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MHT CET Medical202623 April 2026Morning ShiftPhysicsThermal Properties of MatterActual

The initial temperature of a body is 80^ C . If its temperature falls to 64^ C in 5 minutes and in the next 10 minutes to 52^ C , then the temperature of the surroundings is

Options

  1. A35^ C
  2. B42.6^ C
  3. C48^ C
  4. D26^ C

Correct answer

C. 48^ C

Step-by-step solution

According to the exact form of Newton's law of cooling, the temperature T at time t is given by: T - T₀ = (T_i - T₀)e^ -Kt where T₀ is the surrounding temperature and T_i is the initial temperature. For the first interval of 5 minutes: T_i = 80^ C , T = 64^ C , t = 5 64 - T₀ = (80 - T₀)e^ -5K e^ -5K = 64 - T₀ 80 - T₀ --- (1) For the next interval of 10 minutes: T_i = 64^ C , T = 52^ C , t = 10 52 - T₀ = (64 - T₀)e^ -10K e^ -10K = 52 - T₀ 64 - T₀ --- (2) Since e^ -10K = (e^ -5K )^2 , equating (2) and the square of (

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