A liquid cools down from 70^\circ C to $60^\circ \mathrm{C}$ in 5 minutes. The time taken to cool it from $60^\circ \mathrm{C}$ to $50^\circ \mathrm{C}$ will be
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According to Newton's law of cooling, Rate of cooling $\alpha$ mean temperature difference
$\frac{\mathrm{d}Q_1}{\mathrm{d}t} = k \left(\frac{70 + 60}{2} - \theta_0 \right)$
$= (65 - \theta_0)$
$\frac{\mathrm{d}Q_2}{\mathrm{d}t} = k \left(\frac{60 + 50}{2} - \theta_0 \right)$
$=(55-\theta_0)$
$\mathrm{As} \quad \frac{dQ_2}{dt} < \frac{dQ_1}{dt}$
As rate of cooling is decreased, therefore liquid will take more than 5 min to cool from 60^\circ C to $50^\circ \mathrm{C}$ .
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