A) \[\text{25}{{\,}^{\circ }}C\]
B) \[33{{\,}^{\circ }}C\]
C) \[67{{\,}^{\circ }}C\]
D) \[75{{\,}^{\circ }}C\]
Correct Answer: D
Solution :
Key Idea: In steady state, the rate of flow of heat in both the conductors is same. Let temperature of junction, when steady state is achieved be\[\theta \], then rate of flow of heat is given by \[H=\frac{{{K}_{c}}A\left( {{\theta }_{c}}-\theta \right)}{{{l}_{c}}}\] \[=\frac{{{K}_{s}}A\left( \theta -{{\theta }_{s}} \right)}{{{l}_{s}}}\] Where \[{{K}_{c}}\] and \[{{K}_{s}}\] are coefficient of thermal conductivities of copper and steel, \[A\] is area, \[{{l}_{c}},\,{{l}_{s}}\] lengths of copper and steel rods. Given, \[{{K}_{c}}=9\,{{K}_{s}}\] \[\therefore \] \[\frac{9\,{{K}_{s}}\left( {{100}^{\circ }}-\theta \right)}{18}=\frac{{{K}_{c}}\left( \theta -{{0}^{\circ }} \right)}{6}\] \[900-9\,\,\theta =3\,\,\theta \] \[\Rightarrow \] \[120=900\] \[\Rightarrow \] \[\theta ={{75}^{\circ }}\,C\]You need to login to perform this action.
You will be redirected in
3 sec