A rectangular block of copper (thermal conductivity K = 0.9) of thickness 10 cm and area of cross-section 20 cm² has one face maintained at 100°C while the opposite face is in contact with ice at 0°C. If there is no loss of heat, the amount of ice that melts in 20 minutes is ______ kg.
Physics · Mixed Chapter
JEE Main Practice

Question

A rectangular block of copper (thermal conductivity K = 0.9) of thickness 10 cm and area of cross-section 20 cm² has one face maintained at 100°C while the opposite face is in contact with ice at 0°C. If there is no loss of heat, the amount of ice that melts in 20 minutes is ______ kg.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The problem supplies K = 0.9 without its unit. If K is taken in the common cgs thermal unit cal cm⁻¹ s⁻¹ °C⁻¹, the steady heat flow is Q = K A ΔT t/L. Step 2: Q = [0.9 × 20 × 100 × (20 × 60)]/10 = 216000 cal. Step 3: With latent heat of fusion of ice ≈ 80 cal g⁻¹, melted mass m = 216000/80 = 2700 g = 2.7 kg. Step 4: The source key is 0.27 kg, a factor of 10 smaller; this does not follow from the stated numbers under these standard units. Source-key answer: 0.27 kg. Calculated under stan…