Question

A bucket full of hot water cools from $75 \,{}^\circ C$ to $70 \,{}^\circ C$ in time $T_{1},$ from $70 \,{}^\circ C$ to $65 \,{}^\circ C$ in time $T_{2}$ and from $65 \,{}^\circ C$ to $60 \,{}^\circ C$ in time $T_{3}$ , then

• A. $T_{1}=T_{2}=T_{3}$
• B. $T_{1}>T_{2}>T_{3}$
• C. $T_{1} < T_{2} < T_{3}$
• D. $T_{1}>T_{2} < T_{3}$

Answer 1

Answer: (C)

According to Newton's law of cooling
$\text{Rate of cooling} \propto Mean \,temperature\, difference$
$\Rightarrow \frac{\text { Fall in temperature }}{\text { Time }} \propto\left(\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0}\right)$
$\because\left(\frac{\theta_{1}+\theta_{2}}{2}\right)_{1}>\left(\frac{\theta_{1}+\theta_{2}}{2}\right)_{2}>\left(\frac{\theta_{1}+\theta_{2}}{2}\right)_{3}$
$\Rightarrow T_{1} < T_{2} < T_{3}$