Q. 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?
CMC MedicalCMC Medical 2012
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 $
