Thermal Properties of Matter

JEE Main level, single correct, medium

68 of 126

Question 68 of 126

Due to cold weather, a 1m1m water pipe of cross-sectional area 1cm21{cm}^{2} is filled with ice at −10∘C.-10^{\circ}C. Resistive heating is used to melt the ice. Current of 0.5A0.5A is passed through 4kΩ4k\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=3.33×105Jkg−1,=3.33\times {10}^{5}J{kg}^{-1}, specific heat of ice =2\times {10}^{3}J{kg}^{-1}^{\circ}{C}^{-1} and density of ice =103kgm−3)={10}^{3}kg{m}^{-3})

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Answer: (C) 35.3s35.3s

The mass of ice, m=ρAL=103×10−4×1=10−1kgm=\rho AL={10}^{3}\times {10}^{-4}\times 1={10}^{-1}kg,
Energy required to melt the ice, =mSΔT+mL=mS\Delta T+mL,
⇒i2Rt=mSΔT+mL\Rightarrow {i}^{2}Rt=mS\Delta T+mL
⇒(1)2×103×t=[(103×1×10−4)×2000×10]+[(103×1×10−4)×330×103]⇒(1)2×103×t=3.53×104⇒t=35.3s\Rightarrow (1{)}^{2}\times {10}^{3}\times t=\left[\left({10}^{3}\times 1\times {10}^{-4}\right)\times 2000\times 10\right]+\left[\left({10}^{3}\times 1\times {10}^{-4}\right)\times 330\times {10}^{3}\right] \Rightarrow (1{)}^{2}\times {10}^{3}\times t=3.53\times {10}^{4} \Rightarrow t=35.3s

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