Q 11-10-067JEE MainJEE Main 2023 (25 Jan, Shift 1)Medium
A bowl filled with very hot soup cools from $98^\circ\text{C}$ to $86^\circ\text{C}$ in $2$ minutes when the room temperature is $22^\circ\text{C}$. How long it will take to cool from $75^\circ\text{C}$ to $69^\circ\text{C}$?
Answer: (B) 1.4 minute
Newton's law (average form): $\dfrac{\Delta T}{t}=k(T_{avg}-T_0)$.
First: $\dfrac{12}{2}=k(92-22)\Rightarrow k=\dfrac{6}{70}$.
Second: $\dfrac{6}{t}=\dfrac{6}{70}(72-22)\Rightarrow t=\dfrac{70}{50}=1.4\ \text{min}$.
Solution by Sreeraj P, M.Sc Physics