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  4. Due to cold weather a 1 m water pipe of cross-sectional area 1 cm 2 is filled with ice at -10° C. Resistive heating is used to melt the ice. Current of 0.5 A is passed through 4 k Ω 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 × 105 J kg -1, specific heat of ice =2 × 103 J kg -1 and density of ice =103 kg / m 3

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Q. Due to cold weather a $1 \,m$ water pipe of cross-sectional area $1 \,cm ^{2}$ is filled with ice at $-10^{\circ} C$. Resistive heating is used to melt the ice. Current of $0.5 \,A$ is passed through $4\, k \Omega$ 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 $=3.33 \times 10^{5} \,J \,kg ^{-1}$, specific heat of ice $=2 \times 10^{3} J \,kg ^{-1}$ and density of ice $=10^{3} \,kg / m ^{3}$

JEE MainJEE Main 2021Thermal Properties of Matter

Solution:

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 $= 35.3 \sec$