An object is cooled from 75^ C to 65^ Cin 2 ~min . The time, it takes to cool from 55^ C to 45^ Cis [The temperature of surrounding is 30^ C ]

Step-by-step solution

Taking the newton's law of cooling in average form: Q t =-K (T_ a v g -T₀ ) , where T_ a v = T₁+T₂ 2 , K is the thermal conductivity. Using, Q=m C_P T the heat and heat capacity relation: m C_P T t =-K (T_ a v g -T₀ ) Case (1) Given soup cools from 75^ C to 65^ C in 2 minutes when the room temperature is 30^ C : m C_P 10^ C 2 =-K (75+65)^ C 2 -30^ C Case (2) Let the soup cools from cool from 55^ C to 45^ C int minutes when the room temperature is 30^ C : m C_P 10^ C t =-K (55+45)^ C 2 -30^ C On taking the ratio of