Question

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 $c{m}^2$, the amount of ice that melts in 1 minute is

• A. 0.125 g
• B. 75 g
• C. 7.5 g
• D. 450 g

Answer 1

The correct option is C

7.5 g

$Givenk=420W/m/K,A=10c{m}^2=10\times {10}^{-1}{m}^2={10}^{-3}{m}^2,{\theta }_1={100}^{\circ }C,t^2=0^{\circ }C,$ t = 1 minute = 60 s and l = 1 m. Using these values in

$Q=\frac{kA({\theta }_1-{\theta }_2)t}{l}wegetQ=2520J=\frac{2520}{4.2}=600cal.$
Therefore, mass of ice melted is $m=\frac{Q}{L}=\frac{600cal}{80cal/g}=7.5g$

Hence the correct choice is (c).