Question

In an experiment ot verify Newton's law of cooling, a graph is plotted between, the temperature difference $(\Delta T)$ of the water and surroundings and time as shown in figure. The initial temperature of water is taken as $80^{\circ} C$. The value of $t _{2}$ as mentioned in the graph will be ______

Answer 1

$T - T _{0}\left( T _{ i }- T _{0}\right) e ^{-\frac{ Bt }{ ms }}$
$6 \lambda=\ln 1.5$
$40=60 e ^{-\lambda(6)} \Rightarrow 6 \lambda=\ln 1.5$
$20=60 e ^{-\lambda t_{2}} \Rightarrow t _{2} \lambda=\ln 3$
$\frac{t_{2}}{6}=\frac{\ln 3}{\ln 1.5}$
$\therefore t _{2}=16.25\, \min$
$So \approx 16$