Two metallic blocks \(M_{1}\) and \(M_{2}\) of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of \(M _{2}\) is \(K\) then the thermal conductivity of \(M _{1}\) will be ]...............\(K\) [Assume steady state heat conduction]

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(B) \(8\)

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\(\Delta T \propto R \propto \frac{\ell}{ k }\),

\(\frac{\Delta T _{1}}{\Delta T _{2}}=\frac{\ell_{1}}{ k _{1}} \times \frac{ k _{2}}{\ell_{2}}=\frac{16}{ k _{1}} \times \frac{ k }{8}\)

\(\frac{20}{80}=\frac{16}{ k _{1}} \times \frac{ k }{8} \rightarrow k _{1}=8 k\)

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