If a body cools down from `80^(@) C`to `60^(@) C` in 10 min when the temperature of the surrounding of the is `30^(@) C` . Then, the temperature of the body after next 10 min will be

Options

A. `50^(@)C`
B. `48^(@)C`
C. `30^(@)C`
D. None of these

Answer

B

Explanation

Apply Newton.s law of cooling,
`(DeltaT)/(t)= -k (T_(av)-T_(theta))`
`(20)/(10)= -k(70-30)" " …(1)`
`(60-T)/(10)= -k((60+T)/(2)-30)" " …(2)`
Divide eq. (2) by eq. (1)
`(60-T)/(20)=(T//2)/(40)rArr 120-2T=(T)/(2) rArr T=48^(@)C`