Question:
Two identical boxes A and B have thermal conductivities 180 and 270 W m$^{-1}$K$^{-1}$. Ice in A melts in 21 min. Time for half ice in B to melt is:}
Two identical boxes A and B have thermal conductivities 180 and 270 W m$^{-1}$K$^{-1}$. Ice in A melts in 21 min. Time for half ice in B to melt is:}
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Melting time ∝ 1 thermal conductivity.
Updated On: Jun 17, 2026
- 14 min
- 10.5 min
- 7 min
- 42 min
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Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Rate of heat transfer: \[ \frac{Q}{t} \propto k \]
Step 2: Time inversely proportional to conductivity: \[ t \propto \frac{1}{k} \]
Step 3: For A: \[ t_A = 21,\quad k_A = 180 \]
Step 4: For B: \[ t_B = t_A \cdot \frac{k_A}{k_B} = 21 \cdot \frac{180}{270} = 14\ \text{min} \]
Step 5: For half melting → time halves: \[ t = 7\ \text{min} \]
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