A body cools in 10 min from `60^(@)`C to `40^(@)`C in 5 min and to `42.5^(@)`C in 7.5 min. Find the temperature of the surroundings.

Explanation

According to Newton's law of cooling.
`((T_(1)-T_(2))/(t))= k[((T_(1)+T_(2))/2)-T_(0)]`
For the given conditions,
`(60-40)/(10) = k[(60-40)/(2)-10]`.....................(i)
Let T be the temperature after next 10 min. Then,
`(40-T)/(10)=K[(40+T)/(2)-10]`..............(ii)
Solving Eqs. (i) and (ii), we get T=`28^(@)`C