Question

A body takes 4 minutes to cool from $100^{\circ }C$ to $70^{\circ }c$. If temperature of the surrounding is $20^{\circ }C$. The time taken by it to $\mathrm{cool}$ from $70^{\circ }C$ to $50^{\circ }C$ is

• A. $13/3min$
• B. $13min$
• C. $3min$
• D. $6min$

Answer 1

Answer: (A)

$\frac{dT}{t}=-K\left(\frac{T_1+T_2}{2}-T_0\right)$
$\Rightarrow \frac{30}{4}=-K\left(\frac{170}{2}-20\right)$...(i)
$\frac{20}{t}=-K\left(\frac{120}{2}-20\right)$...(ii)
Divide $(i)\&(ii)$ we get
$\frac{t}{20}\times \frac{30}{4}=\frac{-K(85-20)}{-K(60-20)}$
$\Rightarrow t=\frac{13}{3}\min$