A cup of coffee cools from 90 ° C to 80 ° C in t   min , when the room temperature is 20 ° C . The time taken by a similar cup of coffee to cool from 80 ° C   to   60 ° C at a room temperature same at 20 ° C is :

Step-by-step solution

From Newton's Law of cooling, Δ T Δ t = k T - T s where, ⇒ T 2 - T 1 t - k T 1 + T 2 2 - T s T s Where, T 1 = Initial temperature of body T 2 = Final temperature of body T s = surrounding temperature t = time taken For case 1 , 90 - 80 t = k 90 + 80 2 - 20 ⇒ 10 t = 65 k ⇒ k = 10 65 t       … i For case 2   , 80 - 60 t ' = k 80 + 60 2 - 20 ⇒ 20 t ' = 50 k Put the value k from eq. i , ⇒ 20 t ' = 50 × 10 65 t ⇒ t ' = 20 &#