Heating of the house problem

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Heating of the house problem

• System as seen by a physicist

House Energy converted into thermal energy inside
Energy flow in
Energy flow Out
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Reminders

• Units of energy or work Joules J
• Other energy units
• Calorie cal 4.184 J
• Calorie kcal 4.184 kJ
• kilo-watt-hour kWh 1000W3600s 36105 J

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Reminders Energy flow

• Power energy flow per unit time or work per unit
  time
• Unit W (Watt) J/s
• Also J/d (Joule per day) 1/86400 W
• MJ/d (Megajoule per day) 12 W
• GJ/d (Gigajoule per day) 12 kW (kilowatt)
• Horsepower hp 745.7 watts

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Power Rate of Energy Transfer
Computer 200 W TV on standby a few W
Refrigerator 1.2 kWh/day Electrical stove 3
5 kW Person on standby lt 100W
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Sources of Energy Flowing In

• Electrical Energy
• External radiation coming in
• Chemical energy
• Natural gas supply
• Heating oil supply
• Fireplace
• Food

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Electrical Energy

• Production (details much later)
• How is it delivered?
• Electrical Potential (voltage) is always there
• Current is zero if we are not using the energy
• Accounting for electrical energy use price per J
  is 1.7 10-8 /J
• Unit used by utilities companies kWh
• 0.0615 per kWh
• kWh 36105 J

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Heat and Chemical Energy
Non-mechanical energy transfer
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Chemical Energy

• Propane 50 MJ/kg 0.5 kg/m3
• Natural gas 47 MJ/kg 0.8 kg/m3
• Heating oil 43 MJ/kg
• Coal 29 MJ/kg
• Wood 16 MJ/kg
• Food (eaten not burned!) 16MJ/kg
• Why food?

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Heat flow of thermal energy

• How it flows?
• Conduction
• Convection
• Radiation

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Water heated in microwave oven
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Temperature

• Measure of thermal energy energy of vibrating
  molecules, atoms
• Units ºC, K, ºF

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Convection

• Convection is the transfer of heat by the actual
  movement of the warmed matter. Heat leaves the
  coffee cup as the currents of steam and air rise.
  Convection is the transfer of heat energy in a
  gas or liquid by movement of currents.
• The heat moves with the fluid. Consider this
  convection is responsible for making macaroni
  rise and fall in a pot of heated water. The
  warmer portions of the water are less dense and
  therefore, they rise. Meanwhile, the cooler
  portions of the water fall because they are
  denser.
• From http//www.mansfieldct.org/schools/mms/staff
  /hand/convcondrad.htm

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• Why some area of the ground could be warmer?
• Why there is strong wind on the ground in the
  area of the forest fire?

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Conduction

• Conduction is the transfer of energy through
  matter from particle to particle. It is the
  transfer and distribution of heat energy from
  atom to atom within a substance. For example, a
  spoon in a cup of hot soup becomes warmer because
  the heat from the soup is conducted along the
  spoon.
• Fun fact Have you ever noticed that metals tend
  to feel cold? Believe it or not, they are not
  colder! They only feel colder because they
  conduct heat away from your hand. You perceive
  the heat that is leaving your hand as cold.
• From http//www.mansfieldct.org/schools/mms/staff
  /hand/convcondrad.htm

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Conduction

• Heat Conduction
• Conduction is heat transfer by means of molecular
  agitation within a material without any motion of
  the material as a whole. If one end of a metal
  rod is at a higher temperature, then energy will
  be transferred down the rod toward the colder end
  because the higher speed particles will collide
  with the slower ones with a net transfer of
  energy to the slower ones.

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Conduction

• Heat Conduction
• For heat transfer between two plane surfaces,
  such as heat loss through the wall of a house,
  the rate of conduction heat transfer is
•           H kA (T2 - T1)/L                  
• H heat transferred in time in J/s
• k thermal conductivity of the barrier
• A area
• T2 - T1 temperature difference
• L thickness of barrier

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Example

• A little brick house with the walls 15 cm thick
  has ten 100 W lights on. The temperature outside
  is 18 ºC. The house is 10 m long and 10 m wide
  and 4 m high. Both floor and roof are very well
  insulated. What is the temperature inside?
• How will it change if two people go in?
• For brick, k 0.84 J/(s m 0C) or 0.84 W/(m K)

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• What assumptions do we have to make about the
  system if we want to use the formula
• The heat loss per second through the walls must
  be equal to the power delivered by the light
  bulbs