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 $\operatorname{cool}$ from $70^{\circ} C$ to $50^{\circ} C$ is

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

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)} $
$\Rightarrow t=\frac{13}{3} \min$