14 Heat

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14 Heat

• Homework
• Problems 3, 5, 13, 21, 33, 47, 49.
• Internal Energy
• Heat Capacity Specific Heat
• Phase Transitions
• Thermal Conduction

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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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example cs

• in J/(kgC)
• aluminum 920
• copper 390
• ice 2100
• water 4186

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specific heat

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

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Calorimetry

• Measure heat lost/gained

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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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Phase Transitions Latent Heat

• L Q/m J/(kg)
• heat needed to melt (f) or vaporize (v) 1kg

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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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Heat transfer

• 2m x 1m window, 4mm thick, single pane glass.
• Assume temp. difference 5C
• Q/t kA(DT)/L (0.84)(2)(5)/0.004
• About 2,000 watts

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R-Factors and Thermal Resistance
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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 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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Summary

• Definition of Internal Energy
• Heat Capacity
• Specific Heat
• Phase Transitions
• Latent Heat
• Phase Diagrams
• Energy Transport by Conduction, Convection, and
  Radiation

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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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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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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