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. `(200/7)^(@)C`
B. `(300/7)^(@)C`
C. `(100/7)^(@)C`
D. `(400/7)^(@)C`

Answer

B

Explanation

`(60-50)/10=K(55-25)=30K`
`therefore30K=1" "thereforeK=1/30`
and `(50-theta)/10=1/30[(50+theta)/2-25]`
`therefore3(50-theta)=[(50+theta-50)/2]`
`150-3theta=theta/2" "therefore150=(7theta)/2" "thereforetheta=(300/7)^(@)C`