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

Option: 1

\mathrm{10\: K}


Option: 2

\mathrm{8\: K}


Option: 3

\mathrm{12.5\: K}


Option: 4

\mathrm{2\: K}


Answers (1)

best_answer


Since, the two blocks are in series, the heat current through both of them will be same of steady state

\mathrm{H_{1}= H_{2}}
\mathrm{\frac{\Delta T_{1}}{R_{1}}=\frac{\Delta T_{2}}{R_{2}} }

\mathrm{\frac{\left ( 100-80 \right )}{\left ( \frac{l_{1}}{\left ( k \right )A_{1}} \right )} = \frac{\left ( 80-0 \right )}{\left ( \frac{l_{2}}{k_{1}\, A_{2}} \right )}}

\mathrm{Here,\; A_{1}= A_{2}= \text{Area of cross-section}\left ( given \right )}
\mathrm{k_{1}\rightarrow \text{Thermal conductivity of block }M_{1}}
\mathrm{l_{1}= 16\, cm,l_{2}= 8 \, cm}

\mathrm{\frac{20}{\left ( \frac{16}{k_{1}} \right )}= \frac{80}{\frac{8}{k_{0}}}}
\mathrm{k_{1}= 8\, k}

The correct option is (2)





 

Posted by

SANGALDEEP SINGH

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