KCET · Physics · Thermal Properties of Matter
Three identical rods \(A, B\) and \(C\) are placed end to end. A temperature difference is maintained between the free ends of \(A\) and \(C\). The thermal conductivity of \(B\) is thrice that of \(C\) and half of that of \(A\). The effective thermal conductivity of the system will be \(\left(K_{A}\right.\) is the thermal conductivity of \(\left.\operatorname{rod} A\right)\)
- A \(\frac{1}{3} K_{A}\)
- B \(3 K_{A}\)
- C \(2 K_{A}\)
- D \(\frac{2}{3} K_{A}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3} K_{A}\)
Step-by-step Solution
Detailed explanation
\(\text {Given, } K_{B}=K_{A} / 2, \)
\( \text {and } K_{B}=3 K_{C} \)
\( \therefore K_{C}=K_{A} / 6\)
Rods are in series form so
\(\frac{L}{K}=\frac{l_{1}}{K_{A}}+\frac{l_{2}}{K_{B}}+\frac{l_{3}}{K_{C}} \)
\(\frac{3 l}{K}=\frac{l}{K_{A}}+\frac{l}{K_{A} / 2}+\frac{l}{K_{A} / 6} \)
\(\frac{3 l}{K}=\frac{9 l}{K_{A}} \)
\(K=\frac{K_{A}}{3}\)
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