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Heat Transfer Physics 202 Professor Lee Carkner Lecture 12

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PAL #11 First Law Final temperature of 20 g, 0 C ice cube dropped into 300 g of hot tea at 90 C. Add up all heats (Q = cm T and Q = Lm) Heat 1: melt ice Q 1 = (333000)(0.02) = 6660 J Heat 2: warm up now melted ice cube Q 2 = (4190)(0.02)(T f -0) Heat 3: cool down tea Q 3 = (4190)(0.3)(T f -90) Step 4: add up heat Q 1 + Q 2 + Q 3 = 0 6660 + 83.8T f + 1257T f –113130 = 0 1340.6T f = 106470 T f = 79.4 C

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Heat Transfer What is moving? In mechanics energy can be transferred through a particle (e.g. a bullet) or a wave (e.g. a sound wave) Heat can also be transferred by radiation both a particle and a wave

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Conduction The end in the fire experiences a large vibration of the molecules of the metal This is called conduction The movement of heat from a high temperature region to a low temperature region through another material

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Conductive Heat Transfer The rate at which heat is transferred by conduction is given by H = Q/t = kA (T H - T C )/L Where: Q is heat and t is time A is the cross sectional area of the material (in the direction of heat transfer) T is the temperature (hot or cold)

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Thermal Conductivities For Al, k=235 for Cu, k=428 (W/ m K) Materials with low k are good thermal insulators We use foam to insulate our houses Down filled winter coats trap air for insulation

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Composite Slabs H = Q/t = A (T H - T C )/ (L/k) Where (L/k) is the sum of the ratios of the thickness and thermal conductivity of each layer of the slab

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Radiation This is how you are warmed by sunlight The power (in Watts) that is emitted by an object depends on its temperature (T), its area (A) and it emissivity ( ) P r = AT 4 Where is the Stefan-Boltzmann constant = 5.6703 X 10 -8 W/m 2 K 4 T must be in absolute units (Kelvin)

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Absorption of Radiation P a = AT env 4 Where T env is the temperature of the environment P n = P a -P r = A(T env 4 - T 4 )

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Emissivity What is the value of emissivity? Objects with an emissivity of 1 are called blackbody emitters or absorbers Every object whose temperature is above 0 K emits thermal radiation People emit thermal radiation at infrared wavelengths and thus can be detected at night with IR goggles

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Convection The hot air is thus lighter and rises If the hot air cools as it rises it will eventually fall back down to be re-heated and rise again Examples: baseboard heating, boiling water, Earth’s atmosphere

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Convection Rate Factors Fluidity Energy exchange with environment How rapidly will the material lose heat? A small temperature difference may result in not enough density difference to move

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Next Time Test #2 For Monday January 9: Read: 19.1-19.7 Do Webassign homework

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Water condenses out of the air onto a cold piece of metal. Due to this condensation, the temperature of the air around the metal, A)Increases B)Decreases C)Stays the same D)Fluctuates unpredictably E)It depends on the temperature of the metal

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Ten joules of heat are added to a cylinder of gas causing the piston at the top to rise. How much work does the piston do? A)0 Joules B)5 Joules C)10 Joules D)-10 joules E)You cannot tell from the information given

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Which of the processes in the diagram produces the least work? A)1 B)2 C)3 D)4 E)All are the same

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Which of the processes in the diagram involves the least change in internal energy? A)1 B)2 C)3 D)4 E)All are the same

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Which of the processes in the diagram must have net heat output? A)1 B)2 C)3 D)4 E)3 and 4

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Which of the processes in the diagram must have net heat input A)1 B)2 C)3 D)4 E)1 and 2

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