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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

Forming three sides of a square, a steel frame ( K = 45 W m ⁻¹ ^ C⁻¹ ) has a total length of 60 cm and a cross sectional area of 0.20 cm ^2 . The two free ends are maintained at 20^ C and 40^ C . Determine the rate of heat flow through a cross section of the frame.

Options

  1. A0.01 W
  2. B0.09 W
  3. C0.03 W
  4. D3.0 W

Correct answer

C. 0.03 W

Step-by-step solution

The rate of heat flow through a conducting rod is given by Fourier's law of heat conduction: H = KA T L Given: Thermal conductivity, K = 45 W m ⁻¹ ^ C ⁻¹ Cross-sectional area, A = 0.20 cm ^2 = 0.20 10⁻⁴ m ^2 = 2 10⁻⁵ m ^2 Total length of the frame, L = 60 cm = 0.6 m Temperature difference between the ends, T = 40^ C - 20^ C = 20^ C Substituting the values into the formula: H = 45 2 10⁻⁵ 20 0.6 H = 1800 10⁻⁵ 0.6 H = 3000 10⁻⁵ W H = 0.03 W

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