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
\[={{100}^{o}}-{{45}^{o}}={{55}^{o}}C\].