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MHT CET202416 May 2024Morning ShiftPhysicsThermal Properties of MatterActual

A bucket full of hot water is kept in a room. If it cools from 75^ C to 70^ C in t ₁ minutes, from 70^ C to 65^ C in t ₂ minutes and 65^ C to 60^ C in t ₃ minutes, then

Options

  1. At ₁ t ₂ t ₃
  2. Bt₁ t₂ t₃
  3. Ct₁=t₂=t₃
  4. Dt ₁ t ₂= t ₃

Correct answer

A. t ₁ t ₂ t ₃

Step-by-step solution

According to Newton's law of cooling, Rate of cooling Mean temperature difference Fall in temperature Time ( t ) ( ₁+ ₂ 2 - ₀ ) Case 1: ( ₁+ ₂ 2 )₁= ( 75+70 2 )₁=72.5 Case 2: ( ₁+ ₂ 2 )₂= ( 70+65 2 )₂=67.5 Case 3: ( ₁+ ₂ 2 )₃= ( 65+60 2 )₃=62.5 aligned & ( ₁+ ₂ 2 )₁ ( ₁+ ₂ 2 )₂ ( ₁+ ₂ 2 )₃ & t ₁ t ₂ t ₃ aligned

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