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Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer

A body cools from 50^ C to 45^ C in 5 minutes, and subsequently to 40^ C in another 8 minutes. Determine the temperature of the surrounding.

Options

  1. A30^ C
  2. B36^ C
  3. C34^ C
  4. D32^ C

Correct answer

C. 34^ C

Step-by-step solution

Using Newton's law of cooling in approximate form: T₁ - T₂ t = K ( T₁ + T₂ 2 - T₀ ) For the first interval: 50 - 45 5 = K ( 50 + 45 2 - T₀ ) 1 = K (47.5 - T₀) For the second interval: 45 - 40 8 = K ( 45 + 40 2 - T₀ ) 5 8 = K (42.5 - T₀) Dividing the two equations: 8 5 = 47.5 - T₀ 42.5 - T₀ 8(42.5 - T₀) = 5(47.5 - T₀) 340 - 8T₀ = 237.5 - 5T₀ 3T₀ = 102.5 T₀ = 34.16^ C 34^ C

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