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A bucket full of hot water cools from $75^{o} C$ to $70^{0} C$ in time $T_{1}$ , from $70^{o} C$ to $65^{o} C$ in time $T_{2}$ and from $65^{o} C$ to $60^{o} C$ in time $T_{3}$ in the same surroundings, then

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$T_{1} = T_{2} = T_{3}$

$T_{1} > T_{2} > T_{3}$

$T_{1} < T_{2} < T_{3}$

$T_{1} > T_{2} < T_{3}$

answer is C.

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Detailed Solution

Rate of cooling $\propto$ Mean temperature difference

$\frac{Fall in temperature}{Time} \propto (\frac{θ_{1} + θ_{2}}{2} - θ_{0})$

$∵$ ${(\frac{θ_{1} + θ_{2}}{2})}_{1} > {(\frac{θ_{1} + θ_{2}}{2})}_{2} > {(\frac{θ_{1} + θ_{2}}{2})}_{3}$

$T_{1} < T_{2} < T_{3} \Rightarrow$

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