A body cools in 7 min from `60^@C` to `40^@C` What will be its temperature after the next 7 min? The temperature of surroundings is `10^@C`.

Explanation

Rate of cooling
`(triangleT)/(trianglet)=K(T-T_(0))`
For cooling from `60^(@)C` to `40^(@)C`
`implies(60-40)/(7)=K((60+40)/(2)-10)`
`impliesK=(20)/(7xx40)=(1)/(14)`
For cooling from `40^(@)C` to T
`(40-T)/(7)=K((40+T)/(2)-10)implies(40-T)/(7)=(1)/(14)((40+T-20)/(2))`
`implies160-4T=20+T`
`implies140=5T`
`impliesT=(140)/(5)=28^(@)C`
`T=28^(@)C`