In a home experiment , Ram brings a new electric kettle with unknown power rating . He puts `1` litre water in the kettle and switches on . But to his dismay , the temperature becomes constants at `60^(@)C` after some time. The room temperature is `20^(@)C`. Ram gets bored and switches off the kittle . He sees that during first `20`s water cools down by `2^(@)C`.
What is the time taken for the water to cool to `40^(@)C`. (Approx)

Answer

B

Explanation

`(d theta)/(dt) = +K(T_(S) - T_(L)) implies (2)/(20) = K(40) implies K = (1)/(400)`
`underset(60^(@))overset(60)int (d theta)/((20-theta)) = +Kunderset(0)overset(1)int"dt" , ln(20-theta)underset(60)overset(40)int = -(1)/(400)t`
`implies ln((20)/(40)) = -(1)/(400)t implies t = 277s`