Thermal Energy

1
Thermal Energy Temperature

• Thermal energy the total potential and kinetic
  energy associated with the random motion and
  arrangement of the particles of a material.
• When a material is hot, it has more thermal
  energy than when it is cold.
• Temperature is the hotness or coldness of a
  material.
• The quantity of thermal energy in a body affects
  its temperature.
• The same quantity of thermal energy in different
  bodies does not give each the same temperature.
• The ratio between temperature and thermal energy
  is different for different materials.

2
Temperature Kinetic Energy

• The temperature of a substance will increase if
  the average kinetic energy of its particles is
  increased.
• If the average kinetic energy of particles
  decreases, so does the temperature of the
  substance.

3
Heat

• Heat is thermal energy that is absorbed, given
  up, or transferred from one body to another.
• Temperature is a measure of a bodys ability to
  give up heat to or absorb heat from another body.
• The temperature of a body determines whether or
  not heat will be transferred to or from any
  nearby body.
• Heat is a form of energy.
• Heat is thermal energy in motion.
• Heat is used when the transfer of thermal energy
  from one body to another body at a different
  temperature is involved.

4
Temperature

• Temperature is a physical quantity that is
  proportional to the average kinetic energy of
  translation of particles in matter.
• To measure the temperature of a body, you place
  the thermometer in contact with the body.
• If you want to know the temperature of a cup of
  hot coffee, you stick the thermometer in the
  coffee as the two interact, the thermometer
  becomes hotter and the coffee cools off a little.
• After the thermometer settles down to a steady
  value, you read the temperature. The system has
  reached a thermal equilibrium condition, in which
  the interaction between the thermometer and the
  coffee causes no further change in the system.

5
Temperature

• Central concept of thermodynamics is temperature.
• Our temperature sense is often unreliable. The
  same quantity of thermal energy in different
  bodies does not give each the same temperature.
• On a cold winter day, an iron railing seems much
  colder to the touch than a wooden fence post,
  even though both are at the same temperature.
  This error in perception results because the iron
  removes energy from our fingers more quickly than
  the wood does.

6
Triple Point Temperature

• Triple-point temperature the single condition
  of temperature and pressure at which the solid,
  liquid, and vapor phases of a substance can
  coexist in stable equilibrium.
• Solid, liquid, and vapor phases in contact and in
  equilibrium.
• Triple-point temperature of water is the SI
  standard for defining temperature (0C 273.16
  K).

7
Temperature Intervals

• Originally, two fixed points were used to define
  the standard temperature interval.
• Steam point (100? C) the boiling point of water
  at standard atmospheric pressure (1 atm or 760
  mmHg).
• Ice point (0? C) melting point of ice when in
  equilibrium with water saturated air at standard
  atmospheric pressure.

8
Kelvin, Celsius, Fahrenheit Temperature Scales

• Celsius to Kelvin K ? C 273
• Kelvin to Celsius ? C K 273
• Celsius to Fahrenheit TF (1.8TC) 32?
• Fahrenheit to Celsius

9
Absolute zero of temperature (0 K)

• The molecules of a substance at absolute zero
  have a minimum amount of kinetic energy, known as
  zero-point energy.
• Molecular energy is at a minimum, but not zero.

10
Heat Units

• Quantities of heat must be measured by the
  effects they produce.
• No instrument directly measures the amount of
  thermal energy a body releases or absorbs.
• Calorie (cal) quantity of heat required to
  raise the temperature of one gram of water one
  degree Celsius.
• 1 calorie 4.186 Joules

11
Thermal Expansion of Solids

• Solids expand when heated and contract when
  cooled (with a few exceptions).
• Heated solids increase or decrease in all
  dimensions (length, width, and thickness).
• When a solid is heated, the increase in thermal
  energy increases the average distance between the
  atoms and molecules of the solid and it expands.

12
Thermal Expansion of Solids

• Thermal expansion can be explained on a molecular
  basis.
• Picture the inter-atomic forces in a solid as
  springs, as shown in the picture on the right.
• Each atom vibrates about its equilibrium
  position. When the temperature increases, the
  amplitude and associated energy of the vibration
  also increase.

13
Thermal Expansion of Solids
14
Thermal Expansion of Solids

• When the amplitude of vibration increases, the
  average distance between molecules also
  increases. As the atoms get farther apart, every
  dimension increases, including the sizes of
  holes.

15
Thermal Expansion of Solids
16
Coefficient of Linear Expansion - Solid

• Coefficient of Linear Expansion (?) the change
  in length per unit of a solid when its
  temperature is changed one degree.
• ?l change in length l original length
• ? coefficient of linear expansion
• Tf final temperature Ti initial temperature
• new length old length ?l

17
Coefficient of Linear Expansion - Solid

• For problems that involve the contraction or
  expansion of two metals with different
  coefficients of expansion ?, set

18
Coefficient of Area Expansion - Solid

• Coefficient of Area Expansion the change in
  area per unit area per degree change in
  temperature. The coefficient of area expansion
  for a solid is twice the coefficient of linear
  expansion.
• new area old area ?A

19
Coefficient of Volume Expansion - Solid

• Coefficient of Volume Expansion the change in
  volume per unit volume per degree change in
  temperature. The coefficient of volume expansion
  for a solid is three times the coefficient of
  linear expansion.
• new volume old volume ?V

20
Thermal Expansion of Solid

• If there is a hole in a solid body, the volume of
  the hole increases when the body expands, just as
  if the hole were a solid of the same material as
  the body. This remains true even if the hole
  becomes so large that the surrounding body is
  reduced to a thin shell. Thus the volume
  enclosed by a thin-walled flask or thermometer
  bulb increases just as would a solid body of
  glass of the same size.

21
Linear Expansion

• Expansion and contraction of solids is considered
  in the design and construction of any structure
  that will undergo temperature changes.
• Allowances must also be made not only for changes
  in size due to expansion and contraction, but
  also for the different rates of expansion and
  contraction of different materials.

22
Examples of Uses of Thermal Expansion

• You can loosen a tight metal jar lid by holding
  it under a stream of hot water. Both the metal
  of the lid and the glass of the jar expand as the
  hot water adds energy to their atoms. With the
  added energy, the atoms can move a bit farther
  from each other than usual, against the
  inter-atomic forces that hold every solid
  together. However, because the atoms in the
  metal move farther apart than those in the glass,
  the lid expands more than the jar and is
  loosened.
• Expansions slots are often placed in bridges to
  accommodate roadway expansion on hot days. This
  prevents buckling of the roadway. Driveways and
  sidewalks have expansion slots for the same
  reason.

23
Thermal Expansion of Liquids

• Since liquids do not have a definite shape, but
  take the shape of their container, we are
  concerned only with their volume expansion.
• Liquids have greater coefficients of volume
  expansion than solids.
• ?V change in volume ? coefficient of volume
  expansion ? T change in temperature
• Tf final temperature Ti initial temperature
• new volume old volume ?V

24
Expansion of Liquid in a Solid Container

• To determine the new volume of a liquid that is
  contained within a solid container, such as a
  flask, when both are heated
• V and ?T are the same for the flask and the
  liquid.

25
Abnormal Expansion of Water

• Increase the temperature of any common liquid and
  it will expand. Water at the temperature of
  melting ice, 0? C contracts when the temperature
  is increased.
• As the water is heated and its temperature rises,
  it continues to contract until it reaches a
  temperature of 4?C.
• With further increase in temperature, the water
  then begins to expand and the expansion continues
  all the way to the boiling point, 100? C.

26
Abnormal Expansion of Water

• Water has its maximum mass density, 1000
  g/cm3, at 4? C. The same amount of water has its
  largest volume, and smallest density, in its
  solid form, ice. Which is why ice floats in
  water ice is less dense than water.
• Ice has a crystalline structure. The crystals of
  most solids are arranged in such a way that the
  solid state occupies a smaller volume than the
  liquid state.
• Water molecules in this open structure occupy a
  greater volume than they do in the liquid state,
  consequently, ice is less dense than water.

27
Abnormal Expansion of Water

• Between 0? C and 4? C, the coefficient of
  expansion of water is negative.
• When ice melts to water at 0? C, the water still
  contains groups of molecules bonded in the open
  crystal structure of ice.
• As the temperature increases the open crystal
  fragments begin to collapse and the molecules
  move closer together.
• The effect of the collapsing crystal structure
  predominates over the increase in the molecular
  speed of the molecules and the density increases.
• Above 4? C, the effect of increasing molecular
  speed exceeds the effect of collapsing crystal
  structures and volume increases.

28
Examples of Uses of Thermal Expansion

29
Examples of Uses of Thermal Expansion

• Dental materials used for fillings must be
  matched in their thermal expansion properties to
  those of tooth enamel, otherwise consuming hot
  drinks or cold ice cream would be painful.
• In aircraft manufacturing, rivets and other
  fasteners are often cooled using dry ice before
  insertion and then allowed to expand to a tight
  fit.
• Anti-scalding device (shown in figure)

30
Linear Expansion Example

• The supersonic airliner Concorde is 62.1 m long
  when sitting on the ground on a 20 C day. It is
  made primarily of aluminum. In flight at twice
  the speed of sound, friction with the air warms
  the Concordes skin and causes the aircraft to
  lengthen by 25 cm. The passenger cabin is on
  wheels and the airplane expands around the
  passengers. What is the temperature of
  Concordes skin in flight?

• What we know
• l 62.1 m
• Ti 20 C
• Dl 25 cm 0.25 m
• a Al 23.8 x 10-6/ C

31
Linear Expansion Example
32
Volume Expansion Example

• A farmer milks a cow into a 20 L steel milk pail.
  The milk comes out of the cow at 37 C. If the
  pail is initially full and also at 37 C, how
  much empty space will there be when the milk and
  the pail cool to 3 C? bmilk 2 x 10-4/ C
  asteel 1.2 x 10-5/ C
• Volume change for steel pail DV 3aVDT

33
Volume Expansion Example

• Volume change for milk DV bVDT
• The change in volume between the milk and the
  pail represents the amount of empty space in the
  pail at the 3 C
• DV 0.136 L 0.02448 L 0.11152 L

34
Final Temperature Example

• A steel tube has an outside diameter of 3 cm at
  room temperature (20 C). A brass tube has an
  inside diameter of 2.997 cm at 20 C. To what
  temperature must the ends of the tubes be heated
  if the steel tube is to be inserted into the
  brass tube? a steel 1.1 x 10-5/ C a brass
  1.9 x 10-5/ C