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Q.
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 $69^{\circ} C$ ?
$ \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] \ldots . \ldots . . \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) $\div$ (i)
$ \frac{6}{\Delta t (6)}=\frac{50}{70} $
$ \Delta t =\frac{7}{5}=1.4 \min$