Question

A rod of 40 cm in length and temperature difference of ${80}^{\circ }$C at its two ends. Another rod B of length 60 cm nd of temperature difference ${90}^{\circ }$C, having the same area of cross-section. If the rate of flow of heat is the same, then the ratio of their thermal conductivities will be

• A. 3 : 4
• B. 4 : 3
• C. 1 : 2
• D. 2 : 1

Answer 1

The correct option is A 3 : 4

$\frac{dQ}{dt}=\frac{KA({\theta }_1-{\theta }_2)}{d}$
$\Rightarrow \frac{K_1\Delta {\theta }_1}{l_1}=\frac{K_2\Delta {\theta }_2}{l_2}$ $(\because \frac{dQ}{dt}andAaresame)$
$\Rightarrow \frac{K_1\times 80}{40}=\frac{K_2\times 90}{60}\Rightarrow \frac{K_1}{K_2}=\frac{3}{4}$