Question

In a steady state of heat conduction the temperature of the ends $A$ and $B$ of a rod $100$cm long are 0${}^o$ C and 100${}^o$C . The temperature of the rod at a point $60$cm distant from the end $A$ is :

• A. $0^{o}C$
• B. ${40}^{o}C$
• C. ${60}^{o}C$
• D. ${100}^{o}C$

Answer 1

The correct option is C ${60}^{o}C$

The linear variance of temperature across the length of the rod is assumed.

If Heat Transfer is considered as a parallel to the Electric Current model, it will be easier to visualize.

Visualize Temperature difference as Voltage Difference; Thermal resistance by definition is $\frac{kA}{L}$
$k$ and $A$ are constant and canceled out since material is the same and has same cross-section.
The current is equal throughout the rod.

Hence, applying the aforementioned equation with ${\theta }_1={100}^o;{\theta }_2=0$

$L={100}^{o}cm;l={60}^{o}cm$

$\frac{{100}^o-0^o}{{100}^o}=\frac{\theta -0^o}{{60}^o}$

$\theta ={60}^o$