PHYSICS 231 Lecture 26 Conduction Convection Conduction Convection Radiation PHY 231 1 Heat transfer to an object The amount of energy transfer Q to an object with mass m when its temperature is raised by T Q cm T Q cm T Change g in temperature Energy transfer J or cal Mass of object j Specific heat k oC or cal g J kg l oC PHY 231 2 Phase Change GAS high T Gas liquid Q mLv Solid low T Q csolid lidm T Q cgasm T liquid medium T Q cliquidm T PHY 231 liquid solid Q mLf 3 question A block of gold room temperature 200C is found to just melt completely after supplying supp y ng 4x103 J of h heat at What was the mass of the gold block Given Lf 6 44x104 J kg Tmelt 1063oC cspecific 129 J kg0C a b c d e 0 01 kg 0 02 kg 0 03 kg 0 03 0 06 kg 10 kg Q cm T mLf 129 m 1043 m 6 44x104 2x105 m m 4000 2x105m m 0 02 kg PHY 231 4 quiz Ice is heated steadily and becomes liquid and then vapor During this process process a the temperature rises continuously b when the ice turns into water water the temperature drops for a brief moment c the temperature is constant during the phase transformations d the temperature cannot exceed 100oC PHY 231 5 How can heat be transferred PHY 231 6 Conduction Touching h different d ff materials l Some feel f l cold ld others h feel warm but all are at the same temperature PHY 231 7 Thermal conductivity metal T 200C wood T 200C The heat transfer in the metal is much faster than in the wood thermal conductivity T 370C T 370C PHY 231 8 Heat transfer via conduction Conduction occurs if there is a temperature difference between two parts of a conducting medium Rate of f energy gy transfer f power p w P Q t unit Watt P kA Th Tc x kA T x k thermal conductivity Unit J msoC metal k 300 J msoC gases k 0 1 J ms g oC nonmetals 1 J msoC PHY 231 9 Example A glass window A 4m2 x 0 5cm separates a living room T 200C from the outside T T 0 0oC A What is the rate of heat transfer through the window kglass 0 84 J msoC B By what fraction does it change if the surface becomes 2x smaller and the temperature drops to 200C A P kA T x 0 84 4 20 0 005 13440 Watt B Porig kA T x Pnew k 0 5A 2 T x P orig The heat transfer is the same PHY 231 10 Another one Heat sink Heat reservoir An insulated gold wire I e no heat lost to the air is at one end connected to a heat reservoir T 1000C and at the other end connected to a heat sink T 200C If its length is 1m and P 200W what is its cross section A kgold 314 314 J ms J 0C C P kA T x 314 A 80 1 25120 A 200 A 8 0E 03 m2 PHY 231 11 Water 0 5L 1000C And another A 0 03m A 0 03m2 thickness 0 0 5cm 5cm 1500C A student working for his exam feels hungry and starts boiling water 0 5L for some noodles He leaves the kitchen when the water just boils The boils The stove stove ss temperature is 1500C C The pan s bottom has dimensions given above Working hard on the exam he only comes back after half an hour Is there still ll water in the h pan Lv 540 540 cal g l kpan 11 cal ms l 0C To boil away 0 5L 500g of water Q Lv 500 270000 cal Heat added by the stove P kA T x 1 0 03 50 0 005 P kA T x 1 0 03 50 0 005 300 cal P Q t t Q P 270000 300 900 s 15 minutes He ll ll be hungry h f for a bit llonger PHY 231 12 i inside Isolation Q A Th Tc P t Li ki Tc Th L1 L2 L3 A house is built with 10cm thick wooden walls and roofs The owner decides to install insulation After installation the walls and roof are 4cm wood 2cm wood 2cm isolation 4cm isolation 4cm wood If kwood 0 10 J ms0C and kisolation 0 02 J ms0C by what factor does he reduce his heating bill Pbefore A T 0 10 0 10 A T Pafter A T 0 04 0 10 0 02 0 02 0 04 0 10 0 55A T Almost a factor of 2 1 1 81 81 PHY 231 13 Convection T high hi h low PHY 231 14 Radiation Nearly all objects emit energy through radiation P AeT4 Stefan s law J s 5 6696x10 8 W m2K4 A surface area e object dependent constant emissivity 0 1 T temperature K P energy radiated di t d per ssecond d PHY 231 15 emissivity Ideal reflector e 0 no energy is i absorbed b b d Ideal d l absorber b b bl black kb body d e 1 all energy gy is absorbed also ideal radiator PHY 231 16 A BBQ The coals in a BBQ cover an area of 0 25m2 If the emissivity of the burning coal is 0 95 and their temperature 5000C C how h much h energy is i radiated di d every minute P AeT4 J s 5 67x10 8 0 25 0 95 773 4 4808 J s 1 minute 2 9x105 J PHY 231 17 radiation balance If an object would only emit radiation it would eventually have 0 K temperature In reality an object emits AND receives radiation radiation P Ae T4 T04 where T temperature of object T0 temperature of surroundings PHY 231 18 example The temperature of the human body is 370C If the room temperature is 200C how much heat is given off ff by b the h h human body b d to the h room in i one minute i Assume that the emissivity of the human body is 0 9 and the surface area is 2 m2 P Ae T4 T04 5 67x10 8 2 0 9 310 54 293 54 185 185 J s Q P T 185 60 1 1x104 J PHY 231 19 Wien Displacement Law 3 2 898 10 m K max m T K The W Wien Law L w explains p the shift of the peak to shorter wavelengths as the temperature increases The Wien Law gives the wavelength of the peak of the radiation distribution distribution while the Stefan Boltzmann Law gives the total energy being emitted at all wavelengths b th by the blackbody bl kb d PHY 231 20
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