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.

Options

A. `38.5^(@)`C
B. `40^(@)`C
C. `45^(@)`C
D. `42.85^(@)`C

Answer

D

Explanation

Newton's cooling law is given as
`[theta_(1)-theta_(2)]/t = k[(theta_(1)+theta_(2))/2 -theta_(0)]`
Given, `theta_(0) = 25^(@)`C and `theta_(2) = 60^(@)`C
By putting values, `k=1/3`
Again, `theta_(2) = theta,theta_(1)=50^(@)`C, `theta_(0)=25^(@)`C `therefore theta=42.8^(@)`C