A rod 1 m long and made of material of thermal conductivity 420 W/m/K has one of its ends in melting ice and the other end in boiling water. If its area of cross-section is 10 cm², the amount of ice that melts in 1 minute is 

Given k = 420 W/m/K,  A = 10 cm² = 10 x 10^-4 m²  = 10^-3 m², ${\theta }_1$ = 100°C, ${\mathrm{\theta }}_2$ = 0°C, t = 1 minute = 60 s and l = 1 m. Using these values in

$$\begin{gathered} Q=\frac{kA\left({\theta }_1-{\theta }_2\right)t}{l} \\ we get Q=2520 \mathrm{J}=\frac{2520}{4.2}=600 \mathrm{cal} \end{gathered}$$

Therefore, mass of ice melted is

              $m=\frac{Q}{L}=\frac{600 \mathrm{cal}}{80 \mathrm{cal}/\mathrm{g}}=7.5 \mathrm{g}$