Heat, temperature, and thermodynamics Chapters 13-15 The

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Heat, temperature, and thermodynamics

• Chapters 13-15

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The atomic theory of matter

• All matter in our everyday lives is made up of
  atoms.
• The motions of these atoms determine what state
  of matter they exist in.
• Relatively slow moving atoms in a solid have a
  balance of attractive and repulsive forces that
  hold them so that they move only slightly around
  a fixed position.

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Continued

• In a liquid, the chemical bonds of a solid have
  been overcome by increased atomic motion, leaving
  only Vanderwaals forces to keep the atoms close
  together, but not actually attached to each
  other.
• In a gas, the atomic motion becomes great enough
  to overcome these electrostatic forces, and allow
  the atoms to separate completely.
• The motion of these atoms is determined by the
  amount of thermal energy they have, specifically
  their kinetic energy.

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Kinetic Theory of Temperature

• The analysis of matter in terms of atoms in
  continuous random motion.
• See page 368 to read the postulates. We will deal
  with these and the math more later.
• In other words, measuring the temperature of
  something measures the average kinetic energy of
  its atoms and molecules.
• However, the motions of the individual atoms and
  molecules may vary greatly within a substance of
  a certain temperature. Thats why we deal with
  average values.
• A side note on absolute zero

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Thermal expansion

• Most materials expand when heated and contract
  when cooled.
• Change in length of almost all solids is close to
  directly proportional to change in temperature
• The proportionality can be modeled by this
  equation
• ?LaL0?T
• LL0(1a?T)

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What does it all mean?!?!

• L is final length
• L0 is initial length
• a is the coefficient of linear expansion, and
  differs from material to material
• ?T is the change in temperature

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Volumes of materials also undergo a change with
varying temperature

• ?VßV0?T
• ß is the coefficient of volume expansion
• Calculations of these types need to be done in
  the design of any material that undergoes changes
  in temperature (roads and bridges, engine parts)
  as part of it use. If not taken into account,
  these stresses can cause failure of the
  materials.

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A bridge is built of 2 slabs of concrete that are
9 m long at 20 degrees C. The ends are fixed with
an expansion joint between the slabs

• How wide should the expansion joints between the
  slabs be (at 20 degrees C) to prevent buckling of
  the bridge if the temperature range is -20 to 45
  degrees Celsius?
• What is the total range the joints must
  accommodate?

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An ordinary glass is filled to the brim with
350.0 ml of water at 100 degrees Celsius. If the
temperature of the water was reduced to 15
degrees Celsius, how much extra water could now
be added to the glass?
10
The 70L steel gas tank of a car is filled to the
top with gasoline at 20 degrees C. The car sits
in the sun and the tank reaches a temperature of
40 degrees C. How much gas do you expect to
overflow from the tank?
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Anomalous behavior of water between 0-4 degrees C

• Due to the formation of ice crystals beginning at
  4 degrees Celsius, water expands when cooled
  between 0-4 degrees C.
• As ice crystals collapse, water contracts when
  heated from 0-4 degrees C.
• At what temperature is water most dense?
• What is found inside an ice crystal?

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Ideal gas law

• Relationship of how P,V, or T will change.
• Must hold two constant to study changes in the
  third.
• The relationship of mass to the other three can
  be incorporated if the number of moles is used to
  represent the mass of the substance
• n in molesmass in grams/molecular mass in g/mol
• Ex CO2 has a molecular mass of 44g/mol. What is
  n for 132 g of CO2?
• 3.0 mol

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PVnRT

• R is the universal gas constant with values found
  on page 364.
• Gases follow this fairly accurately unless they
  are at very high pressures and/or close to
  boiling point
• Ex 2L of nitrogen are at 00Celsius and 1 atm.
  Determine the number of moles of nitrogen in this
  container

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STP-standard temperature and pressure

• T273K
• P1.00atm101.3kPa1.013x105 N/m2
• Ex A given sample of CO2 contains 3.01x1023
  molecules at STP. What volume does this sample
  occupy?
• 11.2L

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A balloon has a volume of 1.0 m3. as it rises in
earths atmosphere, its volume expands. What will
be its new volume if its original temperature and
pressure are 20oC and 1.0 atm, and its final
temperature and pressure are -40oC and 0.10 atm?
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Homework

• Due Monday from page 379
• Questions3,5,9,15
• Problems 7,9,13,14,26,29,34

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Heat-the energy transferred from one object to
another due to a difference in temperature

• Heat spontaneously flows from an area of higher
  temperature to lower temperature
• Measured in joules or calories
• The direction of heat flow depends upon
  temperature, the amount of heat flow depends on
  thermal energy.
• Thermal energy is the internal energy of all the
  molecules of a substance

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What determines how much an objects temperature
will change when heat flows into it?

• Qmc?T
• Q is heat
• m is mass
• C is specific heat capacity-a characteristic of a
  material due to its bonds and electrostatic
  forces that effects how much heat it can absorb
  before changing temperature
• Page 387-low specific heats mean little energy is
  needed to change and objects temperature

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Waters high specific heat has a huge effect on
the earths climate

• West and east coast of US
• Bermuda vs. N. Carolina

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Specific heat calculations

• Imagine you have a 1kg copper pan on the
  stovetop. How much heat would be required to
  raise its temperature from 10 degrees C to 90
  degrees C?
• What if it was filled with 1kg of water, then how
  much heat would it take to raise the temperature
  of the entire system from 10 to 90 degrees C?

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Consider an iron block of 0.5 kg at 75 degrees C
dropped into a container of water at 15 degrees
C. Assume no heat transfer outside the system.
Which of the following statements are true?

• The decrease in iron temperature is equal to the
  increase in water temperature.
• The quantity of heat lost by the iron is equal to
  the quantity of heat gained by the water
• The iron and water will both reach the same
  temperature
• The final temperature of the iron and water is
  half way between the initial temperature of both.

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Consider an iron block of 0.5 kg at 75 degrees C
dropped into a container of water at 15 degrees
C. Assume no heat transfer outside the system. If
there is 1.2 kg of water present, solve the final
temperature of each.
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Latent heat

• Latent means hidden
• Latent heat is the name given to the heat used to
  change the state of a substance
• Temperature does not change during phase change,
  even though additional heat is being added. Why?
• 335 J/g for latent heat of fusion of water
• 2255J/g for latent heat of vaporization of water
• 4.18 J/g to raise the temperature 1 degree C in
  liquid state

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A note on evaporation

• Evaporation can take place below 100 degrees C,
  but requires slightly more energy at lower
  temperatures (2450J/g at 20 degrees )
• Evaporation is a cooling process
• Condensation is warming process
• Basketball players and coolie cups

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Latent heat calculations

• If you put 0.2 kg of ice at -8 degrees C into a
  glass of water at 20 degrees C, can the ice cool
  the water to 0 degrees C?

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At what temperature will the water end up?
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0.05 kg of water vapor at 100 degrees C condenses
on your skin and cools to 80 degrees before you
can remove it. How much heat is transferred to
your skin?
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Homework due Friday

• Questions 1,2
• Problems 1,2,8,9,11,12,21,28,30,31

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Heat transfer by conduction

• Transfer of kinetic energy by collisions of
  atoms, molecules, or electrons of a material.
• Must be a difference in temperature for heat to
  flow by conduction
• Ice on plates
• Some materials are better conductors than others
  due to their grasp on electrons
• See page 396

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Insulative properties of air

• Windows and goosebumps
• Thermal resistivity of building materials defined
  by R values, higher R values mean a better
  insulator
• Also depends on thickness of the material

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Heat transfer by convection

• Movement of large numbers of molecules over large
  distances
• Only occurs in fluids
• Forced convection vs. natural convection
• Heating and cooling vents, fan direction
• Convection and natural processes of the earth
  plate movement, weather patterns, sea breezes

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Heat transfer by radiation

• Requires no material for heat transfer, occurs by
  electromagnetic radiation emitted by one object
  and absorbed by another
• Heat from sun or fire, infrared radiation
• How does color affect emission and absorption of
  radiant energy?
• Mr. Stewart wants to drink his coffee in 10
  minutes. If he wants his coffee to cool fastest,
  should he add room temperature cream right away,
  or wait until he is ready to drink it?

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Angle of radiation can have effect on heat
transferred

• Seasons are not caused by the closeness of the
  earth to the sun, but rather by the angle of the
  suns rays on the earth
• Earth is closer to N Hemisphere during December
  than in July, but the rays in December are less
  direct than in July
• See 14-13 on page 402

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Thermodynamics

• The study of the processes of the transfer of
  energy as heat and work
• Law 1 the change of the internal energy of a
  closed system is equal to the energy added to the
  system by heat minus the work done by the system
  on the surroundings
• ?UQ-W
• KEPE?UQ-W

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This is a restatement of the law of conservation
of energy

• A systems internal energy is U and is a state
  variable. Other state variables include
  P,V,T,m,and n.
• Q and W are not state variables as they are not
  characteristics of the material or state, rather
  something that is added or done to that material

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Other important first law vocab

• Isothermal process- takes place at a constant
  temperature. See page 410, 15-2
• Since the temperature is kept constant, the U
  does not change. Therefore, in an isothermal
  process, WQ
• Heat added to the gas equals the work done
  (output) by the gas

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Adiabatic process- no heat is allowed to flow
into or out of the system. Therefore, Q0

• ?U-W
• Internal energy and also temperature decrease if
  the gas expands
• Adiabatic processes can either occur in a well
  insulated system, or in one where expansion or
  contraction happens very quickly so that heat
  flow cannot take place during the process

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Isobaric process- pressure is kept constant as
volume changes

• For an isobaric process, work can be solved by
  WP?V
• Isovolumetric process-volume is kept constant as
  pressure changes
• For isovolumetric, no volume change means no work
  done
• See table 15-1 on page 412

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Second law- heat only spontaneously flows from
areas of higher temperature to lower temperature.

• Entropy is another state variable of a system.
• Entropy is a measure of disorder of a system.
  More about this later.
• Heat is the graveyard of all other forms of
  energy
• To get work from heat energy is difficult.

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Third law- no system can reach absolute zero

• Would require a sample of matter to exist at zero
  volume
• Bose-Einstein condensates are closest
  experimenters have come
• In a Bose-Einstein condensate, the atoms all
  exist in the same quantum state, and act as a
  single super atom
• Displays bizarre properties, such as being able
  to slow light down to the speed of a bicycle.

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Heat and refrigeration cycles

• Pair up for a small research project
• Heat engines, any device that transforms thermal
  energy into mechanical work
• Steam engine/Rankine cycle, internal combustion
  engine/otto cycle, Carnot Engine,
• Air Conditioner/refrigeration cycle, Heat pump
• Diesel Cycle, Stirling Cycle, Brayton Cycle

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Requirements

• Classify as either a power cycle or a heat pump
  cycle
• When applicable, explain the design features and
  what it is used for
• Describe the processes that take place within it
  and what it is designed to do
• Include the thermodynamic processes that take
  place (ieisothermal, isobaric, isometric) and
  explain what they mean
• Give a brief historical perspective on your
  cycle, including any impact its evolution has
  had on modern society
• Will be presented as a powerpoint.

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Thermo calculations

• Keep in mind if heat is added to a system Q is
  positive
• If heat is lost by a system, Q is negative
• If work is done by a system, W is positive
• If work is done on a system, W is negative

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2200 J of heat is added to a system and 1450 J of
work is done on the system. What is the change in
internal energy of the system?

• ?UQ-W
• 3650 J

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An ideal gas expands isothermally performing
1900J of work in the process. Solve the change in
internal energy of the gas and the heat absorbed
during expansion.

• ?U0 since no change in temp
• Heat absorbed must be equal to work done1900J

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At constant pressure of 1 atmosphere (101000
N/m2), 45,800J of heat is added to a gas in a
container fitted with a frictionless movable
piston. Solve the work done by the gas if the
volume changes by 0.3 m3. Also solve the change
in internal energy of the gas.

• For an isobaric process, work can be solved by
  WP?V
• 30300 J
• 15500 J

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The pressure in an ideal gas is cut in half
slowly while being kept in a container with rigid
walls. In this process, 24,000J of heat left the
gas. How much work was done during this process
and what was the change in internal energy of the
gas?

• Isovolumetric, so W0
• ?Q-24,000J

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In an engine, an almost ideal gas is compressed
adiabatically to half its volume. In doing so,
2000 J of work is done on the gas. How much heat
flows into or out of the gas, and what is its
change in internal energy?

• None, it is adiabatic
• 2000 J

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Heat cycles and engines

• It is easy to turn work into heat
• It is difficult to get usable work from heat
• Power cycles using heat require much more energy
  input in the form of heat than they give output
  work
• They also require a temperature difference from
  one part of the process to the other

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Heat must be able to flow from an area of high
temp to low temp for work to be done by the system

• In all thermo cycles, the ?U0 because it returns
  to its starting state at the end of each cycle
• Heat input (QH) at a high temperature (TH) is
  partly transformed to work and partly exhausted
  as unused heat (QL)
• QH W x QL
• TH and TL are operating temperatures

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Heat engines and efficiency

• Why must we have a difference in temperature to
  run a heat engine?
• Without a temperature gradient, the pressure
  would be the same in all parts of the engine and
  equal amounts of work would be needed during
  intake and exhaust and would give no net work

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See page 418 for efficiency equations