hw_6_solu

hw_6_solu - ME 125NT Intro to Nanotechnology Due: 5/15/2008...

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ME 125NT Intro to Nanotechnology Due: 5/15/2008 1 Solution Set 6 Problem 7.4 in book A free electron in a block of gold has an energy of 3.8×10 -21 J. What is the approximate temperature (°C) of the block? ANSWER T k E B K 273 B k E T That’s 0°C. Problem 7.10 in book A copper wire 3 μ m in diameter and 300 μ m long has a temperature at one end of 35°C and 32°C at the other. Calculate the rate of heat flow though the wire, in watts. (For copper k c =400 W·m ±1 ·K ±1 .) ANSWER ( ) ( ) = × - × = Δ Δ - = - - m 10 300 K 305 K 308 2 m 10 3 ·K W·m 400 6 2 6 1 ± 1 ± π x T A k Q c conduct 2.83×10 -5 W Problem 7.11 in book The thermal conductivity of air at room temperature is 0.028 W·m ±1 ·K ±1 and its density is 1.16 kg/m 3 . The average “air” molecule travels at 524 m/s and collides about every 267 picoseconds with another air molecule. How much heat (in joules) is needed to raise the temperature of a cubic meter of air by 10°C? ANSWER We know from Equations 7.4 and 7.5 that: 3 3 2 τ ρ cv cv k carrier , c = Λ = Rearranging to solve for specific heat, c , (the amount of heat per unit mass needed to raise the carrier’s temperature by one degree Celsius), gives: ( ) ( )( ) ( ) 1 ± 1 ± 12 2 3 ±1 ±1 2 ·K J·kg 988 s 10 267 m/s 524 kg/m 1.16 ·K W·m 0.028 3 3 = × = = - v k c carrier , c A cubic meter of air weighs (1 m 3 )( 1.16 kg/m 3 )=1.16 kg. To raise that mass by 10°C would require: ( )( )( ) = kg 16 1 K 10 ·K J·kg 988 ±1 ±1 . 12 kJ
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ME 125NT Intro to Nanotechnology Due: 5/15/2008 2 Problem 7.12 in book Very thin films are usually deposited under vacuum conditions to prevent contamination and ensure that atoms can fly directly from the source to the depositing surface without being scattered along the way. (a) To get an idea of how few and far between the air molecules are in a thin-film
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This note was uploaded on 08/06/2008 for the course ME 125 taught by Professor Pennathur during the Spring '08 term at UCSB.

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hw_6_solu - ME 125NT Intro to Nanotechnology Due: 5/15/2008...

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