JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry
- JEE Mains 2021
- Hard
- MCQ
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 ? (In \({s}\)) (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 \(=10^{3}\, {kg} / {m}^{3}\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(35.3\)
Step-by-step Solution
Detailed explanation
mass of ice \({m}=\rho {A} \ell=10^{3} \times 10^{-4} \times 1=10^{-1}\, {kg}\)
Energy required to melt the ice
\({Q}={ms} \Delta {T}+{mL}\)
\(=10^{-1}\left(2 \times 10^{3} \times 10+3.33 \times 10^{5}\right)=3.53 \times 10^{4} {J}\)
\({Q}={i}^{2} {RT} \Rightarrow 3.53 \times 10^{4}=\left(\frac{1}{2}\right)^{2}\left(4 \times 10^{3}\right)({t})\)
\(\text { Time }=35.3 \,{sec}\)
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