Question

A bowl filled with very hot soup cools from $98^{\circ }C$ to $86^{\circ }C$ in 2 minutes when the room temperature is $22^{\circ }C$. How long it will take to cool from $75^{\circ }C$ to $69^{\circ }C$ ?

• A. 2 minutes
• B. 1 minute
• C. $1.4$ minutes
• D. $0.5$ minute

Answer 1

Answer: (C)

$\frac{\Delta Q}{\Delta t}=-K\left(T-T_0\right)$
$\frac{\Delta Q}{\Delta t}=-K\left(T_{avg}-T_0\right)$
(i) $\frac{ms\times 12}{2}=-K\left(\frac{98+86}{2}-22\right)$
$6=-\frac{K}{ms}\left[\frac{98+86}{2}-22\right]$
$6=-\frac{K}{ms}[70]\dots .\dots ..\text{ (i) }$
(ii) $\frac{ms\times 6}{\Delta t}=-K\left(\frac{75+69}{2}-22\right)$
$\frac{6}{\Delta t}=-\frac{K}{ms}(50).....$(ii)
(ii) $÷$ (i)
$\frac{6}{\Delta t(6)}=\frac{50}{70}$
$\Delta t=\frac{7}{5}=1.4\min$