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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

As shown in the figure, an aluminium rod is joined to a copper rod. Both rods possess a length of 20 cm and a cross-sectional area of 0.20 cm ^2 . The junction between them is kept at a constant temperature of 40^ C , while their outer ends are maintained at 80^ C . Determine the amount of heat extracted from the cold junction in one minute once the steady state has been reached. The thermal conductivities are given

Options

  1. A288 J
  2. B48 J
  3. C144 J
  4. D96 J

Correct answer

C. 144 J

Step-by-step solution

Given: Length of each rod, L = 20 cm = 0.2 m Cross-sectional area, A = 0.20 cm ^2 = 2 10⁻⁵ m ^2 Temperature of outer ends, T_ hot = 80^ C Temperature of junction, T_ cold = 40^ C Temperature difference across each rod, T = 80^ C - 40^ C = 40^ C The rate of heat flow (heat current) through the aluminium rod is: H_ Al = K_ Al A T L = 200 2 10⁻⁵ 40 0.2 = 0.8 W The rate of heat flow through the copper rod is: H_ Cu = K_ Cu A T L = 400 2 10⁻⁵ 40 0.2 = 1.6 W The total rate at which heat reaches the cold junction is: H_ t

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