Q 11-10-092JEE MainJEE Main 2021 (22 Jul, Shift 1)Medium
In 5 minutes, a body cools from 75 °C to 65 °C at room temperature of 25 °C. The temperature of body at the end of next 5 minutes is ______ °C.
Numerical value type. Enter your answer.
Answer: 57
Using the average form of Newton's law of cooling, $\dfrac{\Delta T}{t} = k(\bar T - T_0)$:
First interval: $\dfrac{10}{5} = k(70 - 25) \Rightarrow k = \dfrac{2}{45}\ \text{min}^{-1}$.
Second interval: $\dfrac{65 - T}{5} = \dfrac{2}{45}\left(\dfrac{65 + T}{2} - 25\right) \Rightarrow 9(65 - T) = T + 15 \Rightarrow T = 57$ °C.
Solution by Sreeraj P, M.Sc Physics