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 \[{{\theta }_{C}}=100-30=70{}^\circ C\]