Calories!
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Question

• Suppose you have two insulated buckets containing
  the same amount of water at room temperature. You
  also happen to have two blocks of metal of the
  same mass, both at the same temperature, warmer
  than the water in the buckets. One block is made
  of aluminum and one is made of copper. You put
  the aluminum block into one bucket of water, and
  the copper block into the other. After waiting a
  while you measure the temperature of the water in
  both buckets. Which is warmer?
• 1. The water in the bucket containing the
  aluminum block
• 2. The water in the bucket containing the copper
  block
• 3. The water in both buckets will be at the same
  temperature

Since aluminum has a higher specific heat than
copper, you are adding more heat to the water
when you dump the aluminum in the bucket
(qmcDT).
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Specific Heat Question
Suppose you have equal masses of aluminum and
copper at the same initial temperature. You add
1000 J of heat to each of them. Which one ends
up at the higher final temperature A)
aluminum B) copper C) the same
?T Q/cm
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Latent Heat L

• As you add heat to water, the temperature
  increases for a while, then it remains constant,
  despite the additional heat!
• Latent Heat L J/kg is heat which must be
  added (or removed) for material to change phase
  (liquid-gas).

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Ice Question

• Which will do a better job cooling your soda, a
  cooler filled with water at 0C, or a cooler
  filled with ice at 0 C.
• A) Water B) About Same C) Ice

Latent Heat L J/kg is heat which must be
added (or removed) for material to change phase
(liquid-gas).
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Example sweat

• During a tough work out, your body sweats (and
  evaporates) 1 liter of water to keep cool (37 C).
  How much water would you need to drink (at 2C) to
  achieve the same thermal cooling? (recall CV
  4.2 J/g for water, Lv2.2x103 J/g)

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Question

• Summers in Phoenix Arizona are very hot (125 F is
  not uncommon), and very dry. If you hop into an
  outdoor swimming pool on a summer day in Phoenix,
  you will probably find that the water is too warm
  to be very refreshing. However, when you get out
  of the pool and let the sun dry you off, you find
  that you are quite cold for a few minutes
  (yes...you will have goose-bumps on a day when
  the air temperature is over 120 degrees).
• How can you explain this?

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Example ice and water

• How much ice (at 0 C) do you need to add to 0.5
  liters of a water at 25 C, to cool it down to 10
  C?
• (L 80 cal/g, c 1 cal/g C , cice 0.5 cal/g C)

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Example ice and water 2

• 0.8kg of ice (at -10o C) is added to 1.4kg of
  water at 20o C, How much of the ice will melt?
  (Lf 33.5x104 J/kg, cwater 4186 J/kg C, cice
  2000 J/kg C)

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Summary

• Temperature measure of average Kinetic Energy of
  molecules
• Thermal Expansion
• ?L ? L0 ?T (linear expansion)
• ?V ? L0 ?T (volume expansion)
• Heat is FLOW of energy
• Flow of energy may increase temperature
• Specific Heat
• Dt 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