A body cools from `60%@C` to `50^@`C in 10 min. Find its temperature at the end of next 10 min if the room temperature is `25^@C`. Assume Newton's law of cooling holds.

Explanation

According to Newton's law of cooling
`(d theta)/(dt)=-k(theta-theta_0)`
`log(theta-theta_0)=-kt+c`
Given as `t=0,theta=60^@C`
`:. log(60-25)=c` or `kt=log35-log(theta-25)`
`:. log(theta-25)=-kt+log35`
`kt=log35-log(theta-25)`
`t-10mintheta=50^@C`
`k10=log35-log25`
`impliesk=(1)/(10)log(7)/(5)`
`((1)/(10)log.(7)/(5))=log35-log(theta-25)`
when `t=20mintheta=?`
`((1)/(10)log.(7)/(5))20=log.(35)/(theta-25)`
`implieslog((7)/(5))^2=log.(35)/(theta-25)implies((7)/(5))^2=(35)/(theta-25)`
`impliestheta=42.8^@C`