One end of a metal rod of length 0.6 m and area 120 cm² is in boiling water and the other end is in melting ice. If 0.36 kg of ice melts per minute, the coefficient of thermal conductivity of the material of the rod is ______ W m⁻¹ K⁻¹.
Physics · Mixed Chapter
JEE Main Practice

Question

One end of a metal rod of length 0.6 m and area 120 cm² is in boiling water and the other end is in melting ice. If 0.36 kg of ice melts per minute, the coefficient of thermal conductivity of the material of the rod is ______ W m⁻¹ K⁻¹.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Area A = 120 cm² = 0.012 m²; length L = 0.6 m; temperature difference ΔT = 100 K. Step 2: Rate of melting ice ṁ = 0.36/60 = 0.006 kg s⁻¹. Step 3: Taking latent heat of fusion Lf = 3.36 × 10⁵ J kg⁻¹, heat current H = ṁLf = 0.006 × 3.36 × 10⁵ = 2016 W. Step 4: Fourier's law H = kAΔT/L gives k = HL/(AΔT) = (2016 × 0.6)/(0.012 × 100) = 1008 W m⁻¹ K⁻¹. Step 5: Original printed key 0.186 W m⁻¹ K⁻¹ conflicts strongly; check source values/units. Source-key answer: 0.186. Computed standard resul…