Three rods of identical cross-section and len | vedclass

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Question

(A) The rods are identical,meaning they have the same length $(\ell)$ and area of cross-section $(A)$.Since the rods are joined in series,the rate of

Vedclass · Accepted Answer

$K_{1}: K_{3}=2: 3 ; K_{2}: K_{3}=2: 5$

Vedclass · Answer

(A) The rods are identical,meaning they have the same length $(\ell)$ and area of cross-section $(A)$.Since the rods are joined in series,the rate of heat flow (heat current) is the same for all rods in a steady state.Let the heat current be $H = \frac{\Delta Q}{\Delta t}$.$H = \frac{K_{1} A (100 - 70)}{\ell} = \frac{K_{2} A (70 - 20)}{\ell} = \frac{K_{3} A (20 - 0)}{\ell}$Simplifying the equation:$30 K_{1} = 50 K_{2} = 20 K_{3}$Dividing by $10$:$3 K_{1} = 5 K_{2} = 2 K_{3}$From $3 K_{1} = 2 K_{3}$,we get $\frac{K_{1}}{K_{3}} = \frac{2}{3}$ or $K_{1}: K_{3} = 2: 3$.From $5 K_{2} = 2 K_{3}$,we get $\frac{K_{2}}{K_{3}} = \frac{2}{5}$ or $K_{2}: K_{3} = 2: 5$.Thus,the correct relationship is $K_{1}: K_{3} = 2: 3$ and $K_{2}: K_{3} = 2: 5$.

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