Question

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

• A. $-{30}^{\circ }\text{C}$
• B. ${70}^{\circ }\text{C}$
• C. $5^{\circ }\text{C}$
• D. None of the above

Answer 1

The correct option is B ${70}^{\circ }\text{C}$

In steady state,
Temperature gradient $=$ constant


$\Rightarrow \frac{({\theta }_A-{\theta }_x)}{6}=\frac{({\theta }_A-{\theta }_B)}{20}\Rightarrow (100-{\theta }_x)=\frac{6}{20}\times (100-0)$
$\Rightarrow {\theta }_x={70}^{\circ }\text{C}$