A body cools from 60^ C to 40^ C in 6 minutes. After next 6 minutes its temperature will be (Temperature of the surroundings is 10^ C )

Step-by-step solution

Newton's Law of Cooling provides the relation T₁ - T₂ t = k ( T₁ + T₂ 2 - T_s ) , where T_s = 10^ C is the ambient temperature. Using the initial cooling data: from T₁ = 60^ C to T₂ = 40^ C over t = 6 minutes, we substitute into the formula: 60 - 40 6 = k ( 60 + 40 2 - 10 ) 20 6 = k (50 - 10) 10 3 = 40k k = 1 12 min ⁻¹ For the next 6 minutes, cooling continues from T₁' = 40^ C to T₃ , with k = 1 12 min ⁻¹ : 40 - T₃ 6 = 1 12 ( 40 + T₃ 2 - 10 ) Multiplying both sides by 12: 2(40 - T₃) = 40 + T₃ 2 - 10 This simplifies