In an experiment to verify Newton's law of cooling. a graph is plotted between. the temperature difference Δ T 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 as mentioned in the graph will be

Step-by-step solution

According to the Newton's law of cooling, - d T d t = K T - T 0 . Applying approximation, - ∆ T ∆ t = K T 1 + T 2 2 - T 0 For first 6   min , T 1 = 80 ° C ,   T 2 = 40 + 20 = 60 ° C ,   T 0 = 20 ° C ⇒ - 60 - 80 6 = K 70 - 20 ⇒ K = - 60 - 80 6 × 70 - 20 ⇒ K = 20 6 × 50 = 1 15 For 6  to  t 2 , T 1 = 60 ° C ,   T 2 = 20 + 20 = 40 ° C ,   T 0 = 20 ° C - 60 - 80 t 2 - 6 = K 50 - 20 ⇒ t 2 - 6 = 15 × 20