Question

Due to cold weather a $1m$ water pipe of cross-sectional area $1c{m}^2$ is filled with ice at $-10^{\circ }C$. Resistive heating is used to melt the ice. Current of $0.5A$ is passed through $4k\Omega$ resistance. Assuming that all the heat produced is used for melting, what is the minimum time required ?
(Given latent heat of fusion for water/ice $=3.33\times 10^{5}Jk{g}^{-1}$, specific heat of ice $=2\times 10^{3}Jk{g}^{-1}$ and density of ice $=10^{3}kg/m^3$

• A. 0.353 s
• B. 35.3 s
• C. 3.53 s
• D. 70.6 s

Answer 1

Answer: (B)

mass of ice $m=\rho A\ell =10^3\times 10^{-4}\times 1=10^{-1}kg$
Energy required to melt the ice
$Q=ms\Delta T+mL$
$=10^{-1}\left(2\times 10^3\times 10+3.33\times 10^5\right)$
$=3.53\times 10^{4}J$
$Q=i^{2}RT$
$\Rightarrow 3.53\times 10^4$
$={\left(\frac{1}{2}\right)}^2\left(4\times 10^3\right)(t)$
Time $=35.3\sec$