596_Physics ProblemsTechnical Physics

596_Physics ProblemsTechnical Physics - 598 P20.69 Heat and...

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598 Heat and the First Law of Thermodynamics P20.69 WW W W W AB BC CD DA =+++ W PdV PdV PdV PdV Wn R T dV V Pd Vn R T dV V V R T V V PV V n R T V V A B B C C D D A A B B C C D D A B CB C AD =− F H G I K J −− F H G I K J zzzz zz 12 21 1 1 22 2 1 ln ln bg b g Now PV AB = and CD = , so only the logarithmic terms do not cancel out. V 1 V 2 P 1 P 2 P BC D A V FIG. P20.69 Also, V V P P B 1 1 2 = and V V P P C 1 = R T P P nRT P P nRT P P nRT P P nR T T P P F H G I K J F H G I K J =+ F H G I K J F H G I K J F H G I K J 1 1 2 2 2 1 1 2 1 2 2 1 2 1 ln ln ln ln ln Moreover nRT 2 = and 11 1 = WP V V P P F H G I K J 12 1 2 1 ln P20.70 For a cylindrical shell of radius r , height L , and thickness dr , the equation for thermal conduction, dQ dt kA dT dx becomes dQ dt kr L dT dr 2 π Under equilibrium conditions, dQ dt is constant; therefore, dT dQ dt kL dr r F H G I K J F H G I K J 1 2 and TT dQ dt kL b a ba −= F H G I K J F H G I K J 1 2 ln But ab > , so dQ dt kL T T = 2 ln P20.71 From problem 70, the rate of energy flow through the wall is
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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