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A frame is made of a single material with uniform cross-section throughout, arranged as shown so that heat splits between a straight path and a bent (longer) path. Which statement about the heat through the bent section is correct?

1. Heat through the bent part is 60 J when 130 J is removed at the hot end.
2. Heat through the bent part is 30 J when 130 J is removed at the hot end.
3. Heat through the bent part is 60 J when 100 J is removed at the hot end.
4. Heat through the bent part is 30 J when 100 J is removed at the hot end.

Correct answer: Heat through the bent part is 30 J when 130 J is removed at the hot end.

Solution

With the bent path longer than the straight one, the heat divides inversely as the path lengths, so the bent branch carries the smaller portion (30 J) of the 130 J total.

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