The quantity of heat flowing for 10 seconds through a rod of length 40 cm and cross-sectional area 50 cm² is 200 J. If the temperature difference between its ends is 80°C, then the coefficient of thermal conductivity of the rod in W m⁻¹ K⁻¹ is ______.
Physics · Mixed Chapter
JEE Main Practice

Question

The quantity of heat flowing for 10 seconds through a rod of length 40 cm and cross-sectional area 50 cm² is 200 J. If the temperature difference between its ends is 80°C, then the coefficient of thermal conductivity of the rod in W m⁻¹ K⁻¹ is ______.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: Q = 200 J, t = 10 s, L = 0.40 m, A = 50 cm² = 0.005 m², ΔT = 80 K. Step 2: Heat current H = Q/t = 200/10 = 20 W. Step 3: Fourier's law: H = kAΔT/L; rearrange k = HL/(AΔT). Step 4: k = (20 × 0.40)/(0.005 × 80) = 8/0.4 = 20 W m⁻¹ K⁻¹. Step 5: PDF's answer key 3.33 does not match these values. Source-key answer: 3.33. Independently calculated result: 20 W m⁻¹ K⁻¹.