A) \[{{85}^{o}}C\]
B) \[{{90}^{o}}C\]
C) \[{{50}^{o}}C\]
D) \[{{70}^{o}}C\]
Correct Answer: D
Solution :
Thermal conductivity of first rod \[{{K}_{1}}=5\alpha \] and thermal conductivity of second rod \[{{K}_{2}}=3\,\alpha \] Temperature of the first rod \[{{T}_{1}}={{100}^{o}}C\] and Temperature of second rod \[{{T}_{2}}={{20}^{o}}C\]. In the steady state, the rate of heat transfer in both the conductors will be same \[\therefore \] \[\frac{{{K}_{1}}A({{T}_{1}}-T)}{d}=\frac{{{K}_{2}}A(T-{{T}_{1}})}{d}\] Where T is the temperature of the junction) \[\Rightarrow \] \[{{K}_{1}}({{T}_{1}}-T)={{K}_{2}}(T-{{T}_{2}})\] \[\Rightarrow \] \[5\alpha (100-T)=3\alpha (T-20)\] \[\Rightarrow \] \[5(100-T)=3\,(T-20)\] \[\Rightarrow \] \[500-5T=3T-60\] \[\Rightarrow \] \[8T=560\] \[\Rightarrow \] \[T={{70}^{o}}C\]
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