A body cools in 7 minutes from 60 ° C to 40 ° C . What will be its temperature after the next 7 minutes ? The temperature of the surrounding is 10 ° C .

Step-by-step solution

According to Newton's law of cooling, - d θ dt = K θ - θ 0 or ∫ 0 t dt = 1 K ∫ θ 1 θ 2 - d θ θ - θ 0 or t = 1 K log e θ 1 - θ 0 θ 2 - θ 0 So here 7 = 1 K log e [ 60 - 10 40 - 10 ] and also 7 = 1 K log e 40 - 10 θ - 10 ∴ log [ 50 30 ] = log 30 θ - 10 or 5 3 = 30 θ - 10 i.e., 5 θ - 50 = 90 or θ = 28 ° C