Hot water cools from 80^ C to 60^ C in 1 minutes. In cooling from 60^ C to 50^ C it will take (room temperature =30^ C )

Step-by-step solution

The rate of heat loss by a body is proportional to the temperature difference between the body and its surroundings, as described by Newton's Law of Cooling. The approximate form for finite temperature changes is expressed as: T₁ - T₂ t = K ( T₁ + T₂ 2 - T_s ) where T_s = 30^ C is the room temperature. Using the initial cooling data from 80^ C to 60^ C in 60 seconds: 80 - 60 60 = K ( 80 + 60 2 - 30 ) 1 3 = K (40) Solving gives the constant K = 1 120 s ⁻¹ . To find the time t for cooling from 60^ C to 50^ C : 60 - 5