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

Options

A. `(7)/(4)`T
B. `(3)/(2)T`
C. `(4)/(3)T`
D. `T`

Answer

B

Explanation

`T_(0)=T`
`((3T-2T)/(10))=c_(1)((3T+2T)/(2)-T)` . . . (i)
`((2T-T_(f))/(10))=c_(1)((2T+T_(f))/(2)-T)` . .. (ii)
`(Eq.(i))/(Eq.(ii))implies(T//10)/((2T-T_(f))/(10))=((5T-2T)/(2))/((T_(f))/(2))`
`(T)/(2T-T_(f))=(3T)/(T_(f))`
`T_(f)=6T-3T_(f)`
`4T_(f)=6T`
`T_(f)=(3)/(2)T`