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288KJ is conducted across two opposite faces of a 3m cube of temperature gradient 90ºCm\(^{-1}\)...

Physics
JAMB 2024

288KJ is conducted across two opposite faces of a 3m cube of temperature gradient 90ºCm\(^{-1}\) in 7200s. Calculate the thermal conductivity.

  • A. 4.9 x 10\(^{-2}\)Wm\(^{-1}\)k\(^{-1}\)
  • A. 5.0 x 10\(^{-2}\)Wm\(^{-1}\)k\(^{-1}\)
  • C. 5.2 x 10\(^{-2}\)Wm\(^{-1}\)k\(^{-1}\)
  • D. 5.1 x 10\(^{-2}\)Wm\(^{-1}\)k\(^{-1}\)
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Correct Answer: Option A
Explanation

k = \(\frac{Q.d}{A. ΔT .t}\)

d = thickness = 3m

A = 9m\(^2\)

Q = 288kJ = 288000J, t = 7200s, ΔT = 90ºC/m → 90K/m x 3 = 270K

k = \(\frac{288000 \times 3}{9 \times 270 \times 7200}\)

k = 4.93 x 10\(^{-2}\)Wm\(^{-1}\)k\(^{-1}\)

There is an explanation video available below.


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