Due to cold weather a 1 m water pipe of cross-sectional area $1 \mathrm{~cm}_2$ is filled with ice at $-10^{\circ} \mathrm{C}$.
Resistive heating is used to melt the ice. Current of 0.5 A is passed through $4 \mathrm{k} \Omega$ 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 $=3.33 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$, specific heat of ice $=2 \times 10^3 \mathrm{~J} \mathrm{~kg}^{-1}$ and density of ice $=10^3 \mathrm{~kg} / \mathrm{m}^3$
Select the correct option:
A
0.353 s
B
35.3s
C
3.53s
D
70.6s
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
mass of ice $m=\rho A \square=10^3 \times 10^{-4} \times 1=10^{-1} \mathrm{~kg}$
Energy required to melt the ice
$$
\begin{aligned}
& Q=m s \Delta T+m L \\
& =10^{-1}\left(2 \times 10^3 \times 10+3.33 \times 10^5\right)=3.53 \times 10^4 J \\
& Q=i^2 R T \Rightarrow 3.53 \times 10^4=\left(\frac{1}{2}\right)^2\left(4 \times 10^3\right)(t) \\
& \text { Time }=35.3 \mathrm{sec}
\end{aligned}
$$
Option (2)
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