University Physics with Modern Physics with Mastering Physics (11th Edition)

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17.125: The rate at which heat is aborbed at the blackened end is the heat current in the rod, ), ( ) ( 1 2 4 2 4 S T T L kA T T - = - where 2 1 and K 00 . 20 T T = is the temperature of the blackened end of the rod. If this were to be solved exactly, the equation would be a quartic, very likely not worth the trouble. Following the hint, approximate 2 T on the left side of the above expression as T 1 to obtain . K 424 . 0 ) )( K 10 79 . 6 ( ) ( 1 4 1 4 s 3 12 1 4 1 2 1 2 S + = - × + = - + = - - T T T T T T k σL T T This approximation for 2 T is indeed only slightly than , 1 T and is a good estimate of the
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Unformatted text preview: temperature. Using this for 2 T in the original expression to find a better value of T ∆ gives the same T ∆ to eight figures, and further, and further iterations are not worth – while. A numerical program used to find roots of the quartic equation returns a value for T ∆ that differed from that found above in the eighth place; this, of course, is more precision than is warranted in this problem....
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