A body cools down from 52.5^ C to 47.5^ C in 5 ~min and from 47.5^ C to 42.5^ C in 7.5 ~min . Then, the temperature of the surroundings is

Step-by-step solution

Given that, for first condition, Initial temperature, T₁=52.5^ C Final temperature, T₂=47.5^ C Average temperature, T_ av = T₁+T₂ 2 = 525+47.5 2 =50^ C For second condition, Initial temperature, T₁=47.5^ C Final temperature, T₂=42.5^ C Average temperature, T_ av = T₁+T₂ 2 = 47.5+42.5 2 =45^ C Let T₀ be the temperature of surroundings. Now, using expression of rate of cooling, R= T t =-K (T_ av -T₀ ) Substituting the values in above equation from lst and 2 nd conditions, we get T₁-T₂ t₁ =-K (T_ av -T₀ ) 52.5-47.5 5