Question

In an experiment to verify Newton’s law of cooling, a graph is plotted between, the temperature difference (ΔT) of the water and surroundings and time as shown in figure. The initial temperature of water is taken as 80ºC. The value of $t_2$ as mentioned in the graph will be ______.

Answer 1

Temperature of surrounding $=$ $20ºC$
For $0$ to $6$ minutes, average temp. $=$ $70ºC$
Rate of cooling $∝70ºC – 20ºC = 50ºC$
For $6$ to $t_2$ minutes, average temp. $= 50ºC$
Rate of cooling $∝30ºC$
$⇒ t_2-6 = \frac 53$ ($6$ minutes)
$⇒ t_2= 16$ minutes

So, the answer is $16$ minutes.