1011 Temperature and Heat

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10-11 Temperature and Heat

• Temperature Scales
• Thermometry
• Thermal Expansion
• Heat and Internal Energy
• Heat Transfer
• Heat and Temperature Change, Specific Heat
  Capacity

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Homework

• Ch. 10
• 13, 20, 24, 45, 50, 58, 59.
• Ch.11
• 1, 3, 4, 5, 6, 9, 11, 21, 23, 54, 63, 64.

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Temperature

• A measure of the average kinetic energy per
  molecule of a substance.
• T increases with average speed of molecules, e.g.
  hammered metal has increased temperature.
• Higher T gas expands or has increased pressure

4
Thermometric property a physical property that
changes with temperature.
Examples pressure or volume of a gas resistance
of a metal length of a piece of metal
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Common Temperature Scales

• Farenheit, water freezes at 32F
• Celsius, water freezes at 0C
• Kelvin, water freezes at 273K
• Size of unit 1K 1C (9/5)F

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Thermal Expansion

• Most materials increase in size when their
  temperature increases due to the increased
  thermal motion.
• basis of much thermometry

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Water Expansion

• Water expands from 4C to 100C.
• However, water contracts when warmed from 0C to
  4C (transient ice disappears as T increases to
  4C)

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Ideal Gas

• PV T
• Ex V is constant P T, if kelvin temperature
  is doubled, pressure of gas is doubled.
• Ex P is constant V T.

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Linear Thermal Expansion

• Length of a solid depends on temperature
• Frequently the change in length is proportional
  to the change in temperature
• The constant is called the coefficient of linear
  thermal expansion (symbol a)

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Linear Thermal Expansion
DL a Lo DT
Example 100C increase in Aluminum causes a
fractional increase in length of 0.0024 0.24
change.
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Bi-Metallic Strips
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Heat

• Heat is energy transferred due to temperature
  difference.
• Symbol, Q J
• Ex. 4186J heat needed to raise 1kg of water one
  degree C.

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specific heat

• c Q/mDT J/(kgK)
• heat needed per kg to raise temperature by 1
  degree C or K.
• slope warming water DT/Q 1/(mc)

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example cs

• in J/(kg-C)
• aluminum 920
• copper 390
• ice 2100
• water 4186

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Example

• A student wants to check c for an unknown
  substance. She adds 230J of heat to 0.50kg of the
  substance. The temperature rises 4.0K.

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Calorimetry

• literally meter the calories emitted by a
  substance as it cools.
• Ex. Heated object is added to water. change in
  temperature of water determines specific heat of
  object.

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Example Calorimetry

• 2kg of substance-A heated to 100C. Placed in
  5kg of water at 20C. After five minutes the water
  temp. is 25C.
• heat lost by substance heat gained water.

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continued
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latent heat

• L Q/m J/(kg)
• heat needed per kg to melt (f) or vaporize (v) a
  substance

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example Ls

• in J/kg
• melting (f) vaporization (v)
• alcohol 100,000 850,000
• water 333,000 2,226,000

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Example

• How much heat must be added to 0.5kg of ice at 0C
  to melt it?
• Q mL (0.5kg)(333,000J/kg)
• 167,000J
• same amount of heat must be removed from 0.5kg
  water at 0C to freeze it.

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Heat Transfer

• Conduction
• Convection
• Radiation

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Conduction

• Heat conduction is the transmission of heat
  through matter.
• dense substances are usually better conductors
• most metals are excellent conductors

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conduction equation

• heat current energy/time watts
• heat current kADT/L
• k thermal conductivity
• DT temperature difference, L below

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conduction example

• some conductivities in J/(m-s-C)
• silver 429 copper 401 aluminum 240
• Ex Water in aluminum pot. bottom 101C, inside
  100C, thickness 3mm, area 280sq.cm.
• Q/t kA(Th-Tc)/L
• (240)(0.028)(101-100)/(0.003)
• 2,240 watts heat current

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Convection

• Convection transfer through bulk motion of a
  fluid.
• Natural, e.g. warm air rises, cool falls
• Forced, e.g. water-cooled engine

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Radiation

• Heat transfer by emission of electromagnetic
  radiation, e.g. infrared.
• Examples
• space heaters with the shiny reflector use
  radiation to heat.
• If they add a fan, they use both radiation and
  convection

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Greenhouse Effect

• dirtier air must be at higher temperature to
  radiate out as much as Earth receives
• higher temperature air is associated with higher
  surface temperatures, thus the term global
  warming
• very complicated model!

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Summary

• T measured in C, K, F. Use K for gas laws.
• thermometry uses thermometric properties
• change in length is proportional to change in
  temperature for many solids
• c heat needed to raise 1kg by 1C.
• L heat needed to melt or vaporize 1kg.
• Heat transfer

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Phase Change

• freeze (liquid to solid)
• melt (solid to liquid)
• evaporate (liquid to gas)
• sublime (solid to gas)
• phase changes occur at constant temperature

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Temperature vs. Heat (ice, water, water vapor)
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Heat and Phase Change

• Latent Heat of Fusion heat supplied to melt or
  the heat removed to freeze
• Latent Heat of Vaporization heat supplied to
  vaporize or heat removed to liquify.

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Newtons Law of Cooling

• For a body cooling in a draft (i.e., by forced
  convection), the rate of heat loss is
  proportional to the difference in temperatures
  between the body and its surroundings
• rate of heat-loss DT

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Real Greenhouse

• covering allows sunlight to enter, which warms
  the ground and air inside the greenhouse.
• the house is mostly enclosed so the warm air
  cannot leave, thus keeping the greenhouse warm (a
  car in the sun does this very effectively!)

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Solar Power

• Solar Constant
• Describes the Solar Radiation that falls on an
  area above the atmosphere 1.37 kW / m².In
  space, solar radiation is practically constant
  on earth it varies with the time of day and year
  as well as with the latitude and weather. The
  maximum value on earth is between 0.8 and 1.0 kW
  / m².
• see solarserver.de