Question

A rod is of 40 cm in length and has a temperature difference of $80^{\circ }C$ at its two ends. Another rod $b$ is of length 60 cm and has a temperature difference $90^{\circ }C$ but has 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

Answer: (A)

$H=\frac{K_{1}A\Delta T_1}{l_1}=\frac{K_2\cdot A\cdot \Delta T_2}{l_2}$
$\Rightarrow \frac{K_1\Delta T_1}{l_1}=\frac{K_2\cdot \Delta T_2}{l_2}$
$\frac{K_1\left(80^{\circ }C\right)}{40cm}=\frac{K_2\left(90^{\circ }C\right)}{60cm}$
$\Rightarrow \frac{K_1}{K_2}=\frac{40cm\times 90^{\circ }C}{60cm\times 80^{\circ }C}=\frac{3}{4}$