If the surrounding air is kept at 25^ C and a body cools from 80^ C to 50^ C in 30 minutes, then temperature of the body after one hour will be

Step-by-step solution

By Newton's law of cooling, we write aligned & d dt ( - ₀ ) & d dt = k ( - ₀ ) ( d - ₀ )= kdt & | - ₀ |= kt + c & When t =0, =80 and ₀=25 & |80-25|=0+ c c = |55| & When t =30, =50 & |50-25|=30 k + |55| & k = 1 30 | 5 11 | aligned From (1), (2), (3) we write | - ₀ |= 1 30 | 5 11 | t+ |55| When t=60 , we get aligned & | - ₀ |= 60 30 | 5 11 |+ |55| & = ( | 5 11 | )^2+ |55|= | 25 121 55 |= | 125 11 | & -25= 125 11 =36.36^ C aligned