Problem 20-1 - Example 20-1 A copper bar 1.2 cm in diameter...

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Example 20-1 A copper bar 1.2 cm in diameter and 1 m long carries 800 A of current. The electrical resistance of the bar is 2 x 10 -4 Ω. If the surface is at 25 ° C, what is the steady state temperature at the center of the bar? Solution: L D r 0 kd dT rS rdr dr ⎛⎞ =+ ⎜⎟ ⎝⎠ at r = 0 0 dT dr = at 2 D r = TT = dd T S r r dr dr k =− 2 1 2 dT Sr rC dr k +

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since at r = 0, 0 dT dr = , C 1 = 0 2 dT Sr dr k =− 2 2 4 Sr TC k + at 2 D r = , TT = so 2 2 42 SD k ⎛⎞ + ⎜⎟ ⎝⎠ 2 2 () Tr r T k ⎡⎤ + ⎢⎥ ⎣⎦ For T max 2 max 0 T k == + To find S ( ) ( ) ( ) 2 4 22 2 800A 2 10 1.2 m1 m 2 2 100 IR S V D L π ×Ω = S = 1.13 x 10
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Problem 20-1 - Example 20-1 A copper bar 1.2 cm in diameter...

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