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BITSAT2023PhysicsThermal Properties of MatterActual

A bowl filled with very hot soup cools from 98^ C to 86^ C in 2 minutes when the room temperature is 22^ C . How long it will take to cool from 75^ C to 69^ C ?

Options

  1. A2 minutes
  2. B1.4 minutes
  3. C0.5 minute
  4. D1 minute

Correct answer

B. 1.4 minutes

Step-by-step solution

The rate of heat flow is given by aligned & Q t =-K (T-T₀ ) Q t =-K (T_ a v g -T₀ ) & Initially T_ a v g = T₁+T₂ 2 & Here, T₁=98^ C & T₂=86^ C aligned aligned & (i) ms 12 2 =- K ( 98+86 2 -22 ) & 6=- K ms [ 98+86 2 -22 ] ( Q = ms T ) aligned Now, cool from T ₁^ =75^ C aligned & T ₂=69^ C & T _ avg = T ₁^ + T ₂^ 2 = 75+69 2 aligned (ii) ms 6 t =- K ( 75+69 2 -22 ) Divide equation (ii) by (i), we have aligned & 6 t(6) = 50 70 & t= 7 5 =1.4 ~min aligned

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