The length of a metal bar is 20 cm and the area of cross section is $4 \times 10^{-4} \mathrm{~m}^2$. If one…

The length of a metal bar is 20 cm and the area of cross section is $4 \times 10^{-4} \mathrm{~m}^2$. If one end of the rod is kept in ice at $0^{\circ} \mathrm{C}$ and the other end is kept in steam at $100^{\circ} \mathrm{C}$, the mass of ice melted in one minute is 5 g . The thermal conductivity of the metal in $\mathrm{Wm}^{-1} \mathrm{~K}^{-1}$ is (Latent heat of fusion $=80 \mathrm{cal} / \mathrm{gm}$ )
  1. $140$
  2. $120$
  3. $100$
  4. $160$

Solution

$1=20 \mathrm{~cm}=0.2 \mathrm{~m}, \mathrm{~A}=4 \times 10^{-4} \mathrm{~m}^2, \theta_1=0^{\circ} \mathrm{c}, \theta_2=100^{\circ} \mathrm{c}$ $\therefore H=\frac{k A\left(\theta_2-\theta_1\right)}{1} \Rightarrow \frac{\mathrm{~mL}}{\mathrm{t}}=\frac{\mathrm{kA}\left(\theta_2-\theta_1\right)}{1}$ $\begin{aligned} & \Rightarrow \frac{5 \times 80 \times 4.2}{60}=\frac{\mathrm{k} \times 4 \times 10^{-4} \times 100}{0.2} \\ & \therefore \quad \mathrm{k}=140 \mathrm{~W}_{\mathrm{m}}{ }^{-1} \mathrm{k}^{-1} .\end{aligned}$

Asked in: AP EAMCET 2024 (18 May Shift 1)

Practice more Thermal Properties of Matter questions on Aicharya