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A sealed insulating cubical box exchanges heat only through two cylindrical metal plugs (each area 12 cm², length 8 cm) in opposite walls, with thermal conductivity 2.0 W/m/C. One plug's outer face is at 100 C and the other's at 4 C. A 13 W source inside the box heats the interior. Find the equilibrium temperature of the inner surface (uniform).

1. 249 C
2. 269 C
3. 289 C
4. 309 C

Correct answer: 269 C

Solution

With kA/L = 2*12e-4/0.08 = 0.03 W/C per plug, the balance 0.03(T-100) + 0.03(T-4) = 13 gives T about 269 C.

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