Physics 103: Lecture 21 Thermal Physics

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Physics 103 Lecture 21Thermal Physics

• Specific Heat
• Phase Changes
• Latent Heat

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To Change Temperature.

• Add internal energy to system
• Heat a form of energy
• Q c m ?T
• Q amount of heat that must be supplied to raise
  the temperature of mass m by an amount ?T
• Q Joules or calories
• 1 cal 4.186 J
• 1 kcal 1 Cal 4186 J
• Specific heat, c
• amount of heat that must be supplied to raise T
  of 1 kg by 1C
• c J/(kg-C)
• Cause inertia x effect (just like Fma)
• cause Q
• effect ?T
• inertia c m

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Specific Heat

• Adding heat energy (Q) to a substance increases
  its temperature (DT)
• The magnitude of change in temperature (DT)
  depends on the amount (m) and the type (specific
  heat - c) of that substance

The specific heat of substance A is greater than
that of substance B. If equal amount of heat
energy is added to equal masses of these two
substances initially at the same temperature,
which one reaches higher final temperature? Solve
the equation for ?T
substance B.
Provided there is no change in the phase of
substances(next subject)
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Specific Heat
You have various types of materials at the same
initial temperature. You add 1000J of heat to
each of them of them. Which one ends up at the
higher final temperature
Substance c in J/(kg-C) aluminum 900 copper 3
87 iron 452 lead 128 human body
3500 water 4186 ice 2000
Lead is used as solder which is designed to be
easy to melt. The answer is consistent with our
knowledge.
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Consequences of Differing Specific Heats

• Water has a high specific heat compared to land
• On a hot day, the air above the land warms faster
• The warmer air flows upward and cooler air moves
  toward the beach

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Calorimetry

• Conservation of energy applies to the whole
  system
• Consider piece of hot metal placed in cooler
  water
• The energy that leaves the warmer substance
  equals the energy that enters the water
• Qcold -Qhot
• Negative sign keeps consistency in the sign
  convention of ?T
• In some cases with more than two materials, it
  may be difficult to determine which materials
  gain heat and which materials lose heat
• You can start with SQ 0, For two substances
  Qcold -Qhot 0
• Each Q m c DT
• and DT Tf Ti
• You dont have to determine before using the
  equation which materials will gain or lose heat

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Problem 1

• Suppose you have an insulated bucket containing 2
  kg water at T25C. You also have a block of
  aluminum of mass 4 kg at T75C. You put the
  aluminum block in the bucket. What is the final
  temperature of the water?

Answer 40C
Suppose you three substances
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Phase Changes

• Solid - Liquid
• Liquid - Gas

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Boiling Water

• You begin to observe water in a beaker beginning
  to boil on a hot plate. As you add more heat to
  the water which is still boiling, its temperature
• Increases
• Stays constant
• Decreases

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Latent Heat
Latent Heat L J/kg amount of heat per kg
needed to add to or remove from a substance to
change the state of that substance
QmLf (melting-freezing) QmLv (vaporization-conde
nsation)
Substance Lf (J/kg) Lv (J/kg)
water 33.4 x 104 22.56 x 105
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Graph of Ice to Steam
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Warming Ice

• Start with one gram of ice at 30.0º C
• During A, the temperature of the ice changes from
  30.0º C to 0º C
• Use Q m c DT

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Melting Ice

• Once at 0º C, the phase change (melting) starts
• The temperature stays the same although energy is
  still being added
• Use Q m Lf

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Warming Water

• Between 0º C and 100º C, the material is liquid
  and no phase changes take place
• Energy added increases the temperature
• Use Q m c DT
• c is different for water than ice!

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Boiling Water

• At 100º C, a phase change occurs (boiling)
• Temperature does not change
• Use Q m Lv

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Heating Steam

• After all the water is converted to steam, the
  steam will heat up
• No phase change occurs
• The added energy goes to increasing the
  temperature
• Use Q m c DT
• However its now a gas and it will expand or go
  up in pressure depending on the situation.

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Summer in Arizona

• 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?

As the water evaporates off of you, it takes a
great deal of heat from your body to gain the
energy needed to evaporate... this makes you cold.
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Next Time Phase Changes

• Ideal Gas at Constant Temperature PV
  Constant
• Deviation at Critical Temperature - phase change
  - transition to liquid phase
• Critical Pressure minimum for which liquid to
  exists at TC

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Equilibrium

• Liquid and Gas phases are in equilibrium at the
  boiling temperature.
• For water and steam that point is (P1 atm,
  T100oC)
• If both temperature and pressure are raised, the
  equilibrium can be maintained.

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Phase Changes

• Not really a ideal gas or a liquid above the
  critical temp, Tc. A supercritical fluid
• Critical point At Tc and the critical pressure
• Liquid to the left (small V large P) of the
  critical point below Tc
• Ideal gas to the right (large V small P) of the
  critical point below Tc
• Liquid or gas below the critical point - phase
  change region
• If P high enough can make a solid

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Phase Changes

• Ideal Gas at Constant Temperature PV
  Constant
• Deviation at Critical Temperature - phase change
  - transition to liquid phase
• Critical Pressure - minimum needed for
  liquid to exist at TC

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Extra
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Phase changes

• Liquid-vapor equilibrium reached
• Boiling occurs when pvap ? partial pressure of
  the water in the air
• Boiling water on mountain
• boils at Tlt100C
• Boiling water in pressure cooker
• boils at Tgt100C

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H2O

• Triple Point and Critical Point
• Triple point provides much more accurate
  calibration than freezing and boiling points
• The freezing and boiling points depend on pressure

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Vapor Pressure and Partial Pressure

• Daltons Law The total pressure is the sum of
  partial pressures of the component gases,
  assuming ideal gas behavior and no chemical
  reactions.
• Vapor pressure is the gas pressure created by the
  liquid and solid phases of a substance.
• Water evaporates and ice sublimates when their
  vapor pressures exceed the partial pressure of
  water in the surrounding mixture of gases (air).
• If the vapor pressure is less than the partial
  pressure of water vapor in the surrounding air,
  then condensation or frost forms.

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Specific Heat
You have equal masses of aluminum and copper at
the same initial temperature T10C. You put both
of these in an insulated container of water at an
initial temperature of TW 50C. Which one ends
up with the higher temperature. a)
aluminum b) copper c) the same
Substance c in J/(kg-C) aluminum 900 copper 3
87 iron 452 lead 128 human body
3500 water 4186 ice 2000

• Q c m ?T
• Q heat given up by the water
• Copper has smaller inertia
• Therefore, copper has larger effect

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Problem 2
A large punch bowl holds 4 kg of water at 20C. A
0.5-kg ice cube at 0C is placed in the water.
What is the final temperature of the system?
Answer all the ice melts 8.9C
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Lecture 20, Preflight 1 2

• 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

Substance c in J/(kg-C) aluminum 900 copper 387

• Q c m ?T
• Q heat given up by the metal
• Copper has smaller inertia
• Therefore, the water has a larger effect on the
  copper
• effect is drop in temperature
• Copper temperature drops more than aluminum
• Thus, water in the bucket with aluminum block
  ends up with higher final temperature

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Lecture 20 Preflight 4
An open 10 ml container filled to the brim with
water is left on the counter in a room held at
constant 20oC at atmospheric pressure. After a
few days, it is observed that the water has
completely disappeared. What happens if the
container were sealed tightly with very little
air enclosed in it? 1. Water in it will still
evaporate in the same number of days 2. Water
in it will still evaporate but will take much
longer time 3. Water in it will still evaporate
but will take much shorter time 4. Water in it
will not evaporate
Water evaporated when placed in the open
container at a temperature much lower than the
boiling point because it was surrounded by air
rather than solely by water vapor. In a sealed
container the water does not evaporate because
the small sealed volume will have sufficient
vapor in equilibrium with liquid water.
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Climbing Everest
One of the most severe problems for those
climbing very high mountains is the extreme
drying of breathing passages. Explain why this
occurs
Much more water in breathing passages evaporates
because the pressure at high altitude is much
lower than at sea level, although temperature
there is lower.
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Lecture 20, Preflight 3

• Which of the following statements is true?
• 1. Energy is released in the process of melting
• 2. Energy is released in the process of
  evaporation
• 3. Energy is released in the process of
  condensation

QmLv Energy is needed to vaporize. Energy is
released in the reverse condensation process.
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Lecture 19(20), Preflight 8(5)
In a sealed pressure cooker water boils
at     1. lower temperature than in an open
container  2. the same temperature as in an open
container 3. higher temperature than in an open
container

• Liquid and Gas phases are in equilibrium at the
  boiling temperature.
• For water and steam that point is (P1 atm,
  T100oC)
• If both temperature and pressure are raised, the
  equilibrium can be maintained.
• Since pressure is higher the boiling point is
  higher in the sealed container.
• Food gets cooked faster
• In contrast, cooking takes much longer at high
  altitude as the water boils off at lower
  temperature.