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A body cools from a temperature 3 T to 2...

A body cools from a temperature `3 T` to `2 T` in `10` minutes. The room temperature is `T`. Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next `10` minutes will be

A

`4/3T`

B

T

C

`7/4T`

D

`3/2T`

Text Solution

Verified by Experts

The correct Answer is:
D
Newton.s law of cooling
`(T_(1)-T_(2))/(t)=k ((T_(1)+T_(2))/2-T)`
`(3T-2T)/(10)=k ((5T-2T)/(2)) rArr T/(10) =k ((3T)/2) ……..(i)`
`(2T-T.)/(10)=k ((2T+T.)/(2)-T) rArr (2T-T.)/(10) =k (T/2) ……….(ii)`
By solving Eqs. (i) and (ii)
`T.=3/2 T`
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