A bucket full of hot water cools from $75^\circ \mathrm{C}$ to $70^\circ \mathrm{C}$ in time $T_1$ , from 70^\circ C to 65^\circ C in time $T_2$ and from $65^\circ \mathrm{C}$ to $60^\circ C$ in time $T_3$ , then
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According to Newton's law of cooling
Rate of cooling ∝ ∝ Mean temperature difference
⇒ ⇒ $\frac{\text{Fall in temperature}}{\text{Time}} \propto \left(\frac{\theta_1 + \theta_2}{2} - \theta_0 \right)$
Q $\left(\frac{\theta_1 + \theta_2}{2}\right)_1 > \left(\frac{\theta_1 + \theta_2}{2}\right)_2 > \left(\frac{\theta_1 + \theta_2}{2}\right)_3$
⇒ ⇒ $T_1 < T_2 < T_3$
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