1. Tardigrade
  2. Question
  3. Physics
  4. A body cools from a temperature 3 T to 2 T in 10 minutes. The room temperature is T . Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A body cools from a temperature $3 T$ to $2 T$ in $10$ minutes. The room temperature is $T$ . Assume that Newton's law of cooling is applicable. The temperature of the body at the end of next $10$ minutes will be

NTA AbhyasNTA Abhyas 2020Thermal Properties of Matter

Solution:

$\frac{T_{1} - T_{2}}{\Delta t}=K\left(\frac{T_{1} + T_{2}}{2} - T_{0}\right)$
$\frac{3 T - 2 T}{10}=K\left(2.5 T - T\right)$
$\Rightarrow \frac{T}{10}=K\left(1.5\right)T$
$K=\frac{1}{15}$
Now, $\frac{2 T - x}{10}=K\left(\frac{2 T + x}{2} - T\right)$
Solving $x=\frac{3 T}{2}$