Question

Temperature of hot end and cold end of a rod, which is in steady state, are ${100}^{\circ }C$ and ${40}^{\circ }C$ respectively. The area of cross section of rod and its thermal conductivity are uniform. The temperature of rod at its mid point is :

(Assume no heat loss through lateral surface).

• A. ${70}^{\circ }C$
• B. ${60}^{\circ }C$
• C. ${80}^{\circ }C$
• D. None of these

Answer 1

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

We know,

$\frac{dQ}{dt}=\frac{k\times A\times (T_2-T_1)}{l}$

Suppose the temperature at midpoint is $T^{0}C$,

Now,

$\frac{dQ}{dt}=\frac{kA(T-40)}{l/2}=\frac{kA(100-T)}{l/2}$

$100-T=T-402T=140T={70}^{0}C$

Hence option $\text{A}$ is correct answer.