A) 24 min
B) 3 min
C) 12 min
D) 6 min
Correct Answer: B
Solution :
When two rods are joined, then the rate of flow of heat is given by \[Q=kA\left( \frac{{{Q}_{1}}-{{Q}_{2}}}{l} \right)t\] where, \[k\]is coefficient of thermal conduction is area and / is length when rods are joined in series. \[\Delta Q=\frac{A({{T}_{1}}-{{T}_{2}}){{t}_{1}}}{\frac{{{l}_{1}}}{{{k}_{1}}}+\frac{{{l}_{2}}}{{{k}_{2}}}}\] \[\Delta Q=\frac{A({{T}_{1}}-{{T}_{2}}){{t}_{1}}}{\frac{l}{k}+\frac{l}{k}}\] \[=\frac{A({{T}_{1}}-{{T}_{2}}){{t}_{1}}}{l}\frac{k}{2}\] When rods are joined in parallel. \[\Delta {{Q}_{2}}=({{k}_{1}}A+{{k}_{2}}A)\times \frac{({{T}_{1}}-{{T}_{2}}){{t}_{2}}}{l}\] \[=\frac{2kA({{T}_{1}}-{{T}_{2}}){{t}_{2}}}{l}\] \[\Delta {{Q}_{1}}=\Delta {{Q}_{2}}\] \[{{t}_{2}}=\frac{{{t}_{1}}}{4}=\frac{12}{4}=3\,\min \]
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