Exam

NTA Abhyas

Year

2020

Subject

Physics

Chapter

Thermal Properties of Matter

NTA Abhyas 2020 · Physics · Thermal Properties of Matter

The end A of a rod AB of length 1m is maintained at 100 ° C and the...

The end $A$ of a rod $AB$ of length $1m$ is maintained at $100 ° C$ and the end $B$at $10 ° C$. What is the temperature (in $° C$) at a distance of $60cm$ from the end $B$?

Step-by-step solution

The situation is given in the figure. Let $\theta$ be the temperature at point C.



We know that the rate flow of heat

$\dfrac{Q}{t} = \dfrac{KA ( {\theta}_{1} - {\theta}_{2} )}{d}$

Here, K = coefficient of thermal conductivity

A = area of cross-section

$⇒ \dfrac{KA ( 100 - \theta )}{40} = \dfrac{KA ( \theta - 10 )}{60}$

$\dfrac{100 - \theta}{2} = \dfrac{\theta - 10}{3}$

$300 - 3\theta = 2\theta - 20$

$5\theta = 320$

$\theta = \dfrac{320}{5}$

$\theta = 64℃$