A) \[{{55}^{o}}C\]
B) \[{{60}^{o}}C\]
C) \[{{75}^{o}}C\]
D) \[{{50}^{o}}C\]
Correct Answer: A
Solution :
Let the temperature of the junction be \[\theta \]. Heat flow through the rod is given by \[Q=\frac{KA\,({{\theta }_{1}}-{{\theta }_{2}})\,t}{d}\] Here, \[{{K}_{1}}(100-\theta )={{K}_{2}}\,\,(\theta -25)\] \[\Rightarrow \] \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{\theta -25}{100-\theta }\] But \[\frac{{{K}_{1}}}{{{K}_{2}}}=\frac{2}{3}\] (given) \[\therefore \] \[\frac{2}{3}=\frac{\theta -25}{100-\theta }\] \[\Rightarrow \] \[3\theta -75=200-2\theta \] \[\Rightarrow \] \[5\,\theta =275\] \[\theta ={{55}^{o}}C\]
You need to login to perform this action.
You will be redirected in
3 sec
