A) \[~{{70}^{o}}C\]
B) \[~{{60}^{o}}C\]
C) \[{{50}^{o}}C\]
D) \[{{90}^{o}}C\]
Correct Answer: A
Solution :
| [a] Temperature of interface \[\theta =\frac{{{k}_{1}}{{\theta }_{1}}+{{k}_{2}}{{\theta }_{2}}}{{{k}_{1}}+{{k}_{2}}}\] |
| It is given that \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{5}{3}\] |
| Let \[{{K}_{1}}=5K\] and \[{{K}_{2}}=3K\] |
| \[\Rightarrow \] \[\theta =\frac{5K\times 100+3K\times 20}{5K+3K}\] |
| \[\Rightarrow \] \[\theta =\frac{560K}{8K}=70{{\,}^{o}}C\] |
| \[\therefore \] \[\theta =70{{\,}^{o}}C\] |
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