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As shown in diagram, AB is a rod of length 30 cm and area of cross section 1 . 0 cm 2 and thermal conductivity 336 SI units . The ends A and B are maintained at temperatures 20 ° C and 40 ° C , respectively. A point C of this rod is connected to a box D , containing ice at 0 ° C , through a highly conducting wire of negligible heat capacity. The rate at which ice melts in the box is (assume latent heat of fusion for

Options

  1. A84 mg s - 1
  2. B84 g s - 1
  3. C20 mg s - 1
  4. D40 mg s - 1

Correct answer

D. 40 mg s - 1

Step-by-step solution

Thermal resistance of AC = L KA = 0.1 3 3 6 × 1 0 - 4 = 1 0 3 3 3 6 = R let Thermal resistance of BC = 0.2 3 3 6 × 1 0 - 4 = 2 R Heat flow rates are H 1 = 2 0 R ; H 2 = 4 0 2 R = 2 0 R undefined = 1 3 4 4 0 1 0 3 = 13.44 W Rate of melting of ice = H L f = 13.44/4.2 8 0 g s -1 = 4 0 mg s - 1

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