Question

A pan filled with hot food cools from ${94}^{\circ }C$ to ${86}^{\circ }C$ in $2$ minutes. When the room temperature is ${20}^{\circ }C$. How long will it cool from ${74}^{\circ }C$ to ${66}^{\circ }C$?

• A. $2$ minutes
• B. $2.8$ minutes
• C. $2.5$ minutes
• D. $1.8$ minutes

Answer 1

Answer: (B)

$2.8$ minutes

Using Newton's law of cooling with approximation, $\frac{dT}{dt}=\frac{-k}{ms}(T_{avg}-T_s)$

Case 1 : $dt=2$ minutes; $T_s=20$

$T_{avg}=\frac{94+86}{2}=90$ and $dT=94-86=8$

$\therefore$ $\frac{-k}{ms}=\frac{dT}{dt}.\frac{1}{T_{avg}-T_s}=\frac{8}{2\times 70}=0.05714$ .......(a)

Case 2 : $T_s=20$

$T_{avg}=\frac{74+66}{2}=70$ and $dT=74-66=8$

$\therefore$ Time in which it cools down $\frac{8}{dt}=0.05714\times (70-20)$

$⟹$ $dt=2.8$ minutes