question_answer

In steady state of thermal conduction, temperature of the ends A and B of a 20 cm long rod are \[100{}^\circ C\] and \[0{}^\circ C\] respectively. What will be the temperature of the rod at a point at a distance of 6 cm from the end A of the rod?

A)  \[5{}^\circ C\]                                  

B)  \[70{}^\circ C\]

C)  \[-\,30{}^\circ C\]                           

D)  \[-50{}^\circ C\]

Correct Answer: B

Solution :

                The given condition can be shown as In steady state, the temperature gradient is constant \[\therefore \]  \[\frac{({{\theta }_{A}}-{{\theta }_{C}})}{6}=\frac{({{\theta }_{A}}-{{\theta }_{B}})}{20}\] \[\Rightarrow \]               \[(100-{{\theta }_{C}})=\frac{6}{20}(100-0)\] \[\Rightarrow \]               \[(100-{{\theta }_{C}})=30\] or            \[{{\theta }_{C}}=100-30=70{}^\circ C\]