Question

A tub of hot water cools from $80^{\circ} C$ to $75^{\circ} C$ in time $t$ from $75^{\circ} C$ to $70^{\circ} C$ in time $t _{2}$, and from $70^{\circ} C$ to $65^{\circ} C$ in time $t _{3}$ then

• A. $t_{1}>t_{2}>t_{3}$
• B. $t_{3}>t_{2}>t_{1}$
• C. $t_{2}>t_{1}>t_{3}$
• D. $t_{1}>t_{2}>t_{4}$

Answer 1

Answer: (B)

According to the Newton's law of cooling.
Rate of cooling $\propto$ Mean temperature difference.
$\frac{\Delta T }{ t } \propto\left(\frac{ T _{1}+ T _{2}}{2}- T _{ 0 }\right)$
$t \propto \frac{1}{\left(\frac{ T _{1}+ T _{2}}{2}- T _{ 0 }\right)}$
So, $t_{3}>t_{2}>t_{1}$