A) \[90{}^\circ C~\]
B) \[50{}^\circ C\]
C) \[10{}^\circ C~\]
D) \[67{}^\circ C\]
Correct Answer: A
Solution :
Let conductivity of steel \[{{K}_{\operatorname{steel}}}=k\] then from question |
Conductivity of copper\[{{K}_{\operatorname{copper}}}=9k\] |
\[{{\theta }_{\operatorname{copper}}}=100{}^\circ \operatorname{C}\] |
\[{{\theta }_{\operatorname{steel}}}=0{}^\circ \operatorname{C}\] |
\[{{l}_{\operatorname{steel}}}={{l}_{copper}}=\frac{L}{2}\] |
From formula temperature of junction; |
\[\theta =\frac{{{K}_{\operatorname{copper}}}{{\theta }_{\operatorname{copper}}}{{l}_{\operatorname{steel}}}+{{K}_{\operatorname{steel}}}{{\theta }_{\operatorname{steel}}}{{l}_{\operatorname{copper}}}}{{{K}_{\operatorname{copper}}}{{l}_{\operatorname{steel}}}+{{K}_{\operatorname{steel}}}{{l}_{\operatorname{copper}}}}\] |
\[=\frac{9k\times 100\times \frac{L}{2}+k\times 0\times \frac{L}{2}}{9k\times \frac{L}{2}+k\times \frac{L}{2}}\] |
\[=\frac{\frac{900}{2}kL}{\frac{10kL}{2}}=90{}^\circ C\] |
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