A hot body is allowed to cool . The surrounding temperature is constant at `30^(@) C` . The body takes time `t_(1)` to cool from `90^(@)` to `89^(@)C` and time `t_(2)` to cool from `60^(@)C ` to `59.5 ^(@) C` . Then ,

Options

A. `t_(2) = 2 t_(1)`
B. `t_(2) = (t_(1))/(2)`
C. `t_(2) = 4 t_(1)`
D. `t_(2) = t_(1)`

Answer

D

Explanation

According to Newton's law of cooling , `(T_(1) + T_(2))/(t) = K ((T_(1) + T_(2))/(2) - T_(s) )`
where `T_(s)` is the surrounding temperature . As per question ,
`((90 - 89))/(t_(1)) = K ((90 + 89)/(2) - 30)`
`(1)/(t_(1)) = K (59.5) " " ... (i)`
and `((60 - 59.5))/(t_(2))= K ((60 + 59.5)/(2) - 30) `
`(0.5)/(t_(2)) = K (29.75) " " ... (ii)`
Divide (i) by (ii) , we get `(t_(2))/(0.5 t_(1)) = (59.5)/(29.75)`
`(t_(2))/(t_(1)) = 1 or t_(2) = t_(1)`