In an experiment to verify Newton's law of cooling, a graph is plotted between the temperature difference (`DeltaT`) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as `80^(@)` C. The value of `t_(2)` mentioned in the graph will be_______

Explanation

`DeltaT = T_("water") - T_("sourrounding") = T- T_(s)`
At t =0, `DeltaT = 60` and `t = 80^(@)` C
`80 - T_(s) = 60, therefore T_(s) = 20^(@)` C
Newton law of cooling
`-(T_(f) - T_(i))/(Deltat) = k(T_(i)+ T_(fi))/2 - T_(s)`
between 0 to 6 minute.
`20/(t_(2)-6) = k[((40 + 20)/2 + 20)-20]`
After dividing by `t_(2) = 16` min.