Question

A heat flux of $4000\text{J/s}$ is to be passed through a copper rod of length $10\text{cm}$ and area of cross section $100{\text{cm}}^2$. The thermal conductivity of copper is $400{\text{W/m}}^{\circ }C$. The two ends of the rod must be kept at temperature difference of

• A. $1^{\circ }C$
• B. ${10}^{\circ }C$
• C. ${100}^{\circ }C$
• D. ${1000}^{\circ }C$

Answer 1

The correct option is C ${100}^{\circ }C$

From conduction law,
$\frac{Q}{t}=\frac{KA({\theta }_1-{\theta }_2)}{L}$
$\Rightarrow 4000=\frac{400\times (100\times {10}^{-4})\times ({\theta }_1-{\theta }_2)}{(10\times {10}^{-2})}$
$\Rightarrow {\theta }_1-{\theta }_2={100}^{\circ }C$
Hence, option $\left(c\right)$ is the correct answer.