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A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two end conduct an amount of heat ' Q₁ ' in time ' t ' the metallic rod is melted and the material is formed into a rod of length four times the length of original rod. The amount of heat conducted by the new rod when placed in thermal contact with the same two reservoirs in time t is ' Q₂ '. Then Q₁ Q₂ is

Options

  1. A16
  2. B1 16
  3. C1 4
  4. D4

Correct answer

A. 16

Step-by-step solution

The heat conduction rate is given by: Q t = k A (T₁-T₂ ) l Considering volume conservation: aligned & A₁ l₁=A₂ l₂ & A₁ l₁=A₂ (4 l₁ ) & A₂= A₁ 4 & Q₂ t = k ( A₁ 4 ) (T₁-T₂ ) 4 l₁ = 1 16 k A₁ (T₁-T₂ ) l₁ = 1 16 Q₁ t & Q₂= 1 16 Q₁ aligned

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