Two rods 1 and 2 of length 2 ℓ and ℓ , thermal conductivities 2 k and 3 k are joined end to end. The area of cross-sectional of each rod be A . This composite rod is connected with another rod 3 of le

Question

Two rods 1 and 2 of length 2 ℓ and ℓ , thermal conductivities 2 k and 3 k are joined end to end. The area of cross-sectional of each rod be A . This composite rod is connected with another rod 3 of length 3 ℓ and conductivity k ′ . The area of cross-section of the rod 3 is 2A. If the rod 3 conducts the heat two times that through the other rods, find the value of k 4 k ′ ​ .

TestHub · Accepted Answer

The top branch has rods 1 and 2 in series; the other branch is rod 3.
$R_{12} = \frac{2 ℓ}{2 k A} + \frac{ℓ}{3 k A} = \frac{4 ℓ}{3 k A}$
$R_{3} = \frac{3 ℓ}{2 A k ^{'}}$
$\dot{Q}_{3} = 2 \dot{Q}_{12} \Rightarrow R_{12} = 2 R_{3}$
$\frac{4 ℓ}{3 k A} = \frac{3 ℓ}{A k ^{'}}$
$\frac{4 k ^{'}}{k} = 9$
Answer 9.

Physics - Heat & Thermo Question with Solution | TestHub

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