question_answer

In a steady state the temperature of the ends A and B of a 20 cm long rod AB are \[100{}^\circ \] and \[0{}^\circ C\]. The temperature at the point C distant 9 cm from A is

A) \[45{}^\circ C\]                     

B) \[55{}^\circ C\]

C) \[60{}^\circ C\]               

D) \[65{}^\circ C\]

Correct Answer: B

Solution :

Temperature gradient = ?                                  Given, \[{{\theta }_{2}}={{100}^{o}}C\],    \[{{\theta }_{1}}={{0}^{o}}C,\]    \[l=20\,cm\] \[\therefore \] Temperature gradient \[=\frac{100}{20}={{5}^{o}}\,C/m\] Temperature difference at point C is                 \[={{100}^{o}}-{{45}^{o}}={{55}^{o}}C\].