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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

A person's normal body-temperature is 97 ^ F . Determine the rate at which heat flows out of their body through the clothes, assuming the following values: room temperature = 47 ^ F , surface of the body under clothes = 1.6 m ^2 , conductivity of the cloth = 0.04 J s ⁻¹ m ⁻¹ ^ C⁻¹ , and thickness of the cloth = 0.5 cm .

Options

  1. A1152 J s ⁻¹
  2. B356 J s ⁻¹
  3. C640 J s ⁻¹
  4. D3.56 J s ⁻¹

Correct answer

B. 356 J s ⁻¹

Step-by-step solution

The temperature difference in Fahrenheit is T_ F = 97 - 47 = 50 ^ F Converting this temperature difference to Celsius: T_ C = 5 9 T_ F = 5 9 50 = 250 9 ^ C The rate of heat flow is given by Fourier's law of heat conduction: dQ dt = KA T d Substituting the given values K = 0.04 J s ⁻¹ m ⁻¹ ^ C⁻¹ , A = 1.6 m ^2 , and d = 0.5 cm = 0.005 m : dQ dt = 0.04 1.6 250 9 0.005 dQ dt = 8 1.6 250 9 = 3200 9 355.56 J s ⁻¹ Rounding to the nearest integer, the rate of heat flow is 356 J s ⁻¹ .

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