A body cools from `60^(@)C,50^(@)C` in 10 minutes. If the room temperature is `25^(@)C` and assuming Newton's law of cooling to hold good, the temperature of the body at the end of the next 10 minutes will be :

Options

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

Answer

D

Explanation

According to Newton.s law of cooling
`(theta_(1)-theta_(2))/(t)=K[(theta_(1)+theta_(2))/(2)-theta_(0)]`
`:." "(60-50)/(10)=K[(60+50)/(2)-25]` . . . (i)
In second case, if T be the final temperature after 10 minutes.
Then `(50-theta)/(10)=K[(50+theta)/(3)-25]` . . . (ii)
Dividing (i) by (ii)
`(10)/(50-7)=(30)/(theta/2)rArr10theta=60xx50-60T`.
`70theta=60xx50`
`theta=(60xx50)/(70)=(300)/(7)=42*85^(@)C`
Correct choice is (d).