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A square frame of side l is made of identical metallic rods. Corners A and C (diagonally opposite) are held at temperatures T1 and T2, and the resulting rate of heat flow from A to C is w. If instead corners A and D (adjacent) are held at T1 and T2, what is the total rate of heat flow?

1. w
2. 2w
3. w/2
4. 4w/3

Correct answer: 4w/3

Solution

For A-C the equivalent resistance is r (giving w = dT/r); for adjacent A-D it is 3r/4, so the rate becomes dT/(3r/4) = (4/3)*w.

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