CET Karnataka Engineering
CET - Karnataka Engineering Solved Paper-2011
question_answer
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 (\[{{K}_{A}}\]a is the thermal conductivity of rod A)
A) \[\frac{1}{3}{{K}_{A}}\]
B) \[3{{K}_{A}}\]
C) \[2{{K}_{A}}\]
D) \[\frac{2}{3}{{K}_{A}}\]
Correct Answer:
A
Solution :
A
B
C
Given, \[{{K}_{B}}={{K}_{A}}/2\] and \[{{K}_{B}}=3{{K}_{c}}\] \[\therefore \] \[{{K}_{C}}={{K}_{A}}/6\] Rods are in series form so \[\frac{L}{K}=\frac{{{l}_{1}}}{{{K}_{A}}}+\frac{{{l}_{2}}}{{{K}_{B}}}+\frac{{{l}_{3}}}{{{K}_{C}}}\] \[(\because \,l={{l}_{1}}={{l}_{2}}={{l}_{3}})\] \[\frac{3l}{K}=\frac{l}{{{K}_{A}}}+\frac{l}{{{K}_{A}}/2}+\frac{l}{{{K}_{A}}/6}\] or \[\frac{3l}{K}=\frac{9l}{{{K}_{A}}}\] or \[K=\frac{{{K}_{A}}}{3}\]